SymbMathSymbMath
Computer Algebra System with Learning计算机代数系统学习
Dr. Weiguang HUANG黄博士郭华巍
226 Anzac Pde, Kensington, Sydney, NSW 2033, Australia226年以前偏微分方程、肯辛顿、悉尼、新南威尔士,澳大利亚
Phone:电话: (61 2) 9313858893138588(61 2)
E-mail: DrHuang@DrHuang.com电子邮件:DrHuang@DrHuang.com
http://www.SymbMath.comhttp://www.SymbMath.com
www.DrHuang.comwww.DrHuang.com
2 June 20092009年6月2
Copyright (C) 1990-2009版权(C)1990 - 2009
Contents内容
PART 1第1部分 User's Guide用户手册......................................... 77
1.1。 Introduction介绍.................................................. 77
1.1. 1.1。What is SymbMath什么是SymbMath.................................................. 77
1.2. 1.2。Capabilities能力............................................................. 77
1.3. 1.3。Shareware and Advanced Versions共享和先进的版本......................... 88
1.41.4 A List of Files in SymbMath在SymbMath某个目录下的文件..................................... 88
2. 2。Calculation计算.................................................... 1010
2.1. 2.1。Exact Calculation精确计算................................................... 1010
2.2. 2.2。Discontinuity and One-sided Value断续性和片面的价值........................ 1111
2.3. 2.3。Undefined and Indeterminate Form与不确定性预定义的形式........................ 1111
3. 3。Simplification简化................................................ 1212
3.1. 3.1。Assuming Domain假设领域.................................................. 1313
3.2. 3.2。Comparing and Testing Numbers比较和测试编号........................... 1414
4.4。 Defining Functions, Procedures and Rules定义功能、程序和规则 1515
4.1.4.1。 Defining Functions定义功能.............................................. 1515
4.1.1.4.1.1。 Defining Conditional Functions条件函数定义............................................................ 1515
4.1.2.4.1.2。 Defining Case Functions功能定义案件...................................................................... 1616
4.1.3.4.1.3。 Defining Piece-wise Functions功能定义分片............................................................ 1616
4.1.4.4.1.4。 Defining Recursion Functions递归函数定义.............................................................. 1717
4.1.5.4.4.5款所述。 Defining Multi-Value Functions价值函数定义............................................................. 1717
4.2.4.2。 Defining Procedures定义程序............................................. 1717
4.3.4.3。 Defining Rules定义规则...................................................... 1818
5.5。 Limits限制......................................................... 1818
5.1.5.1。 One-sided Limits片面限制.................................................. 1818
5.2.5.2。 Numeric Limits: nlim()数字限制:nlim()........................................... 2020
6. 6。Differentiation分化............................................... 2020
6.1.6.1。 One-sided Derivatives片面的衍生品.......................................... 2121
6.2.6.2。 Defining f '(x)定义f '(x)........................................................ 2121
7.7。 Integration整合.................................................... 2121
7.1. 7.1。Indefinite Integration不确定性整合.............................................. 2222
7.2. 7.2。Definite Integration明确的整合................................................ 2323
7.3. 7.3。Numeric Integration: ninte()数字集成:ninte().................................... 2424
8.8。 Solving Equations求解方程..................................... 2424
8.1.8.1。 Solving Algebraic Equations求解代数方程................................. 2424
8.2.8.2。 Equation Solver: solve()方程求解解决()....................................... 2525
8.3.8.3。 Polynomial Solver: psolve()多项式求解:psolve().................................. 2727
8.4.8.4。 Numeric Solver: nsolve()数值求解:nsolve()...................................... 2727
8.5.8.5。 Solving Differential Equations解微分方程............................... 2727
8.6.8.6。 Differential Solver: dsolve()微分求解:dsolve().................................. 2727
9.9。 Sums, Products, Series and Polynomials总结、产品、系列和多项式... 2828
9.1.9.1。 Partial Sum部分和........................................................... 2929
9.2.9.2。 Infinite Sum无限金额.......................................................... 2929
9.3.9.3。 Series系列.................................................................. 2929
9.4.9.4。 Polynomials多项式.......................................................... 3030
10. 10。Lists and Arrays, Vectors and Matrices列表和阵列、向量和矩阵..... 3030
10.1.10.1。 Lists名单................................................................. 3131
10.1.1.10.1.1。 Entering Lists进入名单.................................................................................... 3131
10.1.2.10.1.2。 Accessing Lists访问列表................................................................................ 3131
10.1.3.10.1.3。 Modifying Lists修改列表.................................................................................. 3232
10.1.4.10.1.4。 Operating Lists操作列表................................................................................. 3232
10.2.10.2。 Arrays阵列.............................................................. 3333
10.2.1.10.2.1。 Entering Arrays进入阵列.................................................................................... 3333
10.2.2.10.2.2。 Accessing Arrays访问数组................................................................................ 3333
10.2.3.10.2.3。 Modifying Arrays修改数组.................................................................................. 3333
10.2.4.10.2.4。 Operating Arrays操作阵列................................................................................. 3333
10.3.10.3。 Vectors and Matrices向量和矩阵...................................... 3434
11.11分。 Statistics统计................................................... 3434
12.12。 Tables of Function Values表的函数值........................ 3434
13.13岁。 Conversion转换................................................ 3535
13.1.13.1。 Converting to Numbers转换到数字....................................... 3535
13.2.13.2。 Converting to Lists转换列出............................................. 3535
13.3.13.3。 Converting to Strings转换成串.......................................... 3636
13.4.13.4。 Converting to Table转换表............................................ 3636
14.14。 Getting Parts of Expression获得部分的表达.................... 3636
14.1.14.1。 Getting Type of Data得到的数据类型.......................................... 3636
14.2.14.2。 Getting Operators获得运营商............................................... 3636
14.3.14.3。 Getting Operands得到操作数............................................... 3737
14.4.14.4。 Getting Coefficients变系数............................................ 3737
15.15。 Database数据库................................................... 3737
15.1.15.1。 Phone Number电话号码.................................................... 3737
15.2.15.2。 Atomic Weight原子的重量.................................................... 3838
15.3.15.3。 Chemical Reaction化学反应............................................. 3838
16.16岁。 Learning from User学习从用户.................................... 3838
16.1.16.1。 Learning Integrals from a Derivative从学习积分衍生工具................... 3838
16.2.16.2。 Learning Complicated Integrals from a Simple Integral学习复杂的积分从一个简单的积分 4040
16.3.16.3。 Learning Definite Integral from Indefinite Integral学习从不定积分定积分 4040
16.4. 16.4。Learning Complicated Derivatives from Simple Derivative学习复杂的衍生工具已从简单的衍生工具 4141
16.5.16.5。 Learning Integration from Algebra学习代数一体化的....................... 4141
16.6.16.6。 Learning Complicated Algebra from Simple Algebra从简单的代数学习复杂的代数 4141
16.7.16.7。 Learning vs. Programming学习与编程。.................................. 4242
PART 2第二部分 Programmer's Guide程序员的指导........................ 4343
17.17岁。 Programming in SymbMath规划在SymbMath....................... 4343
17.1.17.1。 Data Types数据类型......................................................... 4343
17.1.1.17.1.1。 Numbers编号............................................................................................... 4343
17.1.2.17.1.2。 Constants常数............................................................................................. 4444
17.1.3.17.1.3。 Variables变量.............................................................................................. 4545
17.1.4.17.1.4。 Patterns模式................................................................................................ 4646
17.1.5.17.1.5。 Functions, Procedures and Rules功能、程序和规则...................................................... 4646
17.1.5.1.17.1.5.1。 Standard Mathematical Functions标准数学函数.................................................. 4646
17.1.5.2.17.1.5.2。 Calculus Functions微积分功能........................................................................... 4747
17.1.5.3.17.1.5.3。 Test Functions测试函数.................................................................................. 4848
17.1.5.4.17.1.5.4。 Miscellaneous Functions功能项目................................................................. 5050
17.1.5.5.17.1.5.5。 User-defined Functions用户自定义函数的................................................................ 5151
17.1.5.6.17.1.5.6。 Procedures程序....................................................................................... 5151
17.1.5.7.17.1.5.7。 Rules规则.................................................................................................. 5151
17.1.6.17.1.6。 Equations方程............................................................................................. 5151
17.1.7.17.1.7。 Inequalities不等式........................................................................................... 5252
17.1.8.17.1.8。 Vectors or Lists向量或列出.................................................................................... 5252
17.1.9.17.1.9。 Matrices or Arrays矩阵或数组............................................................................... 5252
17.1.10.17.1.10。 Strings字符串................................................................................................ 5252
17.2.17.2。 Expressions表达式...................................................... 5353
17.2.1.17.2.1。 Operators运营商............................................................................................ 5353
17.2.1.1.17.2.1.1。 Arithmetic Operators算术运算符........................................................................ 5454
17.2.1.2.17.2.1.2。 Relational Operators关系运算符........................................................................ 5454
17.2.1.3.17.2.1.3。 Logical Operators逻辑运算符.......................................................................... 5454
17.2.2.17.2.2。 Function Calls函数调用...................................................................................... 5555
17.3.17.3。 Statements报表....................................................... 5555
17.3.1.17.3.1。 Comment Statements评论语句......................................................................... 5555
17.3.2.17.3.2。 Evaluation Statements评价报表........................................................................ 5656
17.3.3.17.3.3。 Assignment Statements赋值语句...................................................................... 5656
17.3.4.17.3.4。 Conditional条件........................................................................................... 5757
17.3.5.17.3.5。 Loop回路...................................................................................................... 5757
17.3.6.17.3.6。 Switch开关................................................................................................... 5858
17.3.6.1.17.3.6.1。 Output Switch输出开关.................................................................................... 5858
17.3.6.2.17.3.6.2。 Case Switch案例开关...................................................................................... 5858
17.3.6.3.17.3.6.3。 Numeric Switch数字开关................................................................................. 5858
17.3.6.4.17.3.6.4。 Expand Switch扩大开关.................................................................................. 5959
17.3.6.5.17.3.6.5。 ExpandExp SwitchExpandExp开关........................................................................... 5959
17.3.7.17.3.7。 Read and Write Statements读和写报告............................................................... 5959
17.3.8.17.3.8。 DOS CommandDOS命令................................................................................... 6060
17.3.9.17.3.9。 Sequence Statements序列报表........................................................................ 6060
17.4.17.4。 Libraries and Packages图书馆和包装...................................... 6060
17.4.1.17.4.1。 Initial Package init.sminit.sm初始包装......................................................................... 6262
17.4.2.17.4.2。 ExpandLn PackageExpandLn包装............................................................................. 6262
17.4.3.17.4.3。 Chemical Calculation Package化学计算软件包......................................................... 6262
17.5.17.5。 Interface with Other Software接口与其它的软件................................................................. 6363
18.18岁。 Graphics图形.................................................... 6363
18.1.18.1。 Drawing Lines and Arcs画线和弧...................................... 6464
18.2.18.2。 Plotting f(x)密谋f(x)......................................................... 6565
18.3.18.3。 Plotting Parametric Functions x(t) and y(t)绘图参数函数x(t)和y(t).......... 6666
18.4.18.4。 Plotting f(t) in Polar Coordinates密谋f(t)在两极的坐标......................... 6666
18.5.18.5。 Plotting Data阴谋数据....................................................... 6767
18.6.18.6。......................................Printing Graphics on Printer印刷机印刷图形... 6767
Part 3 Reference Guide第三部分参考指南..................................... 6868
19.19岁。 SymbMath Environment: Windows and MenusSymbMath环境:窗口、菜单 6868
19.1.19.1。 File Menu文件菜单........................................................... 6868
19.1.1.19.1.1。 Open开放..................................................................................................... 6868
19.1.2.19.1.2。 New新....................................................................................................... 6969
19.1.3.19.1.3。 Save Input保存输入............................................................................................. 6969
19.1.4.19.1.4。 Save Output拯救输出.......................................................................................... 6969
19.1.5.19.1.5。 DOS ShellDOS壳............................................................................................. 6969
19.1.6.19.1.6。 Exit出口........................................................................................................ 6969
19.2.19.2。 Input Menu输入菜单.......................................................... 7070
19.3.19.3。 Run Menu运行菜单........................................................... 7070
19.4.19.4。 Output Menu输出菜单....................................................... 7070
19.5.19.5。 Color Menu颜色的菜单......................................................... 7070
19.5.1.19.5.1。 Menu Line菜单线............................................................................................. 7070
19.5.2.19.5.2。 Input Window输入窗口........................................................................................ 7070
19.5.3.19.5.3。 Input Border输入边境.......................................................................................... 7171
19.5.4.19.5.4。 Output Window输出窗口..................................................................................... 7171
19.5.5.19.5.5。 Output Border输出边境....................................................................................... 7171
19.5.6.19.5.6。 Status Line状态行........................................................................................... 7171
19.6.19.6。 Help Menu帮助菜单.......................................................... 7171
19.7.19.7。 Example Menu例如菜单.................................................... 7272
19.8.19.8。 Keyword Menu关键字菜单................................................... 7272
19.9.19.9。 Editor and Edit Help Menu编辑器和编辑帮助菜单.................................. 7272
19.9.1.19.9.1。 Edit Help Menu编辑帮助菜单.................................................................................... 7272
19.9.1.1.19.9.1.1。 Show Help File显示帮助文件................................................................................. 7373
19.9.1.2.19.9.1.2。 Cursor Movement Commands光标移动命令........................................................ 7373
19.9.1.3.19.9.1.3。 Insert and Delete Commands插入和删除命令......................................................... 7373
19.9.1.4.19.9.1.4。 Search and Replace Commands搜索和替换的命令................................................... 7474
19.9.1.5.19.9.1.5。 Block Commands块命令............................................................................. 7474
19.9.1.6.19.9.1.6。 Special Block Commands特殊区块的命令.............................................................. 7676
19.9.1.9.19.9.1.9。 Miscellaneous Commands杂命令.............................................................. 7676
19.9.1.10.19.9.1.10。 Global Commands全球命令........................................................................ 7777
19.9.2.19.9.2。 Edit Commands编辑命令................................................................................... 7777
19.9.3. 19.9.3。Copy and Paste复制并粘贴.................................................................................... 8080
20.20。 Inside SymbMathSymbMath内...................................... 8282
20.1.20.1。 Internal Structure内部结构................................................ 8282
20.2.20.2。 Internal Format内部格式................................................... 8383
21. 21。System Limits系统限制............................................. 8383
22.22。 Keywords关键词............................................... 8484
22.1.22.1。 Keywords in Topic Order关键词主题为.................................. 8484
22.2.22.2。 Keywords in Alphabetical Order关键词按字母顺序排列........................ 9191
22.3.22.3。 Library Name图书馆的名字.................................................... 9292
22.4.22.4。 Glossary词汇........................................................... 9393
SymbMath (an abbreviation for Symbolic Mathematics) is a symbolic calculator that can solve symbolic math problems.SymbMath(缩写符号数学)是一个象征符号计算器那样能解决数学问题。
SymbMath is a computer algebra system that can perform exact, numeric, symbolic and graphic computation. SymbMath计算机代数系统是一个能够进行精确、数字、符号和图形的计算。It manipulates complicated formulas and returns answers in terms of symbols, formulas, exact numbers, tables and graph.操纵复杂的公式和返回它的答案从符号、公式、数目、表格和图表。
SymbMath is an expert system that is able to learn from user's input. SymbMath是一个专家系统是能够学习,从用户的输入。If the user only input one formula without writing any code, it will automatically learn many problems related to this formula (e.g. it learns many integrals involving an unknown function f(x) from one derivative f'(x)).如果用户只输入一个不需要任何代码的公式,它会自动学习很多相关的问题,这个公式(例如它可以学习,许多积分未知函数f(x)从一个衍生f '(x))。
SymbMath is a symbolic, numeric and graphics computing environment where you can set up, run and document your calculation, draw your graph.SymbMath是一个象征,数字和图形计算的环境,你可以建立、运行和文件你的计算,拔出你的图形。
SymbMathSymbMathuses external functions as if standard functions since the external functions in library are auto-loaded.使用外部功能,如果标准自外部函数功能auto-loaded图书馆。
SymbMath is a programming language in which you can define conditional, case, piecewise, recursive, multi-value functions and procedures, derivatives, integrals and rules.SymbMath是一种编程语言,你可以定义有条件,情况下,分段,递归,多元化的价值功能和程序、衍生物、积分和规则。
SymbMath is database where you can search your data.SymbMath是资料库,在那里你可以搜索你的数据。
It runs on IBM PCs (8086) with 400 KB free memory under MS-DOS.它运行在IBM个人电脑(8086)与400 KB释放内存在ms - dos。
It can provide analytical and numeric answers for:它可以提供分析和数字回答:
* Differentiation: regular or higher order, partial or total, mixed and implicit differentiation, one-sided derivatives.分化:经常或者高阶,全部或部分一次性、混合和含蓄的分化、片面的衍生物。
* Integration: indefinite or definite integration, multiple integration, infinity as a bound, parametric or iterated implicit integration.整合:不确定或明确的集成、多元整合、无限,当约束、参数或迭代隐含的整合。
* Solution of equations: roots of a polynomial, systems of algebraic or differential equations.解决方程:一个多项式的根、系统的代数或微分方程组。
* Manipulation of expressions: simplification, factoring or expansion, substitution, evaluation.操纵表现:简单化,保理业务或扩充、替代、评价。
* Calculation: exact and floating-point numeric computation of integer, rational, real and complex numbers in the range from minus to plus infinity, even with different units.计算:准确、浮点数值计算对整数的、理性的、真实、复杂的数字范围从减加上无穷大,即使有不同的单位。
* Limits: real, complex or one-sided limits, indeterminate forms.限制:真实、复杂或片面的范围、不确定的形式。
* Complex: calculation, functions, derivatives, integration.复杂:计算、功能、衍生物、整合。
* Sum and product: partial, finite or infinite.金额和产品:部分,有限的或无限的。
* Others: series, lists, arrays, vectors, matrices, tables, etc.其他:系列、列表、阵列、向量,矩阵、表格等。
Also included are:也包括了:
* External functions in library as if standard functions.图书馆作为外部函数如果标准功能。
* Plot: functions, polar, parametric, data, and list.情节:功能、极性、参数、数据、列表。
* Draw: lines, arcs, ellipse, circles, ovals.画画:线,弧,椭圆形、圆形、椭圆形。
*Procedural, conditional, iteration, recursive, functional, rule-based, logic, pattern-matching and graphic programming.程序、条件、迭代,递归,功能齐全,以规则为基础的、逻辑、模式匹配和图形编程。
* Searching database.检索数据库。
You should register with the author if you use SymbMath.你应该登记,如果你使用SymbMath作者。
Please read all *.请仔细阅读所有的*。TXT files before running SymbMath. 在运行SymbMath TXT文件。Please copy-and-past examples in the Help window to practise. 请copy-and-past例子帮助窗口来练习。The printed documents (100+ pages) is available from author.印刷文件(100 +页)可以从作者。
If you get the SymbMath on ZIP format (e.g. sm32a.zip), you should unzip it with parameter -d by如果你得到这个SymbMath在ZIP格式(例如sm32a.zip),你应该用参数d解压
pkunzip -d sm32a c:\symbmathsm32a pkunzip维c:\ symbmath
If you get the SymbMath with the install file, you should install it by如果你得到这个SymbMath与安装档案,你应该先把它安装到你 install安装
On the MS-DOS prompt to run it, type在ms - dos提示运行它,类型 SymbMathSymbMath
SymbMath has two versions: Shareware Version A, and Advanced Version C. The Shareware version lacks the solve(), trig (except sin(x) and cos(x)), and hyperbolic functions, (lack 10% keywords). SymbMath有两个版本:Shareware版本,和先进的版本c Shareware版本缺乏解决()、三角法(除罪(x),因为(x))和双曲线函数,缺乏10%关键字)。You cannot input these lack functions in Shareware version.你不能输入这些缺乏Shareware版本功能。
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Version版本 Class类 Lacked functions缺乏功能
Shareware共享 A一个 solve(), hyperbolic,解决()、双曲线,
trig (except sin(x), cos(x))三角法(除罪(x),因为(x))
Advanced先进 CC
Libraries图书馆 * . *。li李
Manual手册 printed印刷
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Upgrade升级 same相同
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Multiple多个 copies拷贝 >2> 2
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Site licence站点许可证 >10 copies> 10本
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You must provide the photocopy of your license or license number for upgrades.你必须提供你的驾照的复印件或许可证号码为升级。
If you send the author your payment by cheque, money order or bank draft that must be drawn in Australia, you will get the latest version. 如果你把作者你的支票付款方式,现金订单或银行汇票必须画在澳大利亚,你会得到最新的版本。If you sign the license (see the LICENSE.如果你签了许可证(见许可证。TXT file) and send it to the author, you will be a legal user for upgrades. TXT文件)和寄给作者,你会是一个合法用户升级。If you write a paper about this software on publication, you will get a free upgrade.如果你写了一篇关于这个软件在出版时,你会得到一个免费升级。
Its two versions (Shareware and Advanced) are available from the author. 它的两个版本(共享和先进的)可于作者。The Shareware version is available from my web sites.该Shareware版本也可以从我的网站。
The Advanced version is copy-protected, so you must insert the original SymbMath disk into drive A or B before you run SymbMath. 高级的版本是copy-protected,所以你必须插入磁盘到驱动器A原SymbMath跑之前先SymbMath或B。By default, it is drive B. If you use drive A, please copy (or rename) the DRIVE.默认情况下,它是动力如果你使用开,请先将该图标拷贝(或重命名)驱动器。A file to the SYMBMATH.一个文件到SYMBMATH。DRI file, or you edit drive(2) into drive(1) in the SYMBMATH.顶吹文件,或者你编辑驱动(2)到驱动器(1)在SYMBMATH。DRI file.顶吹文件。
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In directory SymbMath:在目录SymbMath:
SymbMath.exeSymbMath.exe executable SymbMath system.执行SymbMath系统。
SymbMath.iniSymbMath.ini initial file.最初的文件。
SymbMath.h*SymbMath.h * help files, * is numbers.帮助文件,*编号。
SymbMath.driSymbMath.dri indicate which drive the original SymbMath disk is inserted into显示磁盘驱动原SymbMath插入
init.sminit.sm initial SymbMath program file.最初的SymbMath程序文件。
*.sm* .sm packages (user SymbMath program files).软件(用户SymbMath程序文件)。
prolog.errprolog.err prolog error message file.prolog错误信息文件。
In directory SymbMath\BGI:在SymbMath \开的目录。
*.bgi* .bgi BGI graphics drives.开图形驱动器。
*.chr* .chr stroked fonts.抚摸的字体。
In directory SymbMath\library:在目录SymbMath \图书馆:
*.li*来将您引见给李先生 the auto loaded libraries (external functions).汽车装载图书馆(外部功能)。
In directory SymbMath\keyword:在目录SymbMath \关键字:
*.key* .key the keyword files.关键字的文件。
In directory SymbMath\text:在目录SymbMath \文字:
SymbMath.txtSymbMath.txt introduction of SymbMath.介绍SymbMath。
readme.txtreadme.txt the read-me file, this file should be read first.read-me的文件,该文件应该读第一。
problem.txtproblem.txt problems that other software cannot solve, but SymbMath can do.其他软件不能解决问题,但SymbMath能做的事。
comment*.txt注释* .txt comments on SymbMath.SymbMath评论。
statisti.txtstatisti.txt the download statistics at FTP site of garbo.uwasa.fi.下载统计在garbo.uwasa.fi FTP站点的。
shareware.txtshareware.txt Shareware concept.共享的概念。
software.txtsoftware.txt software available from the author.软件可以从作者。
update.txtupdate.txt the latest updates in SymbMath.在SymbMath最新公布的。
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In the following examples, a line of "IN: " means input, which you type in the Input window, then leave the Input window by pressing <Esc>, finally run the program by the command "Run"; while a line of "OUT: " means output. 在以下的例子,一行“:”是指输入,输入窗口类型,然后让输入窗口按< Esc >,最后由命令运行该程序“跑”;而行":"是指输出。You will see both input and output are displayed on two lines with beginning of "IN: " and "OUT: " in the Output window. 你将会看到两个输入和输出显示在两线开始“:”和“道:“在输出窗口。You should not type the word "IN: ". 你不应该类型单词“:”。Some outputs may be omitted on the examples.一些输出可以省略的例子。
# is a comment statement.号是一个评论的声明。
You can split a line of command into multi-lines of command by the comma ,. 你可以将一条指令为命令multi-lines由逗号。The comma without any blank space must be the last character in the line.逗号没有任何空格必须在最后一个字就行了。
Note that you should not be suprised if some functions in the following examples are not working when their libraries are not in the default directory or missing.注意,你不应该惊讶如果一些功能在以下的例子是当他们不工作的图书馆不是默认目录或者失踪。
SymbMath gives the exact value of calculation when the switch numeric := off (default), or the approximate value of numeric calculation when the switch numeric := on or by num().SymbMath给计算的准确价格开关数字:=关(默认),或近似数值计算值开关数字:=或由胡()。
Mathematical functions are usually not evaluated until by num() or by setting numeric := on.通常不被计算数学函数由胡直到()或通过设置数字:=。
SymbMath can manipulate units as well as numbers, be used as a symbolic calculator, and do exact computation. SymbMath可以操作单位以及编号,做为一个象征性的计算器,准确计算。The range of real numbers is from -infinity to +infinity, e.g. ln(-inf), exp(inf+pi*i), etc. SymbMath contains many algorithms for performing numeric calculations. 实数的范围是从-infinity +无限,例如淋巴结(-inf),实验(无穷大+ pi *我)等。SymbMath包含许多算法数值计算执行。e.g. ln(-9), i^i, (-2.3)^(-3.2), 2^3^4^5^6^7^8^9, etc.例如;(9),我^我,(-2.3)^(-3.2),2 ^ ^ ^ ^ 3 4 ^ ^ 5 ^ 7八6 9等。
Note that SymbMath usually gives a principle value if there are multi-values, but the solve() and root() give all values.注意SymbMath通常会给一个有价值的多维价值原则,但解决()和根系()给所有的值。
Example:例如:
Exact and numeric calculations of 1/2 + 1/3.数值计算准确、1/2 +的1/3。
IN:在: 1/2+1/31/2 + 1/3 # exact calculation#精确计算
OUT: 5/6出:5/6
IN:在: num(1/2+1/3)胡(1/2 + 1/3) # numeric calculation#数值计算
OUT: 0.8333333333出:1 .
Evaluate the value of the function f(x) at x=x0 by f(x0).评估有价值的函数f(x)= x0 x由f(x0)。
Example:例如:
Evaluate sin(x) when x=pi, x=180 degree, x=i.评估罪(x)当x = pi、x = 180度,x =我。
IN:在: sin(pi), sin(180*degree)罪(pi)、罪(180 *度)
OUT: 0, 0出:0,0
IN:在: sin(i), num(sin(i))罪(我),胡(罪(我)
OUT: sin(i), 1.175201 i出:罪(我),1.175201我
Example:例如:
Set the units converter from the minute to the second, then calculate numbers with different units.设置单位转换器的第二分钟,计算不同单位数。
IN:在: minute:=60*second分钟:= 60度第二
IN:在: v:=2*meter/second老板:= 2 *米/秒
IN:在: t:=2*minute师:= 2 *分钟
IN:在: d0:=10*meterd0:= 10 *米
IN:在: v*t+d0v * t + d0
OUT: 250 meter出:250米
Evaluate the expression value by评估表达式的值
subs(y, x = x0)替补(y,x = x0)
Example:例如:
Evaluate z=x^2 when x=3 and y=4.z = x ^ 2评估当x和y = = 3 4。
IN:在: z:=x^2赵:= x ^ 2 # assign x^2 to z指定x ^ 2 #始末
IN:在: subs(z, x = 3)替补(z、x = 3) # evaluate z when x = 3当x #评估z = 3
OUT: 9出:9
IN:在: x:=4谢:= 4 # assign 4 to x4 #指定x
IN:在: zz # evaluate z#评估z
OUT: 16出:16
Note that after assignment of x by x:=4, x should be cleared from assignment by clear(x) before differentiation (or integration) of the function of x. Otherwise the x values still is 4 until new values assigned. 注意:当作业x x:= 4,x应该允许从分配(x)之前明确分化(或集成的功能。除此之外,x值x还是4直到新的赋值。If evaluating z by the subs(), the variable x is automatically cleared after evaluation, i.e. the variable x in subs() is local variable. 如果评估由潜艇z(),那么这个变量x是自动清除评估之后,即变量x的局部变量替补()。The operation by assignment is global while the operation by internal function is local, but operation by external function is global. 操作时通过转让是全球性的内部功能的操作是当地人,由外部函数可操作是全球性的问题。This rule also applies to other operations.这个规则同样适用于其它业务。
The complex numbers, complex infinity, and most math functions with the complex argument can be calculated.复杂的数字,复杂的无穷远处,而大多数数学函数复杂的参数可以计算出来。
Example .例子。
IN:在: sign(1+i), sign(-1-i), i^2签署(1 + 1)、标志(1-i),我^ 2
OUT: 1, -1, -1出:1、1,1
Example:例如:
IN:在: exp(inf+pi*i)实验(无穷大+ pi *我)
OUT: -inf出:-inf
IN:在: ln(last)淋巴结(最后)
OUT: inf + pi*i出:步+ pi *我
The built-in constants (e.g. inf, zero, discont, undefined) can be used as numbers in calculation of expressions or functions.内置的常数(例如无穷大,零,discont、不可解释的),可用于计算数字的表情或功能。
Some math functions are discontinuous at x=x0, and only have one-sided function value. 一些数学函数不连续在x = x0、只有片面函数值的大小。If the function f(x0) gives the discont as its function value, you can get its one-sided function value by f(x0-zero) or f(x0+zero).如果函数f(x0)给discont作为其功能价值,你就会得到它的片面的功能价值f(x0-zero)或f(x0 +零)。
Example:例如:
IN:在: f(x_) := exp(1/x)f(x_):=经验(1 / x) # define function f(x)#定义函数f(x)
IN:在: f(0)f(0)
OUT: discont出:discont # discontinuity at x=0在x = 0 #不连续
IN:在: f(0-zero)f(0-zero) # left-sided value at x=0-左值号x = 0 -
OUT: 0出:0
IN:在: f(0+zero)f(0 + 0) # right-sided value at x=0+右值号x = 0 +
OUT: inf出:步
If the function value is undefined, it may be indeterminate form (e.g. 0/0, inf/inf), you can evaluate it by lim() (see Chapter如果函数值的大小是未定义的,它可能不确定的形式(例如。0/0,步/ inf),你就可以评价由小林()(见章节 Limits).限制)。
SymbMath automatically simplifies the output expression. SymbMath自动输出表达式,简化了。You can further simplify it by using the built-in variable last in a single line again and again until you are happy with the answer.你可以进一步简化它采用内置可变最后在一个单独的一行一次又一次,直到您满意的答案。
Expressions can be expanded by表达式可能会被扩展
expand(x)扩大(x)
expand := on拓展:=在
expandexp := onexpandexp:=在
Remember that the operation by assignment is global while operation by function is local. 记住,操作时通过转让是全球性的操作功能的本地产品。So expand(x) only expands the expression x, but the switch expand := on expands all expressions between the switch expand := on and the switch expand := off. Second difference betwen them is that the switch expand := on only expands a*(b+c) and (b+c)/p, but does not expands the power (a+b)^2. 扩大(x)只有扩大表达x,但是这种转变扩大:=在膨胀,所有的表情连接交换器扩大:=和开关扩大:=了。第二个变化是,前后开关扩大:=只有扩大一个*(b + c)和(b + c)/ p,但不扩大电源(+ b)^ 2。The expandexp is exp expand.expandexp是经验的扩大。
Example:例如:
IN:在: expand((a+b)^2+(b+c)*p)扩大(a + b)^ 2 +(b + c)* p)
OUT: a^2 + 2 a b + b^2 + b p + c p:一个^ 2 + 2 b + b ^ 2 + b p + c p
IN:在: expand := on拓展:=在
IN:在: (a+b)^2 + (b+c)*p(a + b)^ 2 +(b + c)* p
OUT: (a+b)^2 + b p + c p出:a + b)^ 2 + b p + c p
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............... expand(x) ....................................................................................扩大(x)
(a+b)^2(a + b)^ 2 to对 a^2+2*a*b+b^2一个^ 2 + 2 * * ^ 2 b + b
(a+b)^n(a + b)^ n to对 a^n+ ...... 一个^ n +……+b^n^ n + b n is positive integer正整数n是
............... ...............expand(x) and expand := on ..........................扩大(x)和扩展:=在..........................
a*(b+c)一个*(b + c) to对 a*b + a*c* * * * * * b + c
(b+c)/p(b + c)/ p to对 b/p + c/pb / p + c/p
............... ...............expandexp := on .....................................expandexp:=在.....................................
e^(a+b)e ^(a + b) to对 e^a *e ^ * * * e^be ^ b
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where a+b can be many terms or a-b.在+ b能有许多条款或故。
Expressions can be factorised by表达式是可以factorised
factor(x)因子(x)
e.g.例句。
IN:在: factor(a^2 + 2*a*b + b^2)因子(一个^ 2 + 2 b + b * * ^ 2)
OUT: (a + b)^2出:a + b)^ 2
Polynomials of order less than 5 can be factorised by多项式的秩序不少于5个可以factorised
factor(y, x)因子(y,x)
Example:例如:
IN:在: factor(x^2+5*x+6, x)因子(x ^ 2 + 5 * x + 6,x)
OUT: (2 + x) (3 + x)出:(2 + x)(3 + x)
Example:例如:
Reduce sqrt(x^2).减少sqrt(x ^ 2)。
IN:在: sqrt(x^2)sqrt(x ^ 2)
OUT: x*sign(x)出:* *签署(x)
This output can be further simplified if you know properties of x.这种输出可以进一步简化如果你知道属性x。
A first way is to evaluate x*sign(x) by substituting sign(x) with 1 if x is positive.一分之一的方法是评价x(x)*标志取代签署(x),如果x是积极的。
IN:在: sqrt(x^2)sqrt(x ^ 2)
OUT: x*sign(x)出:* *签署(x)
IN:在: subs(last, sign(x) = 1)替补(最后签署(x)= 1)
OUT: x出:x
where a special keyword last stands for the last output, e.g. here last is x*sign(x).在一个特殊的关键字的最后一站在过去的输出,例如在这里签个是x(x)*。
A second way is to assume x>0 before evaluation. 另一种是x > 0之前认为的评价。If you assume the variable x is positive or negative, the output expression is simpler than that if you do not declare it.如果你承担变量x是积极的还是消极的,输出表达简单的比,如果你不申报。
IN:在: assume(x > 0, y <0)假设(x > 0,y < 0) # assume x > 0, y < 0> 0 #假设x,y < 0
OUT: assumed出:假设
IN:在: sqrt(x^2), sqrt(y^2), sqrt(z^2)sqrt(x ^ 2),sqrt(y ^ 2),sqrt(z ^ 2)
OUT: x*sign(x), y*sign(y), z*sign(z)出:* *签署(x),y *签署(y)、z *签署(z)
IN:在: last最后 # simplify last output#简化最后输出
OUT: x, -y, z*sign(z)出:x,消息、z *签署(z)
In this way, all of x is affected until the assume() is cleared by clear(). 这样,所有的x是影响承担(),直到被清楚()。The first method is local simplification, but the second method is global simplification.第一种方法是当地的简单化,但第二种方法是全球性的简单化。
By default, |x| < inf and all variables are complex, except that variables in inequalities are real, as usual only real numbers can be compared. 默认情况下,| | < inf和x��量是复杂的,除了变量不等式是很实际的,像往常一样唯一真正的编号可比的。e.g. x is complex in sin(x), but y is real in y > 1.如x是复杂的罪(x),但y是真实的y > 1。
Table 3.1表3.1 Assuming假设
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Assume承担 Assignment作业 Meaning意义
assume(x>y)假设(x > y) x>y := 1x >杨:= 1 # assume x > y假设x >号y
assume(x>=y)假设(x > = y) x>=y := 1x > =杨:= 1 # assume x >= y假设x > =号y
assume(x<y)假设(x < y) x<y := 1杨:x < = 1 # assume x < y假设x号< y
assume(x<=y)假设(x < = y) x<=y := 1杨:x < = = 1 # assume x <= y假设x < =号y
assume(x==y)假设(x = = y) x==y := 1x = =杨:= 1 # assume x == y#假设x = = y
assume(x<>y)假设(x < > y) x<>y := 1x < >杨:= 1 # assume x <> y假设x < >号y
iseven(b) := 1iseven(b):= 1 # assume b is even假设b是平坦的。#
isodd(b) := 1isodd(b):= 1 # assume b is odd#假设b很奇怪
isinteger(b) := 1isinteger(b):= 1 # assume b is integer假设b号整数
isratio(b) := 1isratio(b):= 1 # assume b is ratio假设b是#比例
isreal(b) := 1来(b):= 1 # assume b is real#假设b是真实的
iscomplex(b) := 1iscomplex(b):= 1 # assume b is complex假设b相当复杂。#
isnumber(b) := 1isnumber(b):= 1 # assume b is number假设b号码是#
islist(b) := 1islist(b):= 1 # assume b is a list假设b是一号名单
isfree(y,x) := 1isfree(y,x):= 1 # assume y is free of x#假设y是免费的x
issame(a,b) := 1issame(a,b):= 1 # assume a is same as b假设一个号一样b
sign(b) := 1签署(b):= 1 # assume b is positive complex假设b是积极#复杂
sign(b) := -1签署(b):= 1 # assume b is negative complex假设b是消极#复杂
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The assume() can be cleared by clear(). 这个假设()能被清理清晰()。e.g. clear(x>y).例如清楚(x > y)。
You can restrict the domain of a variable by assuming the variable is even, odd, integer, real number, positive or negative.你可以限制一个变量的领域通过假设变量为均匀,奇怪,整数,实数、积极还是消极的。
Example:例如:
IN:在: isreal(b) := 1来(b):= 1 # assume b is real#假设b是真实的
IN:在: sqrt(b^2)sqrt(b ^ 2)
OUT: abs(b)出:abs(b)
Table 3.3表3.3 Simplification in different domains简化在不同领域
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expression表达 complex复杂 real真正 x > 0x > 0
sqrt(x^2)sqrt(x ^ 2) x sign(x)x签署(x) |x|| | x xx
x*sign(x)x *签署(x) x sign(x)x签署(x) |x|| | x xx
|x|*sign(x)| | *标志x(x) |x| sign(x)| |标志x(x) xx xx
|x|/x| | x / x |x|/x| | x / x 1/sign(x)1 /签署(x) 11
x+infx + inf x+infx + inf infinf
x-infx-inf x-infx-inf -inf-inf
abs'(x)abs的(x) |x|/x| | x / x 1/sign(x)1 /签署(x) 11
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You can compare two numbers by relational operators:你可以比较两个编号的关系运算符。
a > b一个> b
a < b一个< b
a <= b一个< = b
a >= b一个> = b
a <> b一个< > b
a == b一个= = b
Example:例如:
IN:在: 2 > 1, 2 < 12 > 1、2 < 1
OUT: 1, 0出:1、0
You also can compare two numbers, even complex numbers z1 and z2 by你也可以比较两个编号,甚至人z1与z2复数
islarger(z1, z2)islarger(z1,本体)
isless(z1, z2)isless(z1,本体)
issame(z1, z2)issame(z1,本体)
Example:例如:
compare 1+i and 1-i.1 +我和1-i比较。
IN:在: islarger(1+i, 1-i)islarger(1 +我,1-i) # is 1+i larger than 1-i ?号是1 +我比1-i吗?
OUT: 1出:1 . # yes, 1+i > 1-i#是的,1 +我> 1-i
You can compare square of a variable a^2 > 0 if you know the property of the variable.你可以比较一下一个变量一个广场^ 2 > 0如果知道你的财产的变量。
Example:例如:
IN:在: assume(a > 0)假设(> 0)
IN:在: a^2 > 0, 1/a > 0一个^ 2 > 0,1 / > 0
OUT: 1, 1出:1、1
You can test if x is even, odd, integer, real, number or list by the functions:你可以测试甚至x,单,整数,真正的、数量或列表的功能:
iseven(x)iseven(x)
isodd(x)isodd(x)
isinteger(x)isinteger(x)
isreal(x)(x)来
isnumber(x)isnumber(x)
islist(x)islist(x)
isfree(y,x)isfree(y,x)
islarger(a,b)islarger(a,b)
isless(a,b)isless(a,b)
issame(a,b)issame(a,b)
Example:例如:
IN:在: iseven(2)iseven(2) # is 2 even ?# 2甚至吗?
OUT: 1出:1 . # yes#是的
Note that comparison by the is* functions return either 1 if it is true or 0 otherwise, but comparison by relational operators gives 1 if it is true, 0 if it is fault, or left unevaluated otherwise.注意的是*功能比较回报或如果它是真实的或0不同的看法,但比较关系运算符给1如果这是真的,如果它是0错误,或离开unevaluated不然。
Anytime when you find yourself using the same expression over and over, you should turn it into a function.当你发现你自己随时都使用同样的表情,你应该把它变成一个功能。
Anytime when you find yourself using the same definition over and over, you should turn it into a library.当你发现你自己随时都使用相同的定义,你应该把它变成一个图书馆。
You can make your defined function as if the built-in function, by saving your definition into disk file as a library with the function name plus extension .你可以让你的定义如果内置功能作用,以节省您的定义到磁盘文件作为一个库函数的名字加上延伸。li as the filename. 李的文件名。e.g. saving the factoria function as the factoria.例如节约factoria factoria的功能。li file (see Section Libraries and Packages).李文件(请看段图书馆和包装)。
You can define your own functions by你可以定义你自己的函数
f(x_) := x^2f(x_):= x ^ 2
Here are some sample function definitions:这里有一些样本函数定义:
f(x_) := cos(x + pi/3)f(x_):=因为(x + pi / 3)
g(x_, y_) := x^2 - y^2g(x_,y_):y = x ^ ^ 2 - 2
The argument in the definition should be the pattern x_. 辩论的定义应该x_模式。Otherwise f() works only for a specific symbolic value, e.g. x when defining f(x):=x^2. 否则f()只能为一个特定的符号价值,例如x当定义f(x)= x ^ 2。The pattern x_ should be only on the left side of the assignment.模式x_只能在左边的这个任务。
Once defined, functions can be used in expressions or in other function definitions:一旦界定、功能可用于表达方式或在其他函数定义:
y := f(3.2)杨:= f(3.2)
z := g(4.1, -5.3)赵:=克(4.1,-5.3)
Example:例如:
Define a new function for x^2, then evaluate it.定义一个新的函数x ^ 2,然后评价它。
IN:在: g(x) := x^2g(x):= x ^ 2
IN:在: g(2), g(a),g(2),g(a), g(x)g(x)
OUT: g(2), g(a),出:g(2),g(a), x^2x ^ 2 # work only for a symbolic value x#工作只有一个象征价值x
IN:在: f(x_) := x^2f(x_):= x ^ 2
IN:在: f(2), f(a)外(2),f(一)
OUT: 4, a^2出:4、一个^ 2 # work for any value#为其工作的价值
You can define a conditional function by the if() function:你可以定义一个条件作用的()如果功能:
f1(x_) := if(x>0 thenf1(x_):要是(x > 0然后 1)1)
f2(x_) := if(x>0 then x^2 else x)f2(x_):要是(x > 0 x ^ 2然后其他x)
or by inequalities:或不平等:
f3(x_) := x>0f3(x_):= x > 0
f4(x_) := (x>0) * x^2 + (x<=0) * xf4(x_):=(x > 0)* x ^ 2 +(x < = 0)* x
On the first definition by if(), when f1() is called it gives 1 if x>0, or left unevaluated otherwise. 在第一个定义,如果(),当f1()把它称为给1 x > 0或者离开unevaluated不然。On the second definition by the if(), when f2() is called it gives x^2 if x>0, x if x<=0, or left unevaluated otherwise. 第二个定义,如(),当f2()把它称为给x ^ 2 x > 0,x x < = 0或者离开unevaluated不然。On the third definition by the inequality, when f3() is called, it gives 1 for x>0, 0 for x<=0, or x>0 for symbolic value of x. On the last definition, when f4() is called, it is evaluated for any numeric or symbolic value of x.在第三的定义的不平等,当f3()被称为,它给1 x > 0,0 x < = 0,或者x > 0 x符号价值。最后定义,当f4()被称为,它对任何数字或符号的价值的x。
Remember that the words "then" and "else" can be replaced by comma ,.记得说“然后”和“其他”可以被逗号。
You cannot differentiate nor integrate the conditional function defined by if(), but you can do the conditional functions defined by inequalities.你不能分辨条件的作用也将规定如果(),但你还可以做条件函数定义为不平等。
You can define a function evaluated only for numbers by你可以定义一个函数只有总数的评价
f(x_) := if(isnumber(x) then x^2)f(x_):要是(isnumber(x)然后x ^ 2)
This definition is different from the definition by f(x_) := x^2. 这个定义不同于定义f(x_):= x ^ 2。On the latter, when f() is called, it gives x^2, regardless whatever x is. 在后者,当f()被称为,它给x ^ 2,不论x。On the former, when f() is called, it gives x^2 if x is a number, or left unevaluated otherwise.对于前者,当f()被称为,它给x ^ 2如果x是一个数字,或左unevaluated不然。
Example:例如:
evaluate to x^2 only if x is number, by defining a conditional function.评估x ^ 2如果x是号码,通过定义一个有条件的功能。
IN:在: f(x_) := if(isnumber(x) then x^2)f(x_):要是(isnumber(x)然后x ^ 2)
IN:在: f(2), f(a)外(2),f(一)
OUT: 4, f(a)出:4 f(a)
IN:在: f(x_) := if(x>0 then x^2)f(x_):要是(x > 0然后x ^ 2)
IN:在: f(2), f(-2), f(a)外(2),外(2),f(一)
OUT: 4, f(-2), f(a)出:4 f(2),f(一)
IN:在: f(x_) := if(x>0 then x^2 else x)f(x_):要是(x > 0 x ^ 2然后其他x)
IN:在: f(2), f(-2), f(a)外(2),外(2),f(一)
OUT: 4, 2, f(a)出:4,2 f(a)
You can define the case function by different pattern name. 你可以定义案件功能不同的模式的名字。The case function is similar to the case statement in BASIC language.情况类似的案件函数声明在基本的语言。
Example:例如:
IN:在: f(x_) := if( x > 0 and x < 1 then 1)f(x_):要是(x > 0和x < 1,那么一)
IN:在: f(u_) := if( u > 1 and u < 2 then 2)f(u_):要是(u > 1和u < 2然后2)
IN:在: f(v_) := if( v > 2 and v < 3 then 3)f(v_):要是(v > 2和v < 3然后,3)
IN:在: f(0.2), f(1.2), f(2.2)f(0.2)、f(1.2),f(2.2)
OUT: 1, 2, 3出:1、2、3
You can define a piece-wise function.你可��定义一个分片功能。
Example:例如:
define定义
/ x/ x if x < 0如果x < 0
f(x) =f(x)= 00 if x = 0如果x = 0
\ x^2\ x ^ 2 if x > 0如果x > 0
then evaluate f(-2), f(0), f(3), f(a), f'(x), diff(f(x), x=3).然后评估外(2)、f(0),f(3)、f(a)、f '(x),差异(f(x)、x = 3)。
IN:在: f(x_) := x*(x<0)+x^2*(x>0)f(x_):* = x(x < 0)+ x ^ 2 *(x > 0)
IN:在: f(-2), f(0), f(3), f(a)外(2)、f(0),f(3)、f(a)
OUT: -2, 0, 9, (a < 0) a + (a > 0) a^2出:2,0,- 9(< 0)+(> 0)一个^ 2
IN:在: f'(x)f '(x)
OUT: (x < 0) + 2 x (x > 0)出:(x < 0 + 2 x(x > 0)
IN:在: diff(f(x), x=3)差异(f(x)、x = 3)
OUT: 6出:6
You can define a recursion function.你可以定义一个递归函数。
Example:例如:
IN:在: factoria(1) := 1factoria(1):= 1
IN:在: factoria(n_) := if(n > 1, (n-1)*factoria(n-1))factoria(n_):要是(n > 1,(n-1)* factoria(n-1)
You can define a function with the multi function values.你可以定义一个函数和多功能的价值观。
Example:例如:
IN:在: squreroot(x_) := [sqrt(x), -sqrt(x)]squreroot(x_):=[sqrt(x),-sqrt(x))
IN:在: squreroot(4)squreroot(4)
OUT: [2, -2]出:[1,2]
You can define a function as a procedure by你可以定义一个函数程序
f(x_) := block(command1, command2, ...f(x_):=区块(command1,command2,……, commandN),commandN)
f(x_) := block(command1, command2, ...f(x_):=区块(command1,command2,……, commandN, local(a)),commandN,当地(a))
By default, all variables within procedure are global, except for variables declared by local(). 默认情况下,所有的变量在程序都是全球性的,除了变量声明当地()。The multi-statement should be grouped by block(). 错误的应按区块()。The block() only outputs the result of the last statement or the second last one as its value. 块()的结果只有输出最后的陈述或第二最后一个为其价值。The multi-line must be terminated by a comma, (not by a comma and a blank space). 线必须终止用逗号,而不是由一个逗号和一个空白的空间)。Local() must be the last one in block().本地()必须在最后一个块()。
Example:例如:
define a numeric integration procedure ninte() and calculate integral of x^2 from x=1 to x=2 by call ninte().定义一个数字集成程序和计算ninte x ^ 2积分x = 1到2 x =叫ninte()。
IN:在: ninte(y_,x_,a_,b_) := block( numeric:=on,ninte(y_ x_ b_已,,,):=区块(数字:=,
dd:=(b-a)/50,戴夫:=(b-a)/ 50人,
aa:=a+dd,aa:= +茶桶空行,
bb:=b-dd,bb:= b-dd,
y0:=subs(y, x = a),y0:=替补(y,x =),
yn:=subs(y, x = b),yn:=替补(y,x = b),
(sum(y,x,aa,bb,dd)+(y0+yn)/2)*dd,(全额(x,y,aa,bb,dd)+(y0 + yn / 2)*茶桶空行,
local(dd,aa,bb,y0,yn) )本地(dd,aa,bb,y0、yn)
IN:在: ninte(x^2, x, 1, 2)ninte(x ^ 2、x、1,2)
You can define transform rules. 你可以定义转换规则。Defining rules is similar to defining functions. 定义定义规则类似的功能。In defining functions, all arguments must be simple variables, but in defining rules, the first argument can be a complicated expression.在定义功能,所有变量参数必须简单,但在确定规则,第一个参数可以是一个复杂的表达式。
Example:例如:
Define log rules.定义日志的规则。
IN:在: log(x_ * y_) := log(x) + log(y)日志(x_ * y_):=日志(x)+日志(y)
IN:在: log(x_ ^ n_) := n*log(x)日志(x_ n_ ^):= n *日志(x)
IN:在: log(a*b)日志(* b)
OUT: log(a) + log(b)出:日志(a)+日志(b)
Example:例如:
IN:在: sin(-x_) := -sin(x)罪(-x_):= -sin(x)
IN:在: sin(-a)罪(-)
OUT: -sin(a)出:-sin(a)
Example:例如:
Define derivatives (see Chapter 4.5.2 Defining f'(x)).定义衍生物(见章定义的4.5.2 f(x))。
IN:在: f'(x_) := sin(x)f '(x_):=罪(x)
IN:在: f'(t)福”(t)
OUT: sin(t)出:罪(t)
Example:例如:
Define integrals (see Chapter 4.6.1 Indefinite Integration).定义积分(见章节不确定性整合4.6.1)。
IN:在: inte(f(x_),x_) := sin(x)希尔(f(x_),x_):=罪(x)
IN:在: inte(f(t),t)希尔(f(t),t)
OUT: sin(t)出:罪(t)
Example:例如:
Define the trig simplification rules.定义三角法简化规则。
IN:在: simplify(sin(x_)^2, x_) := 1/2*(1-cos(x))简化(罪(x_)^ 2、x_):= 1/2 *(1-cos(x))
IN:在: simplify(sin(x)^2,x)简化(罪(x)^ 2、x)
OUT: 1/2 (1 - cos(x))出:1/2(1 - cos(x))
Example:例如:
Define Laplace transform rules.定义拉普拉斯变换规则。
IN:在: laplace(sin(t_), t_) := 1/(t^2+1)拉普拉斯(罪(t_),t_):= 1 /(t ^ 2 + 1)
IN:在: laplace(sin(s), s)拉普拉斯(罪(s),s)
OUT: 1/(s^2 + 1)出:1 /(s ^ 2 + 1)
You can finds real or complex limits, and discontinuity or one-sided value.你可以找到真正的或复杂的限制,以及不连续或片面的价值。
First find the expression value by subs(y, x = x0) or the function value by f(x0) when x = x0.首先找到表达式的值由替补(y,x = x0)或功能价值由f(x0)当x = x0。
If the result is the discont (i.e. discontinuity), then use the one-sided value x0+zero or x0-zero to try to find the one-sided function or expression value.如果结果是discont(即中断),然后用片面x0 +零或x0-zero价值,试图寻找片面函数或表达式的值。
For a function f(x), you can evaluate the left- or right-sided function value, similar to evaluate the normal function value:为一个函数f(x),你就可以评价左-右函数值或类似于正常功能的评估价值。
f(x0-zero)f(x0-zero)
f(x0+zero)f(x0 + 0)
For an expression y, you can evaluate its one-sided expression value by为一个表达式y,你就可以评价其片面表达式的值
subs(y, x = x0-zero)替补(y,x = x0-zero)
subs(y, x = x0+zero)替补(y,x = x0 + 0)
The discont (discontinuity) means that the expression has a discontinuity and only has the one-sided value at x=x0. 这discont(中断)意味着有一个传统的表情,只有在x = x0片面的价值。You should use x0+zero or x0-zero to find the one-sided value. 你应该用x0 +零或x0-zero找到片面的价值。The value of f(x0+zero) or f(x0-zero) is the right-sided or left-sided function value as approaching x0 from positive (+inf) or negative (-inf) direction, respectively, i.e. as x = x0+ or x = x0-.f的价值(x0 + 0)或f(x0-zero)是右侧或左侧函数值从接近x0正(+ inf)或负(-inf)的方向,分,即x = = x0 x0 +或x -。
If the result is undefined (indeterminate forms, e.g. 0/0, inf/inf, 0*inf, and 0^0), then find its limit by如果结果是未定义的(不确定的形式、例句。0/0,步/无穷大,0 * ^ 0 inf,0),然后找到它的限制
lim(y, x = x0)小林(y,x = x0)
If the limit is discont, then you can find a left- or right-sided limit when x approaches to x0 from positive (+inf) or negative (-inf) direction at discontinuity by如果这个限制是discont,然后你可以找到一个左-右限制或当x方法从x0正(+ inf)或负(-inf)方向不连续
lim(y, x = x0+zero)小林(y,x = x0 + 0)
lim(y, x = x0-zero)小林(y,x = x0-zero)
Example:例如:
Evaluate y=exp(1/x) at x=0, if the result is discontinuity, find its left-sided and right-sided values (i.e. when x approaches 0 from positive and negative directions).y =实验评估(1 / x)在x = 0,如果结果不连续性、找到它的左和右值(例如当x方法0从积极和消极的方向。
IN:在: y:=exp(1/x)杨:=经验(1 / x)
IN:在: subs(y, x = 0)替补(y,x = 0)
OUT: discont出:discont # discontinuity at x=0在x = 0 #不连续
IN:在: subs(y, x = 0+zero), subs(y, x = 0-zero)替补(y,x = 0 + 0),替补(y,x = 0-zero)
OUT: inf, 0出:无穷大,0
Example:例如:
How to handle the following one-sided values ?如何处理好以下片面的价值观吗?
Let f(x) = 1 when x < 1, f(x) = 1 when x > 1 (and not defined at x = 1).让f(x)= 1当x < 1,f(x)= 1当x > 1(而不是定义于x = 1)。
Let g(x) = 1 when x < 1, g(x) = 1 when x > 1, and g(1) = 2.让克(x)= 1当x < 1,g(x)= 1当x > 1、g(1)= 2。
Let h(x) = 1 when x < 1, h(x) = 2 when x >= 1.让h(x)= 1当x < 1、h(x)= 2当x > = 1。
Let k(x) = 1 when x < 1, k(x) = 2 when x > 1, and k(1) = 3.让k(x)= 1当x < 1、钾(x)= 2当x > 1,k(1)= 3。
Now ask SymbMath to compute现在问SymbMath计算
(1) the limit as x approaches 1,(1)限制1 x的方法,
(2) the limit as x approaches 1 from the left, and(2)限制一号从x方法(左)和
(3) the limit as x approaches 1 from the right(3)限制一号从x方法正确
for each of the above piecewise defined functions.对于每一种分段函数上面。
# define functions#定义功能
f(x_) :=f(x_):= if(x<1 or x>1, 1)如果(x < 1或x > 1,1)
f(1+zero):=1外(1 + 0):= 1
f(1-zero):=1f(1-zero):= 1
g(x_) := if( x<1 or x>1, 1)g(x_):要是(x < 1或x > 1,1)
g(1):=2g(1):= 2
g(1+zero):=1g(1 + 0):= 1
g(1-zero):=1g(1-zero):= 1
h(x_) := if( x<1, 1, 2)h(x_):要是(x < 1、1、2)
h(1+zero):=2h(1 + 0):= 2
h(1-zero):=1h(1-zero):= 1
k(x_) := if( x<1, 1, if( x>1, 2))k(x_):要是(x < 1,1,如果(x > 1、2))
k(1):=3凯西(1):= 3
k(1+zero):=2凯西(1 + 0):= 2
k(1-zero):=1k(1-zero):= 1
# evaluate functions#评估功能
IN:在: f(1), g(1), h(1), k(1)外(1),g(1),h(1)、钾(1)
OUT: f(1), 2, 2, 3出:f(1)、2、2、3位
IN:在: f(1+zero), g(1+zero), h(1+zero), k(1+zero)外(1 + 0),g(1 + 0),h(1 + 0)、钾(1 + 0)
# right-hand side value at x=1+右手边值# x = 1 +
OUT: 1, 1, 1, 1出:1,1,1,1
IN:在: f(1-zero), g(1-zero), h(1-zero), k(1-zero)f(1-zero),g(1-zero),h(1-zero)、钾(1-zero)
# left-hand side value at x=1-左手边值号x = 1 -
OUT: 1, 1, 2, 2出:1、1、2、2
Example:例如:
Find limits of types 0/0 and inf/inf.找到0/0和限制类型步/无穷大。
IN:在: p:=(x^2-4)/(2*x-4)警:=(x ^ 2 - 4)/(2 * x-4)
IN:在: subs(p, x = 2)替补(p、x = 2)
OUT: undefined出:未定义
IN:在: lim(p, x = 2)小林(p、x = 2)
OUT: 2出:2
IN:在: subs(p, x = inf)替补(p、x = inf)
OUT: undefined出:未定义
IN:在: lim(p, x = inf)小林(p、x = inf)
OUT: inf出:步
If symbolic limit falls, you should try numeric limit by如果象征性的限制下,你应该试试数字限制
nlim(y, x=x0)nlim(y,x = x0)
e.g. nlim(sin(x)/x, x=0)例如nlim(罪(x)、x / x = 0)
Differentiate an expression y with respect to x by区分一个表达式y就x
d(y, x)d(y,x)
Differentiate a simple function f(x) with respect to x by划分出一个简单的函数f(x)关于x
f'(x)f '(x)
Differentiate y in the n order ( n > 0 ) by在划分为y氮(n > 0)
d(y, x, n)d(x,y,n)
Differentiate y at x = x0 by在x = x0划分y
diff(y, x = x0)比较(y,x = x0)
Differentiate y at x = x0 in the n order (n > 0) by在x = x0划分y在n秩序(n > 0)
diff(y, x = x0, n)比较(y,x = x0、n)
Example:例如:
Differentiate sin(x) and x^(x^x).区分罪(x)和x ^(x ^ x)。
IN:在: sin'(x)罪”(x) # sin'(x) is the same as d(sin(x), x).#罪”(x)是一样的d(罪(x)、x)。
OUT: cos(x)出:因为(x)
IN:在: d(x^(x^x), x)d(x ^(x ^ x)、x)
OUT: x^(x^x) (x^(-1 + x) + x^x ln(x) (1 + ln(x)))出:x ^(x ^ x)(x ^(1 + x)+ x ^;x(x)(1 +淋巴结(x))
If you differentiate f(x) by f'(x), x must be a simple variable and f(x) must be unevaluated.如果你区分f(x)f”(x)、x必须是一个简单的变量和f(x)必须unevaluated。
f'(x0) is the same as d(f(x0),x0), but different from diff(f(x), x=x0). f '(x0)是一样的d(f(x0),x0),但不同于差异(f(x)、x = x0)。f'(x0) first evaluates f(x0), then differentiates the result of f(x0). f '(x0)首先评估f(x0),然后划分结果f(x0)。But diff(f(x), x=x0) first differentiates f(x), then replace x with x0. 但是差异(f(x)、x = x0)首先划分f(x),然后替换与x0 x。Note that sin'(x^6) gives cos(x^6) as sin'(x^6) is the same as d(sin(x^6), x^6). 注意罪”(x ^ 6)给因为(x ^ 6)如罪”(x ^ 6)是一样的d(罪(x ^ 6)、x ^ 6)。sin'(0) gives d(0,0) as sin(0) is evaluated to 0 before differentiation, you should use diff(sin(x),x=0) which gives 1.罪”(0)给d(0,0)如罪(0)评估为0,你应该用在分化差异(罪(x)、x = 0)为1。
Example:例如:
Differentiate the expression f=sin(x^2+y^3)+cos(2*(x^2+y^3)) with respect to x, and with respect to both x and y.区分表达式女=罪(x ^ 2 + y ^ 3)+因为(2 *(x ^ 2 + y ^ 3)关于x,并就两个x和y。
IN:在: f := sin(x^2+y^3)+cos(2*(x^2+y^3))女:=罪(x ^ 2 + y ^ 3)+因为(2 *(x ^ 2 + y ^ 3))
IN:在: d(f, x)d(f,x)
OUT: 2 x cos(x^2 + y^3) - 4 x sin(2 (x^2 + y^3))出:2 *因为(x ^ 2 + y ^ 3),4×罪(2(x ^ 2 + y ^ 3))
IN:在: d(d(f, x), y)d(d(f,x,y) # mixed derivative with x and y.与#混合衍生物x和y。
OUT: -6 x y^2 sin(x^2 + y^3) - 12 x y^2 cos(2 (x^2 + y^3))出:6倍^ 2 y罪(x ^ 2 + y ^ 3)- y ^ 2的12倍,因为(2(x ^ 2 + y ^ 3))
Differentiate y at x = x0-zero or 0+zero (the left- or right- sided derivative) by在x = x0-zero划分y或0 + 0(左边或右边- - - - - - - - - - - -站导数)
diff(y, x = x0-zero)比较(y,x = x0-zero)
diff(y, x = x0+zero)比较(y,x = x0 + 0)
Example:例如:
IN:在: diff(ln(x), x=0)齿轮淋巴结(x)、x = 0)
OUT: discont出:discont # discontinuity at x=0在x = 0 #不连续
IN:在: diff(ln(x), x=0-zero)齿轮淋巴结(x)、x = 0-zero) # left-sided derivative at x=0-#左导数时,x = 0 -
OUT: -inf出:-inf
IN:在: diff(ln(x), x=0+zero)齿轮淋巴结(x)、x = 0 + 0) # right-sided derivative at x=0+右导数时,# x = 0 +
OUT: inf出:步
Defining derivatives is similar to defining rules. 类似的定义界定衍生物的规则。You only need to define derivatives of a simple function, as SymbMath automatically apply the chain rule to its complicated function.你只需要定义衍生物的简单的函数,运用SymbMath自动链法则,其复杂的功能。
Example:例如:
IN:在: f'(x_) := sin(x)f '(x_):=罪(x)
IN:在: f'(x)f '(x)
OUT: sin(x)出:罪(x)
IN:在: f'(x^6)f '(x ^ 6) # the same as d(f(x^6), x^6)#一样的d(f(x ^ 6)、x ^ 6)
OUT: sin(x^6)出:罪(x ^ 6)
IN:在: d(f(x^6), x)d(f(x ^ 6)、x)
OUT: 6 x^5 sin(x^6)出:6 ^ 5罪x(x ^ 6)
You can find integrals of x^m*e^(x^n), x^m*e^(-x^n), e^((a*x+b)^n), e^(-(a*x+b)^n), x^m*ln(x)^n, ln(a*x+b)^n, etc., (where m and n are any real number).你能找到x ^ m *积分的e ^(x ^ n)、x ^ ^ m * e(-x ^ n)、e ^((* x + b)^ n)、e ^(-(* x + b)^ n)、x ^ m *淋巴结(x)^ n、淋巴结(* x + b)^ n等,(在m和n是任何真正的数字)。
It is recommended that before you do symbolic integration, you should simplify integrand, e.g. expand the integrand by expand() and/or by setting the switch expand:=on and/or expandexp:=on.建议你象征整合前,你应该被积函数进行简化,例如扩大被积函数的扩展()和/或设定的开关扩大:=在和/或expandexp:=。
If symbolic integration fails, you can define a simple integral and/or derivative, (or adding integral into the inte.如果符号整合失败,你可以定义一个简单的积分和/或衍生品(或添加到强烈的积分。li library), then do integration again (see Chapter Learning From User).李图书馆),然后再做整合(见一章的学习,从用户)。
Find the indefinite integrals of expr by发现不定积分的expr
inte(expr, x)希尔(expr、x)
Find the double indefinite integrals by发现双不定积分
inte(inte(expr, x), y)希尔(交互(expr、x、y)
Note that the arbitrary constant is not represented.注意,任意常数并不代表。
Example:例如:
Find integrals of 1/a, 1/b and 1/x, knowing a >0, b is real.发现积分的1、1 / b和1 / x,知道> 0,b是真实的。
IN:在: assume(a>0), isreal(b):=1假设(>),来(b):= 1
IN:在: inte(1/a, a), inte(1/b, b), inte(1/x, x)希尔(1 / a,一个),交互(1 / b、b),交互(1 / x,x)
OUT: ln(a), ln(|b|), ln(x*sign(x))出:淋巴结(a)、淋巴结(b | |),淋巴结(x *签署(x))
Example:例如:
Find indefinite integrals.发现不定积分。
IN:在: inte(sin(a*x+b), x)强烈的(罪(一个* x + b),x) # integrands involving sin(x)# integrands涉及罪(x)
OUT: -cos(b + a x)/a出:-cos(b +一个x)
IN:在: inte( sin(x)/x^2, x)强烈的(罪(x)/ x ^ 2、x)
OUT: ci(x) - sin(x)/x出:ci(x)-罪/ x(x)
IN:在: inte( x*sin(x), x)强烈的(x *罪(x)、x)
OUT: -x cos(x) + sin(x)出:-x因为(x)+罪(x)
IN:在: inte(sin(x)*cos(x), x)强烈的(罪(x)*因为(x)、x)
OUT: (1/2)*sin(x)^2出:(1/2)* ^ 2罪(x)
IN:在: inte( e^(x^6), x)希尔(e ^(x ^ 6)、x) # integrands involving e^xintegrands涉及e ^ x号
OUT: 1/6 ei(-5/6, x^6)出:1/6 ei(-5/6、x ^ 6)
IN:在: inte( x^2*e^x, x)强烈的(x ^ 2 * e ^ x,x)
OUT: ei(2, x)出:ei(2 x)
IN:在: inte( x*e^(-x), x)强烈的(x ^ * e(-x)、x)
OUT: -e^(-x) - x e^(-x)出:. ^(-x)- x e ^(-x)
IN:在: inte( e^x/sqrt(x), x)希尔(e ^ x / sqrt(x)、x)
OUT: ei(-0.5, x)出:ei(-0.5 - x)
IN:在: inte(x^1.5*exp(x), x)强烈的(x ^ 1.5 *经验(x)、x)
OUT: ei(1.5, x)出:ei(1.5 - x)
IN:在: inte(sin(x)*e^x, x)强烈的(罪(x)* e ^ x,x) # integrals involving sin(x) and e^x涉及犯罪#积分(x)和e ^ x
OUT: 1/2 * (sin(x) - cos(x)) * e^x出:1/2 *(罪(x)- cos(x))* e ^ x
IN:在: inte( x*ln(x), x)强烈的(x *淋巴结(x)、x) # integrands involving ln(x)# integrands涉及淋巴结(x)
OUT: -1/4 x^2 + 1/2 x^2 ln(x)出:1/4 x ^ 2 ^ 2 + 1/2 x(x);
IN:在: inte( ln(x)^6, x)希尔(淋巴结(x)^ 6,x)
OUT: li(6, x)出:李(6、x)
IN:在: inte( ln(x)/sqrt(x), x)希尔(淋巴结(x)/ sqrt(x)、x)
OUT: -4 sqrt(x) + 2 sqrt(x) ln(x)出:4 sqrt(x)+ 2 sqrt(x)淋巴结(x)
IN:在: inte( ln(x)/sqrt(1 + x), x)希尔(淋巴结(x)/ sqrt(1 + x)、x)
OUT: -4 sqrt(1 + x) + 2 sqrt(1 + x) ln(x) - 2 ln((-1 + sqrt(1 + x))/(1 + sqrt(1 + x)))出:4 sqrt(1 + x)+ 2 sqrt(1 + x);取出(x)- 2(1 + sqrt(1 + x))/(1 + sqrt(1 + x))
IN:在: inte( 1/(a x + b), x)希尔(1 /(x + b),x) # integrands involving polynomials# integrands涉及多项式
OUT: ln((b + a x) sign(b + a x))/a出:淋巴结((b +一个x)签署(b +一个x))
IN:在: inte( x/(x^2 + 5 x + 6), x)强烈的(x(x ^ 2 + 5倍+ 6)、x)
OUT: 1/2 ln(|6 + 5 x + x^2|) - 5/2 ln(|(2 + x)/(3 + x)|)出:1/2淋巴结(| 6 + 5倍+ x ^ 2 |)-整合淋巴结(|(2 + x)/(3 + x)|)
IN:在: inte( (x^3 + x)/(x^4 + 2 x^2 + 1), x)希尔((x ^ 3 + x)/(x ^ ^ 4 + 2×2 + 1)、x)
OUT: 1/4 ln((1 + 2 x^2 + x^4) sign(1 + 2 x^2 + x^4))出:1/4淋巴结(1 + 2 x ^ ^ 2 + x 4)签订(1 + 2 x ^ ^ 2 + x 4))
Example:例如:
Find the line integral.找到的线积分。
IN:在: x:=2*t谢:= 2 * t
IN:在: y:=3*t杨:= 3 * t
IN:在: z:=5*t赵:= 5 * t
IN:在: u:=x+y你:= x + y
IN:在: v:=x-y老板:= x - y
IN:在: w:=x+y+z魏:= x + y + z
IN:在: inte(u*d(u,t)+v*d(v,t)+w*d(w,t), t)希尔(u * d(u、t)+ v * d(v,t)+ w * d(w,t),t)
OUT: 63 t^2出:63 t ^ 2
Example:例如:
Integrate x^2*e^x, then expand it by the mean of the packages "ExpandEi.整合x ^ ^ 2 * e x,然后扩大它的“ExpandEi意味着的包装。sm" (expand ei(n,x)).sm”(扩大ei(n、x))。 The packages "ExpandGa.ExpandGa包”。sm" (expand gamma(n,x)) and "ExpandLi.sm”(扩大伽玛(氮、x))和“ExpandLi。sm" (expand li(n,x)) are similar one.sm”(扩大李(氮、x))相似的对话。
IN:在: inte(x^2*e^x, x)强烈的(x ^ 2 * e ^ x,x)
OUT: ei(2,x)出:ei(2 x) # ei()# ei()
IN:在: readfile("ExpandEi.sm")readfile(“ExpandEi.sm”)
IN:在: ExpandEi(ei(2, x))ExpandEi(ei(2 x))
OUT: x^2 e^x - 2 x e^x + 2 e^x出:x ^ ^ 2 e ^ 2 x e x - x + 2 e ^ x # ei() is expanded美国饭店协会教育学院()号扩展
Defining integrals is similar to defining rules.类似于定义界定积分规则。
Example:例如:
IN:在: inte(f(x_), x_) := sin(x)希尔(f(x_),x_):=罪(x)
IN:在: inte(f(t), t)希尔(f(t),t)
OUT: sin(t)出:罪(t)
Find definite integrals by external functions找到明确由外部功能积分
inte(expr, x from xmin to xmax)希尔(expr,从x xmin到xmax)
inte(expr, x from xmin to singularity to xmax)希尔(expr,从x xmin奇异性,对xmax)
Example:例如:
Find the definite integral of y=exp(1-x) with respect to x taken from 0 to infinity.找到了定积分的y =经验(1-x)关于x采取从0到无限。
IN:在: inte(exp(1-x), x from 0 to inf)强烈的预期(1-x)、x从0到无穷大)
OUT: e出:呃
Example:例如:
do discontinuous integration of 1/x^2 and 1/x^3 with discontinuity at x=0.做整合/ x不连续^ 1 ^ 2和1 / x第三不连续在x = 0。
IN:在: inte(1/x^2, x from -1 to 2)希尔(1 / x ^ 2、x从1到2) # singularity at x=0x = 0 #奇异点
OUT: inf出:步
IN:在: inte(1/x^3, x from -1 to 1)希尔(1 / x ^ 3、x从1到1) # singularity at x=0x = 0 #奇异点
OUT: 0出:0
IN:在: inte(sqrt((x-1)^2), x from 0 to 2)希尔(sqrt(x-1)^ 2)、x从0到2) # singularity at x=1x = 1 #奇异点
OUT: 1出:1 .
SymbMath usually detect singularity, but sometime it cannot, in this case you must provide singularity.通常SymbMath检测奇异点,但是有时它进不去的,在这种情况下,你必须提供奇异点。
Example:例如:
IN:在: inte(1/(x-1)^2, x from 0 to 1 to 2)希尔(1 /(x-1)^ 2、x从0到1 - 2) # provide singularity at x=1#提供奇异点x = 1
OUT: inf出:步
Example:例如:
complex integration.复杂的整合。
IN:在: inte(1/x, x from i to 2*i)希尔(1 / x,从x我2 *我)
OUT: ln(2)出:;(2)
The external function对外功能
ninte(y, x from xmin to xmax)ninte(y,从x xmin到xmax)
does numeric integration.做数字集成。
Example:例如:
Compare numeric and symbolic integrals of 4/(x^2+1) with respect to x taken from 0 to 1.积分的数值和符号比较4(x ^ 2 + 1)关于x是从0到1。
IN:在: ninte(4/(x^2+1), x from 0 to 1)ninte(4 /(x ^ 2 + 1)、x从0到1)
OUT: 3.1415出:1 .
IN:在: num(inte(4/(x^2+1), x from 0 to 1))胡(交互(4 /(x ^ 2 + 1)、x从0到1))
OUT: 3.1416出:1 .
The equations can be operated (e.g. +, -, *, /, ^, expand(), diff(), inte()). 方程可操作(例如。+,-,*,/,^,扩大()()、强烈的差别()。The operation is done on both sides of the equation, as by hand. 操作上做双方的方程,为手工做的。You can find roots of a polynomial, algebraic equations, systems of equations, differential and integral equations.你可以找到一个多项式的根,代数方程,方程系统,微分和积分方程。
You can get the left side of the equation by你能得到的方程的左侧
left(left_side = right_side)左(left_side = right_side)
or get the right side by或者让右边
right(left_side = right_side)右(left_side = right_side)
You can assign equations to variables.你可以指定方程变量。
Example:例如:
IN:在: eq1:= x + y = 3eq1:= x + y = 3
IN:在: eq2:= x - y = 1eq2:= x - y = 1
IN:在: eq1+eq2eq1 + eq2
OUT: 2 x = 4出:2 x = 4
IN:在: last/2最后2
OUT: x = 2出:x = 2
IN:在: eq1-eq2eq1-eq2
OUT: 2 y = 2出:2 y = 2
IN:在: last/2最后2
OUT: y = 1出:y = 1
Example:例如:
Solve an equation sqrt(x+2*k) - sqrt(x-k) = sqrt(k), then check the solution by substituting the root into the equation.sqrt解决一个方程(x + 2 * k)- sqrt(x-k)= sqrt(k),然后检查溶液代替这个根方程。
IN:在: eq1 := sqrt(x + 2*k) - sqrt(x - k) = sqrt(k)eq1:= sqrt(x + 2 * k)- sqrt(x - k)= sqrt(k)
OUT: eq1 := sqrt(x + 2*k) - sqrt(x - k) = sqrt(k)出:eq1:= sqrt(x + 2 * k)- sqrt(x - k)= sqrt(k)
IN:在: eq1^2eq1 ^ 2
OUT: ((2*k + x)^0.5 - ((-k) + x)^0.5)^2 = k出:(2 * k + x)^ 0.5 -((-k)+ x)^ 0.5)^ 2 = k
IN:在: expand(last)扩大(最后)
OUT: 2*x + k + (-2)*(2*k + x)^0.5*((-k) + x)^0.5 = k出:2 * x + k +(2)*(2 * k + x)^ 0.5 *(-k)+ x)^ 0.5 = k
IN:在: last-k-2*xlast-k-2 * x
OUT: (-2)*(2*k + x)^0.5*((-k) + x)^0.5 = (-2)*x出去。(2)*(2 * k + x)^ 0.5 *(-k)+ x)^ 0.5 =(2)* x
IN:在: last/(-2)最后(2)
OUT: (2*k + x)^0.5*((-k) + x)^0.5 = x出:(2 * k + x)^ 0.5 *(-k)+ x)^ 0.5 = x
IN:在: last^2最后^ 2
OUT: (2*k + x)*((-k) + x) = x^2出:(2 * k + x)*(-k)+ x)= x ^ 2
IN:在: expand(last)扩大(最后)
OUT: (-2)*k^2 + k*x + x^2 = x^2出去。(2)* ^ 2 k + k * x + x ^ 2 = x ^ 2
IN:在: last-x^2+2*k^2last-x ^ ^ 2 + 2 * 2 k
OUT: k*x = 2*k^2出:阿k * x = 2 * ^ 2 k
IN:在: last/k最后/ k
OUT: x = 2*k出:x = 2 * k
IN:在: subs(eq1, x = right(last))替补(eq1、x =权利(最后))
OUT: k^0.5 = k^0.5出:阿k ^ ^ 0.5 = 0.5 k
You can solve algebraic equations step by step, as above. 你可以解决代数方程一步一步,如上。This method is useful in teaching, e.g. showing students how to solve equations.在教学中,那么这个方法是非常有用,例如为学生们展示如何解决方程。
The solve() functions()功能解决
solve(expr1 = expr2, x)解决(expr1 = expr2、x)
solve([expr1 = expr2, expr3 = expr4], [x, y])解决([expr1 = = expr4 expr2,expr3]、[x,y])
solve a polynomial and systems of linear equations on one step. 解决一个多项式和系统的线性方程组在足下。It is recommended to set the switch expand:=on when solve the complicated equations. 建议设置开关扩大:=当解决复杂的方程式。All of the real and complex roots of the equation will be found by solve(). 所有真正的和复杂的方程的根必被找到解决()。The function solve() outputs a list of roots when there are multi-roots. 解决()输出功能表有multi-roots根。You can get one of roots from the list, (see Chapter 4.9 Arrays, Lists, Vectors and Matrices).你可以找一个根从名单上,(见章节4.9阵列、列表、向量和矩阵)。
Example:例如:
Solve a+b*x+x^2 = 0 for x, save the root to x.解决一个+ b * x + x ^ 2 = 0 x,节省了根系对x。
IN:在: solve(a+b*x+x^2 = 0, x)解决a + b * x + x ^ 2 = 0,x) # solve or re-arrange the equation for x#解决的公式或自行x
OUT: x = [-b/2 + sqrt((b/2)^2 - a),出:x =[-b / 2 + sqrt(b / 2)^ 2 - a), -b/2 - sqrt((b/2)^2 - a)]-b / 2 - sqrt(b / 2)^ 2 -一个)
IN:在: x := right(last)谢:=权利(最后) # assign two roots to x指派两根x号
OUT: x := [-b/2 + sqrt((b/2)^2 - a),出:谢:=[-b / 2 + sqrt(b / 2)^ 2 - a), -b/2 - sqrt((b/2)^2 - a)]-b / 2 - sqrt(b / 2)^ 2 -一个)
IN:在: x[1]x[1] # the first root#第一根
OUT: -b/2 + sqrt((b/2)^2 - a)出:-b / 2 + sqrt(b / 2)^ 2 - a)
IN:在: x[2]x[2] # the second root#第二根
OUT: -b/2 - sqrt((b/2)^2 - a)出:-b / 2 - sqrt(b / 2)^ 2 - a)
Example:例如:
Solve x^3 + x^2 + x + 5 = 2*x + 6.解决x ^ 3 + x ^ 2 + x + 5 = 2 * x + 6。
IN:在: num(solve(x^3+x^2+x+5 = 2*x+6, x))胡(解决(x ^ 3 + x ^ 2 + x + 5 = 2 * x + 6,x))
OUT: x = [1, -1, -1]出:x =[1]1,1)
The function solve() not only solves for a simple variable x but also solves for an unknown function, e.g. ln(x).解决()的功能不仅可以解决了一个简单的变量x还解决了一个未知的功能,例如淋巴结(x)。
Example:例如:
Solve the equation for ln(x).为解决方程;(x)。
IN:在: solve(ln(x)^2+5*ln(x) = -6, ln(x))解决(淋巴结(x)^ 2 + 5 *淋巴结(x)= 6、淋巴结(x))
OUT: ln(x) = [-2, -3]出:淋巴结(x)=[2、3)
IN:在: exp(last)(最后)实验
OUT: x = [exp(-2), exp(-3)]出:x =[实验,实验(2)(3))
Example:例如:
Rearrange the equations.重新安排方程。
IN:在: eq := [x+y = 3+a+b, x-y = 1+a-b]情商:=[x + y = 3 + + b,x - y = 1 +故) # assign equations to eq#分配方程式式
IN:在: solve(eq, [x,y])解决(eq(x,y) # rearrange eq for x and y#重排eq为x和y
OUT: [x = -1/2*(-4 - 2 a), y = -1/2*(-2 - 2 b)]出:[x = 1/2 *(4 - 2 a),y = 1/2 *(2 - 2 b)
IN:在: solve(eq, [a,b])解决(eq(a,b) # rearrange eq for a and b#重排eq为a和b
OUT: [a = -1/2*(4 - 2 x), b = -1/2*(2 - 2 y)]出:[= 1/2 *(4 - 2 x),b = 1/2 *(2 - 2 y)
IN:在: solve(eq, [a,y])解决(eq,[一个,y]) # rearrange eq for a and y#重新排列为一个和y情商
OUT: [b = -1/2*(2 - 2 y), x = -1/2*(-4 - 2 a)]出:[b = 1/2 *(2 - 2 y)、x = 1/2 *(4 - 2 a))
IN:在: solve(eq, [x,b])解决(eq(x,b]) # rearrange eq for x and b#重新排列x和b情商
OUT: [a = 1/2*(-4 + 2 x), y = 1/2*(2 + 2 b)]出:[= 1/2 *(4 + 2 x),y = 1/2 *(2 + 2 b)
The external function对外功能
psolve(f(x), x)psolve(f(x)、x)
solves f(x)=0 for x. It is similar to solve(), but it only can solve polynomial with order < 3.解决了f(x)= 0 x。这就像解决(),但是它只能求解多项式订单< 3。
e.g.例句。
IN:在: psolve(x^2+5*x+6, x)psolve(x ^ 2 + 5 * x + 6,x)
OUT: [-2, -3]出:[2、3)
The external functions外部功能
nsolve(f(x) = x, x)nsolve(f(x)= x,x)
nsolve(f(x) = x, x,x0)nsolve(f(x)= x,x,x0)
numerically solves an algebraic equation with an initial value x0. 一种代数方程数值解决x0一个初始值。By default x0=1. 默认情况下x0 = 1。nsolve() only gives one solution near x0, omitting other solutions.nsolve()只给一个解决办法靠近x0、删除其他的解决方案。
Example:例如:
IN:在: nsolve( cos(x) = x, x)nsolve(因为(x)= x,x)
OUT: x = 0.73911289091出:x = 0.73911289091
IN:在: nsolve( sin(x) = 0, x,0)nsolve(罪(x)= 0,x,0) # similar to asin( sin(x)=0 )asin #相似(罪(x)= 0)
OUT: x = 0出:x = 0 # only gives one solution near x0=0解决#只给附近x0 = 0
IN:在: nsolve( sin(x) = 0, x,3)nsolve(罪(x)= 0,x,3)
OUT: x = 3.14出:x = 3.14 # only gives one solution near x0=3解决#只给附近x0 = 3
You can solve the differential equations:你能解决这个微分方程:
y'(x) = f(x)y”(x)= f(x)
by integrating the equation.通过整合方程。
y'(x) is the same as d(y(x),x).y”(x)是一样的d(y(x)、x)。
Example:例如:
solve y'(x)=sin(x) by integration.解决y”(x)=罪(x)整合。
IN:在: inte( y'(x) = sin(x), x)希尔(y”(x)=罪(x)、x)
OUT: y(x) = constant - cos(x)出:y(x)=持续不断的——因为(x)
The external function对外功能
dsolve(y'(x) = f(x,y), y(x), x)dsolve(y”(x)= f(x,y),y(x)、x)
can solve the first order variables separable and linear differential equations能解决这一阶变量和线性微分方程可分离
y'(x) = h(x)y”(x)= h(x)
y'(x) = f(y(x))y”(x)= f(y(x))
y'(x) = f(y(x))*xy”(x)= f(y(x))* x
y'(x) = g(x)*y(x)y”(x)= g(x)性感(x)
y'(x) = g(x)*y(x)+h(x)y”(x)= g(x)性感(x)+ h(x)
on one step. 在一个步骤。Notice that y'(x) must be alone on the left hand side of the equation. 注意到y”(x)必须独自在左手边的方程。It is recommended to set the switch expand:=on when solving the complicated differential equations.建议设置开关扩大:=当解决这个复杂微分方程组。
Example:例如:
Solve y'(x) = sin(x) by dsolve().解决y”(x)=罪(x)dsolve()。
IN:在: dsolve( y'(x) = sin(x), y(x), x)dsolve(y”(x)=罪(x),y(x)、x)
OUT: y(x) = constant - cos(x)出:y(x)=持续不断的——因为(x)
Example:例如:
Solve differential equations by dsolve(). 通过求解微分方程dsolve()。If the result is a polynomial, then rearrange the equation by solve().如果结果是一个多项式,然后重新排列方程解决()。
IN:在: dsolve(y'(x) = x/(2+y(x)), y(x), x)dsolve(y”(x)= x /(2 + y(x)),y(x)、x)
OUT: 2*y(x) + 1/2*y(x)^2 = constant + x^2出:2 * y(x)+ 1/2性感(x)^ ^ 2 =不断+ x 2
IN:在: solve(last, y(x))解决(最后,y(x))
OUT: y(x) = [-2 + sqrt(4 - 2*(-constant - x^2)),出:y(x)=[2 + sqrt(4 - 2 *(-constant - x ^ 2)),
-2 - sqrt(4 - 2*(-constant - x^2))]sqrt 2 -(4 - 2 *(-constant - x ^ 2))
Example:例如:
Solve differential equations by dsolve().通过求解微分方程dsolve()。
IN:在: dsolve(y'(x) = x*exp(y(x)), y(x), x)dsolve(y”(x)= x *经验(y(x)),y(x)、x)
OUT: -e^(-y(x)) = constant + x^2出:. ^(可能的(x))+ x ^ 2 =不变
IN:在: dsolve(y'(x) = y(x)^2+5*y(x)+6, y(x), x)dsolve(y”(x)= y(x)^ 2 + 5性感(x)+ 6,y(x)、x)
OUT: ln((4 + 2 y(x))/(6 + 2 y(x))) = constant + x出:淋巴结(4 + 2 y(x))/(6 + 2 y(x))=不断+ x
IN:在: dsolve(y'(x) = y(x)/x, y(x), x)dsolve(y”(x)= y(x)/ x,y(x)、x)
OUT: y(x) = constant x sign(x)出:y(x)=不断x签署(x)
IN:在: dsolve(y'(x) = x + y(x), y(x), x)dsolve(y”(x)= x + y(x),y(x)、x)
OUT: y(x) = -1 - x + constant*e^x出:y(x)= 1 - x + e ^不断* x
You can compute partial, finite or infinite sums and products. 你可以计算部分,有限的或无限的金额和产品。Sums and products can be differentiated and integrated. 金额和产品可分化和综合。You construct functions like Taylor polynomials or finite Fourier series. 你喜欢泰勒多项式函数或构建有限傅立叶级数。The procedure is the same for sums as products so all examples will be restricted to sums.程序是相同的,所以所有款项作为产品的例子将会限制在总结。 The general formats for these functions are:一般格式为这些功能有:
sum(expr, x from xmin to xmax)钱,从x xmin expr对xmax)
sum(expr, x from xmin to xmax step dx)钱,从x xmin expr xmax一步,dx)
prod(expr, x from xmin to xmax)促进(expr,从x xmin到xmax)
prod(expr, x from xmin to xmax step dx)促进(expr,从x xmin xmax一步,dx)
The expression expr is evaluated at xmin, xmin+dx, ...表达是xmin expr的评估,xmin + dx,… up to the last entry in the series not greater than xmax, and the resulting values are added or multiplied.到最后条目不能大于xmax系列,产生的价值观是添加或成倍增加。 The part "step dx" is optional and defaults to 1.部分“步dx”是可选择的而且默认1。 The values of xmin, xmax and dx can be any real number.xmin的价值,xmax和dx可以是任何的实数。
Here are some examples:这里是一些例子:
sum(j, j from 1 to 10)和(j,j从1到10)
for 1 + 2 + .. 1 + 2 +…+ 10.+ 10。
sum(3^j, j from 0 to 10 step 2)金额(3 ^ j,j从0到10第二步)
for 1 + 3^2 + ... 1 + 3 ^ 2 +…+ 3^10.10 + 3 ^。
Here are some sample Taylor polynomials:这里有一些样品泰勒多项式:
sum(x^j/j!(x ^总和j / j !, j from 0 to n)[j].从0到n)
for exp(x).为实验(x)。
sum((-1)^j*x^(2*j+1)/(2*j+1)!(1)和(x ^ ^ j *(2 * m + 1)/(2 * m + 1)!, j from 0 to n)[j].从0到n)
for sin(x) of degree 2*n+2.罪(x)的程度2 * n + 2。
Remember, the 3 keywords (from, to and step) can be replaced by the comma ,.记住,三个关键词(从与措施)可以被逗号。
The function功能
partsum(f(x),x)partsum(f(x)、x)
finds the partial sum (symbolic sum).发现部分和(象征性金额)。
Example:例如:
Find the sum of 1^2 + 2^2 ... 找到的总和^ 1 ^ 2 + 2 2…+ n^2.+ n ^ 2。
IN:在: partsum(n^2, n)partsum(n ^ 2 n)
OUT: 1/6 n (1 + n) (1 + 2 n)出:1/6 n(1 + n)(1 + 2 n)
The function功能
infsum(f(x), x)infsum(f(x)、x)
finds the infinite sum, i.e. sum(f(x), x from 0 to inf).发现无限和,即和(f(x)、x从0到无穷大)。
Example:例如:
IN:在: infsum(1/n!infsum(1 / n !, n),n)
OUT: e出:呃
The external functions外部功能
series(f(x), x)系列(f(x)、x)
series(f(x), x, order)系列(f(x)、x、顺序)
to find the Taylor series at x=0. 找到泰勒级数在x = 0。The argument (order) is optional and defaults to 5.的论点(顺序)是可选的,默认为5。
Example:例如:
Find the power series expansion for cos(x) at x=0.发现幂级数增长因为(x)在x = 0。
IN:在: series(cos(x), x)系列(因为(x)、x)
OUT: 1 - 1/2 x^2 + 1/24 x^4出:1 - 1/2 x ^ ^ 4×2 + 1/24
The series expansion of f(x) is useful for numeric calculation of f(x). 本系列扩展f(x)是有效的数值计算f(x)。If you can provide derivative of any function of f(x) and f(0), even though f(x) is unknown, you may be able to calculate the function value at any x, by series expansion. 如果您能提供任何函数的导数,f(x)和己(0),即使f(x)是未知的,你可以计算函数值的大小在任何x,级数展开。Accuracy of calculation depends on the order of series expansion. 计算的准确性取决于级数展开的顺序。Higher order, more accuracy, but longer calculation time.高阶、更准确,但计算时间长。
Example:例如:
calculate f(1), knowing f'(x)=-sin(x) and f(0)=1, where f(x) is unknown.计算f(1),知道f(x)= -sin”和f(x)= 1(0),在f(x)是未知的。
IN:在: f'(x_) := -sin(x)“(x_):f(x)= -sin
IN:在: f(0) := 1f(0):= 1
IN:在: f(x_) := eval(series(f(x), x))f(x_):=:(系列(f(x)、x)) # must eval()必须():
OUT: f(x_) := 1 - 1/2 x^2 + 1/24 x^4出:f(x_):= 1 - 1/2 x ^ ^ 4×2 + 1/24
IN:在: f(1)外(1)
OUT: 13/24出:13/24
Polynomials are automatically sorted in order from low to high.自动分类为多项式从低到高。
You can pick up one of coefficient of x in polynomials by你可以选择一个x在多项式系数
coef(poly, x^n)系数(聚、x ^ n)
e.g.例句。
IN:在: coef(x^2+5*x+6, x)系数(x ^ 2 + 5 * x + 6,x)
OUT: 5出:5
Note that you cannot pick up the coefficient of x^0 by coef(y,x^0).注意,你不能拿起系数x ^ 0系数(y,x ^ 0)。
You can pick up one of coefficient of x in polynomials with order < 5 by你可以选择一个系数多项式与秩序x的< 5
coef(poly, x,n)系数(聚,x,n)
e.g.例句。
IN:在: coef(x^2+5*x+6, x,0)系数(x ^ 2 + 5 * x + 6,x,0)
OUT: 6出:6
You can pick up all of coefficients of x in polynomials with order < 5 by你可以选择所有的系数多项式与秩序x的< 5
coefall(poly, x)coefall(聚、x)
e.g.例句。
IN:在: coefall(x^2+5*x+6, x)coefall(x ^ 2 + 5 * x + 6,x)
OUT: [6, 5, 1]出:[6、5,1] # 6 + 5*x + x^26 # + 5 * x + x ^ 2
IN:在: coefall(a*x^2+b*x+c, x)coefall(x ^ 2 + b * * x + c,x)
OUT: [c, b, a]出:[c、b,) # symbolic values of coefficients#符号价值系数
You can pick up the highest order of x in polynomials with order < 5 by你可以选择最高的秩序为x的多项式与< 5
order(poly, x)订单(聚、x)
e.g.例句。
IN:在: order(x^2+5*x+6, x)订单(x ^ 2 + 5 * x + 6,x)
OUT: 2出:2
You can factor polynomials in order < 5 with respect to x by你可以为因素多项式< 5就x
factor(poly, x)因子(多边形,x)
e.g.例句。
IN:在: factor(x^2+5*x+6, x)因子(x ^ 2 + 5 * x + 6,x)
OUT: (2 + x) (3 + x)出:(2 + x)(3 + x)
You can construct lists and arrays of arbitrary length, and the entries in the lists and arrays can be of any type of value whatsoever: constants, expressions with undefined variables, or equations.可以构建清单和任意长度的数组,数组列表条目,可以是任何类型的价值无论:常数,与未定义的变量表达式或方程。
A vector or matrix can be represented by a list or array. 一个向量和矩阵可以表示为一个列表或阵列。In a matrix, the number of elements in each row should be the same, e.g. [[a11, a12], [a21, a22]].在一个母体中,大量的元素在每一行应当是相同的,例如。[[a11,a12]、[,38,a22]]。
You can define a list by putting its elements between two square brackets. 你可以定义一个列表把它的元素在两个方括号。e.g. [1,2,3]例句。[1、2、3)
You can define lists another way, with the command:你可以定义列表另一种方式,该命令:
[ list(f(x), x from xmin to xmax step dx) ][列表(f(x),从x xmin xmax一步,dx)
This is similar to the sum command,这是类似于金额的命令, but the result is a list:但结果是一个列表:
[f(xmin), f(xmin+dx), ...(f(xmin),f(xmin + dx),…, f(xmin+x*dx), ...]f(xmin + x * dx),…)
which continues until the last value of xmin + x*dx持续到最后的价值xmin + x * dx吗 <= xmax.xmax < =。
You also can assign the list to a variable, which variable name become the list name:你也可以指定一个变量的名单,名单上的名字成为变量的名字:
a := [1,2,3]答:=[1、2、3) # define the list of a定义列表的号
b := [f(2), g(1), h(1)]乙:=[外(2),g(1),h(1) # assumes f,g,h defined#承担f,g、h定义
c := [[1,2],3,[4,5]]顾客:=[[1,2],3,[4、5]] # define the list of c#定义的名单c
Lists are another kind of value in SymbMath, and they can be assigned to variables just like simple values. 列表是一个SymbMath另一种价值,他们可以被指定给变量就像简单的值。(Since variables in SymbMath language are untyped, you can assign any value to any variable.).(因为untyped SymbMath语言变量,你可以指定任何价值任何变量)。
A function can have a list for its value:一个函数可以拥有一张价值:
f(x_) := [sqrt(x), -sqrt(x)]f(x_):=[sqrt(x),-sqrt(x))
e.g.例句。
IN:在: squreroot(x_) := [sqrt(x), -sqrt(x)]squreroot(x_):=[sqrt(x),-sqrt(x))
IN:在: squreroot(4)squreroot(4)
OUT: [2, -2]出:[1,2]
A function can have a list for its argument:一个函数可以有它的参数列表:
abs([-1,2])abs([1,2])
Try试着
a := [ list(j^2, j from 0 to 10 step 1) ]答:=[列表(m ^ 2、j从0到10个步骤1)
f(x_) := [ list(x^j, j from 0 to 6 step 1) ]f(x_):=[列表(x ^ j,j从0到6步骤1)
b := f(-2)乙:= f(2)
You can find the value of the j-th member in a list by你能找到j-th成员的值在一个列表
member([a,b], j)会员(会员(a,b),j)
The first member of a list is always member(x, 1).第一届会员总是成员名单(x,1)。
If you have assigned a list to a variable x, you can access the j-th element by the list index x[j]. 如果你有分配给一个变量x的一个列表,您可以访问列表的元件,j-th指数x[j].The first element of x is always第一个元素的x是永远 x[1].x[1]。 If the x[j] itself is a list, then its j-th element is accessed by repeating the similar step.如果x[j]本身就是一个名单,那么它的j-th元素是通过重复类似的步骤。But you can not use the list index unless the list is already assigned to x.但是你不能使用,除非清单列表索引已分配给x。
e.g.例句。
IN:在: x := [[1,2],3,[4,5]]谢:=[[1,2],3,[4、5]] # define the x list定义x名单。#
IN:在: x[1], x[2]x[1]、[2]x # take its first and 2nd element#取其第一和2nd元素
OUT: [1, 2], 3出:[1,2],3
IN:在: xx # access the entire list of x#访问的整个目录x
OUT: [[1, 2], 3, [4,5]]出:[[1,2],3,[4、5]]
IN:在: member(x, 2)会员(x,2) # same as x[2]# x[2]一样
OUT: 3出:3
An entire sub-list of a list x整个sub-list名单x can be accessed with the command x[j], which is the list:该命令可以被存取x[j],这是列表:
[x[j], x[j+1], ... [j],[x x[j + 1],……]]
The subs() replaces the value of the element in the list, as in the variables. 潜艇()代替了价值的元素在列表,如在变量。e.g.例句。
IN:在: subs([a,b,c], a = a0)替补([a、b、c)之后,一个= a0)
OUT: [a0, b, c]出:[a0,b,c)
Note that you cannot modify lists by assignment.注意,你不能修改列表通过转让。
Lists can be added, subtracted, multiplied, and divided by other lists or by constants.名单可以补充道,扣、增多,其他的名单或除以常量。 When two lists are combined, they are combined term-by-term, and the combination stops when the shortest list is exhausted.当两个列表是结合之后,他们term-by-term相结合,会在最短的列表结合款子已提清。 When a scalar is combined with a list, it is combined with each element of the list.当一个标量结合一个列表,结合每个元素的列表。 Try:试一试:
a := [1,2,3]答:=[1、2、3)
b := [4,5,6]乙:=[4、5、6)
a + b+ b
a / ba / b
3 * a3 *
b - 4b - 4
Example 4.9.2.4.1.4.9.2.4.1例子。
Two lists are added.两个列表是补充说。
IN:在: [a1,a2,a3] + [b1,b2,b3][a1、a2、a3]+[b1、b2、b3)
OUT: [a1 + b1, a2 + b2, a3 + b3]出:[a1,a2 + + b1,b2 a3 + b3)
IN:在: last[1]最后一个[1]
OUT: a1 + b1出:a1 + b1
If L is a list, then如果我是一个清单,然后 f(L) results in a list of the values, even though f() is the differentiation or integration function (d() or inte()).f(L)会导致一连串的价值,即使f()或整合功能分化(d()或交互()。
IN:在: sqrt([a, b, c])sqrt([a、b、c])
OUT: [sqrt(a), sqrt(b), sqrt(c)]出:[sqrt(a)、sqrt(b),sqrt(c))
IN:在: d([x, x^2, x^3], x)d((x ^ 2、x、x ^ 3]、x)
OUT: [1, 2*x, 3*x^2]出:[1、2、3 * * * x ^ 2]
If you use a list as the value of a variable in a function, SymbMath will try to use the list in the calculation.如果你使用一个列表,作为一个变量的价值功能,SymbMath将试图把这张清单的计算。
You can sum all the elements in a list x by你只能全额的所有元素。在一个列表x
listsum(x)listsum(x)
Example:例如:
IN:在: listsum([a,b,c]^2)listsum([a、b、c]^ 2)
OUT: a^2 + b^2 + c^2:一个^ ^ 2 + 2 + b c ^ 2
This function takes the sum of the squares of all the elements in the list x.这个函数之和的广场的所有元素列表x。
You can do other statistical operations (see Section 4.10. 你可以做其它的统计操作(请参见第4.10节。Statistics) on the list, or plot the list of numeric data (see Section 5. 统计)在列表上,或者情节的名单(见第5节数字数据。Plot).情节)。
You can find the length of a list (the number of elements in a list) with:你能找到一个列表的长度(所包含的元素数量在一个列表):
length(a)长度(a)
You can define an array of a by assigning its element value into its index:你可以定义一个数组的元素值,在通过赋值指标:
a[1]:=1一个[1]:= 1
a[2]:=4一个[2]:= 4
or you can define arrays another way, with the command:或者你可以定义数组的另一种方式,该命令:
do(a[x]:=f(x), x from xmin to xmax step dx)做一个[x]:= f(x),从x xmin xmax一步,dx)
e.g.例句。
do(a[j] := 2*j, j from 1 to 2)做一个[j]:[j]. = 2 * j从1到2)
You can define 2-dimentional array by你可以定义2-dimentional阵列
a[1,1]:=11一个[- 1,1]:= 11
a[1,2]:=12一个[1,2]:= 12
a[2,1]:=21一个(2,1]:= 21
a[2,2]:=22一个[2,2]:= 22
or或
do(do(a[j,k]:=j+k, j,jmin,jmax,dj), k,kmin,kmax,dk)(做一个[j、k]:= j + k,j,jmin,dj,jmax)、钾、kmin,kmax,骑士)
After defining an array of a, you can access one of its element by its index以一个数组的形式返回一个定义,你可以访问它的一个元件,其指标
IN:在: a[1]一个[1]
OUT: 1出:1 .
You also can list out all of its elements by你也可以列出所有的要素
list(a[j], j,1,2,1)列表(一个[j],j,第1、2、1)
e.g.例句。
IN:在: do(a[j]:=2*j, j,1,2,1)做一个[j]:= 2 * j,j,第1、2、1)
IN:在: list(a[j], j,1,2)列表(一个[j],j,1,2)
OUT: 1, 4出:1、4
You can modify an array by assigning new value into its index你能修改数组通过指定新的价值转化为指标
IN:在: a[1]:=2一个[1]:= 2
e.g.例句。
after defining 2 arrays a and b, find their dot time, a .2数组定义a和b,找出他们的点时间,一个。* b.* b。
IN:在: a[1]:=1, a[2]:=2一个[1]:= 1,一个[2]:= 2 # define array a#定义一个数组
IN:在: b[1]:=11, b[2]:=12b(1):= 11,b[2]:= 12 # define array b#定义数组b
IN:在: p:=0警:= 0
IN:在: do(p:=p + a[j]*b[j], j,1,2,1)(鲍西娅:= p +一个[j]. * b[j],j,第1、2、1) # a .#。* b* b
You can uses arrays or lists to represent vectors, and lists of lists to represent matrices.你可以使用数组或列表来代表向量,并列举的列表来代表矩阵。
Vectors and matrices can be operated by "+" and "-" with vectors and matrixes, by "*" and "/" with a scalar, and by diff() and inte(). 向量和矩阵可以经营以“+”和“-”与向量和矩阵,以“*”和“/”与一个标量,和强烈的差别()和()。These operations are on each element, as in lists.这些操作都在每个元素,就像在列表。
You can use lists as vectors, adding them and multiplying them by scalars. 你可以使用,列出矢量,增加他们的多元化他们标量。For example, the dot product of two vectors of a and b is:例如,两个向量积的a、b是:
sum(a[j]*b[j], j from 1 to jmax)和一个[j]. * b[j],j从1到jmax)
You can even make this into a function:你甚至可以使这成为一个功能:
dottime(x_, y_) := listsum(x*y)dottime(x_,y_):= listsum(x性感)
e.g.例句。
represent the dot product of two vectors by arrays代表了两个向量的数量积的数组
IN:在: a[1]:=1, a[2]:=2一个[1]:= 1,一个[2]:= 2 # define array a#定义一个数组
IN:在: b[1]:=11, b[2]:=12b(1):= 11,b[2]:= 12 # define array b#定义数组b
IN:在: p:=0警:= 0
IN:在: do(p:=p + a[j]*b[j], j,1,2,1)(鲍西娅:= p +一个[j]. * b[j],j,第1、2、1) # a .#。* b* b
represent the dot product of two vectors by lists代表点两个向量的产品列表
IN:在: dottime([1,2], [11,12])dottime([1,2],[11、12]) # by lists in function dottime()通过列表功能dottime号()
How about the cross product:十字架如何产品:
cross(a,b) = [a[2]*b[3]-b[2]*a[3],a[3]*b[1]-b[3]*a[1],a[1]*b[2]-b[1]*a[2]]飞越(a,b)=[[2][3]-b b * *[2][3],一个[3]* b[1][3]-b *[1],一个[1][2]* b * -b[1][2]]
Some statistical functions are:一些统计功能有:
average(x), max(x), min(x), listsum(x), length(x)平均(x)马克斯(x)、最小(x),listsum(x),长度(x)
A list of numbers can be calculation on statistics.一串数字的计算可以统计。
Example:例如:
IN:在: p := [1, 2, 3]警:=[1、2、3)
IN:在: average(p), max(p), min(p), length(p)平均水平(p),马克斯(p)、最小(p)、长度(p)
OUT: 2, 3, 1, 3出:2、3、1、3
Not only a list of number but also a list of symbolic data can be operated by some statistic functions to show how to do the statistic operation.不仅是一个列表的列表的号码,但也具有象征意义的数据可以操作的一些统计功能,说明统计操作。
IN:在: p := [a, b, c]警:=[a、b、c)
IN:在: average(p)平均(p)
OUT: 1/3*(a + b + c)出:1/3 * a + b + c)
IN:在: listsum(p)listsum(p)
OUT: a + b + c:一个+ b + c
IN:在: length(p)长度(p)
OUT: 3出:3
If you want to look at a table of values for a formula, you can use the table command:如果你想看看表值的一种模式,你可以用桌子的命令:
table(f(x), x)表(f(x)、x)
table(f(x), x from xmin to xmax)表(f(x),从x xmin到xmax)
table(f(x), x from xmin to xmax step dx)表(f(x),从x xmin xmax一步,dx)
It causes a table of values for f(x) to be displayed with x=xmin, xmin+dx, ...它导致了一个价值表f(x),以显示x = xmin,xmin + dx,…, xmax.,xmax。 If xmin, xmax, and step omit, then xmin=-5, xmax=5, and dx=1 for default. 如果xmin,xmax,步骤省略,然后xmin = 5,xmax = 5,dx = 1为默认值。You can specify a function to be in table(),你可以指定一个功能表(),
Example:例如:
Make a table of x^2.做一张桌子,x ^ 2。
IN:在: table(x^2, x)表(x ^ 2、x)
OUT:出去。
-5,5, 2525
-4,4, 1616
-3,3, 99
-2,2, 44
: :
: :
Its output can be written into a disk file for interfacing with other software (e.g. the numeric computation software).其输出可以写进一个磁盘文件与其它的软件接口(如数值计算软件)。
Different types of data may be converted each other.不同类型的数据可以被转换彼此。
The complex number is converted to the real number by复杂的号码是转化为实际数字
re(z), im(z), abs(z), arg(z), sign(z)稀土(z),我(z)、abs(z)、高温(z)、标志(z)
The real number is converted to the integer number by实际数字转换为整数数字
trunc(x)trunc(x)
round(x)圆(x)
The real number is converted to the rational number by实际数字转化为有理数
ratio(x)比(x)
The rational number is converted to the real number by有理数转化为实际数字
num(x)胡(x)
numeric:=on数字:=在
The rational number is converted to the integer number by有理数转换为整数数字
nume(x)nume(x)
deno(x)deno(x)
The string is converted to the real number if possible, by这个字符串转换为实际数字,如果可能
number("123")数字(“123”)
You can convert sum to a list of terms by您可以转换和术语的列表
term(a+b)术语a + b)
IN:在: term(a+b)术语a + b)
OUT: [a, b]出:[a,b)
You can convert product to a list of multipliers by您可以转换产品名单乘数
mult(a*b)mult(* b)
IN:在: mult(a*b)mult(* b)
OUT: [a, b]出:[a,b)
You can convert an array x to a list by你可以转换成一个数组列表x
[ list(x[j], j,1,jmax,1) ][列表(x[j],j,1、jmax,1)
You can convert numbers to strings by您可以转换数字字符串
string(123)字符串(123)
IN:在: string(123)字符串(123)
OUT: "123"出:“123”
A list of real numbers can be converted to a table by真正的数字列表可以转化成一个表
table()表()
Example:例如:
IN:在: x := [5,4,3,2,1]谢:=[5、4、3、2、1]
IN:在: table(x[j], j from 1 to 4 step 1)表(x,j[j]. 1至4步骤1)
OUT:出去。
1,1, 55
2,2, 44
3,3, 33
4,4, 22
You can get type of data by你可以使用的一种数据类型
type(x)类型(x)
IN:在: type(2)类型(2)
OUT: "integer"出:“整数”
You also can get operators by你也能得到运营商
type(x)类型(x)
IN:在: type(a>b)(a > b)型
OUT: ">"出:“>”
IN:在: type(sin(x))型(罪(x))
OUT: "sin()"出:“罪()”
The functions功能
left(x=a), left(a > b)左(x =),左(一个> b)
right(x=a), right(a > b)正确的(x =),右(a > b)
pick up the left- and right- side of the equation and inequality.捡起左和右- - - - - - - - - - - -等式两边的和不平等现象。
IN:在: left(a>b), right(a>b)左(一个> b),右(> b)
OUT: a, b出:a、b
You can get the j-th term of sum by你能得到的j-th学期之
member(term(a+b), j)会员(术语a + b),j)
IN:在: member(term(a+b), 1)会员(术语a + b),1)
OUT: a:一个
You can get the arguments of a function by你可以得到���个函数的参数
argue(f(x))认为(f(x))
IN:在: argue(sin(x))认为(罪(x))
OUT: x出:x
A coefficient of x^n in an expression can be picked up by系数x ^ n在一个表达式可以捡起
coef(p, x^n)系数(p、x ^ n)
e.g.例句。
IN:在: coef(a + b*x + c*x^2 + d*x^3, x)系数a + b * x + c * * ^ * x ^ 2 + d 3、x)
OUT: b指出:b
You can get a coefficient of x^n (where 0<= n < 4) in polynomials ordered up to 4 by你会得到一个系数x ^ n(其中0 < = n < 4)命令4个多项式
coef(poly, x,n)系数(聚,x,n)
(see Chapter Polynomials for detail).(见章节多项式细节)。
After you create a database file as a library (external function), you can search your data by finding its function value.在你创建一个数据库文件作为一个图书馆(外部功能,您可以搜索您的数据通过找到它的功能价值。
If you have created the database file "phoneNo.如果你创建了“phoneNo数据库文件。li" as follow:李”如下:
-------------------------------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
phoneno("huang") := "6974643"phoneno(“璜”):= " 6974643 "
phoneno("john")phoneno(“约翰”) := "12345":= " 12345 "
--------------------------------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
You can find out phone No. 你可以找到电话号码。of someone from the phone No. 从电话号码的人。database file "phoneNo.“phoneNo数据库文件。li" by the external function李”由外在功能
phoneno("name")phoneno(“名字”)
Example:例如:
find out phone No. 找到电话号码。of huang.黄的。
IN:在: phoneno("huang")phoneno(“黄”)
OUT: 6974643出:6974643
You can search atomic weight of chemical element from the database file "atom_wei.li".您可以搜索您的化学元素原子的重量从数据库文件”atom_wei.li”。
e.g.例句。
What is atomic weight of chemical element H ?什么是化学元素H原子的重量吗?
IN:在: atom_wei(H)atom_wei(H)
OUT: 1出:1 .
You can predict products for chemical reactions from the database file "react.li".你能预测产品从数据库文件的化学反应”react.li”。
Example 4.14.2.4.14.2例子。
What are the products when HCl + NaOH react ?什么是产品当盐酸+氢氧化钠反应?
IN:在: react(HCl+NaOH)反应(盐酸+氢氧化钠)
OUT: H2O + NaCl出:H2O +盐
One of the most important feature of SymbMath is its ability to deduce and expand its knowledge. 其中一个最重要的特征就是它能SymbMath演绎并扩大自己的知识。If you provide it with the necessary facts, SymbMath can solve many problems which were unable to be solved before. 如果你为其提供必要的事实,SymbMath可以解决许多问题无法解决过的。The followings are several ways in which SymbMath is able to learn from your input.以下几种方法,SymbMath是能够学习,从你的投入。
Finding derivatives is much easier than finding integrals. 衍生工具是更加容易的找到比找到积分。Therefore, you can find the integrals of a function from the derivative of that function.因此,你可以在网上找到的一个函数的积分及衍生的功能。
If you provide the derivative of a known or unknown function, SymbMath can deduce the indefinite and definite integrals of that function. 如果你提供的衍生已知的或未知的功能,SymbMath就可以推断出不确定性和积分的功能,明确。If the function is not a simple function, you only need to provide the derivative of its simple function. 若功能并不是一个简单的函数,你只需要提供的衍生物,它简单的功能。For example, you want to evaluate the integral of f(a*x+b), you only need to provide f'(x).例如,你想要评价积分f(* x + b),你只需要提供f '(x)。
If you know a derivative of an function f(x) (where f(x) is a known or unknown function), SymbMath can learn the integrals of that function from its derivative.如果你知道一个衍生的一个函数f(x)(在f(x)是一个已知或未知函数),SymbMath能学会了那个函数的积分从它的衍生工具。
Example:例如:
check SymbMath whether or not it had already known integral of f(x)SymbMath检查是否已经知道积分的f(x)
IN:在: inte(f(x), x)希尔(f(x)、x)
OUT: inte(f(x), x)出:强烈的(f(x)、x)
IN:在: inte(f(x), x, 1, 2)希尔(f(x)、x、1,2)
OUT: inte(f(x), x, 1, 2)出:强烈的(f(x)、x、1,2)
As the output displayed only what was typed in the input without any computed results, imply that SymbMath has no knowledge of the indefinite and definite integrals of the functions in question. 作为输出显示稿子只有在输入没有任何的计算结果,暗示SymbMath没有知识的不确定性和明确的函数积分的问题。Now you teach SymbMath the derivative of f(x) on the first line, and then run the program again.现在你教SymbMath导数,f(x)在第一排,然后运行节目了。
IN:在: f'(x_) := exp(x)/xf '(x_):=经验/ x(x)
IN:在: inte(f(x), x)希尔(f(x)、x)
OUT: x*f(x) - e^x出:* * f(x)- e ^ x
IN:在: inte(f(x), x, 1, 2)希尔(f(x)、x、1,2)
OUT: e - f(1) + 2*f(2) - e^2出:e - f(1)+ 2 *外(2)- e ^ 2
As demonstrated, you only supplied the derivative of the function, and in exchange SymbMath logically deduced its integral.示范,你只供衍生的功能,并在交换SymbMath整体逻辑演绎。
Another example is另一个例子是
IN:在: f'(x_) := 1/sqrt(1-x^2)f '(x_):= 1 / sqrt(1-x ^ 2)
IN:在: inte(f(x), x)希尔(f(x)、x)
OUT: sqrt(1 - x^2) + x*f(x)出:sqrt(1 - x ^ 2)+ x * f(x)
IN:在: inte(k*f(a*x+b), x)希尔(k * f(* x + b),x)
OUT: k*(sqrt(1 - (b + a*x)^2) + (b + a*x)*f(b + a*x))/a出:阿k *(sqrt(1 -(b +一* x)^ 2)+(b +一* x)* f(b +一* x))
IN:在: inte(x*f(a*x^2+b), x)强烈的(x * f(x ^ * 2 + b),x)
OUT: sqrt(1-(a*x^2 + b)^2) + (a*x^2 + b)*f(a*x^2 + b)出:sqrt(1 -(* x ^ 2 + b)^ 2)+(* x ^ 2 + b)* f(x ^ * 2 + b)
The derivative of the function that you supplied can be another derivative or integral.导数,贵公司所提供的功能可以是另一个衍生著作或构成一个整体。
Example:例如:
IN:在: f'(x_) := eval(inte(cos(x),x))f '(x_):=:(交互(因为(x)、x))
OUT: f'(x_) := sin(x)出:f '(x_):=罪(x)
IN:在: inte(f(x), x)希尔(f(x)、x)
OUT: -sin(x)出:-sin(x)
IN:在: inte(f(a*x + b), x)希尔(f(* x + b),x)
OUT: -sin(b + a*x)/a出:-sin(b +一* x)/
IN:在: inte(x*f(x), x)强烈的(* * f(x)、x)
OUT: -cos(x) - x*sin(x)出:-cos(x)- x *罪(x)
IN:在: inte(x^1.5*f(x), x)强烈的(x ^ 1.5 * f(x)、x)
OUT: 1.5*inte(sqrt(x)*sin(x), x) - x^1.5*sin(x)出:1.5 *交互(sqrt(x)*罪(x)、x)- x ^ 1.5 *罪(x)
IN:在: inte(x^2*f(x), x)强烈的(x ^ 2 * f(x)、x)
OUT: -2*x*cos(x) + 2*sin(x) - x^2*sin(x)出:2 * * *因为(x)+ 2 *罪(x)- x ^ 2 *罪(x)
IN:在: inte(x*f(x^2), x)强烈的(* * f(x ^ 2)、x)
OUT: -sin(x^2)出:-sin(x ^ 2)
IN:在: inte(x^3*f(x^2), x)强烈的(x ^ 3 * f(x ^ 2)、x)
OUT: -0.5*cos(x^2) - 0.5*x^2*sin(x^2)出:-0.5 *因为(x ^ 2)- 0.5 * x ^ 2 *罪(x ^ 2)
IN:在: inte(f(x)/(x^1.5), x)希尔(f(x)/(x ^ 1.5)、x)
OUT: -2/sqrt(x)*f(x) + 2*inte(sin(x)/sqrt(x), x)出:2 / sqrt(x)* f(x)+ 2 *交互(罪(x)/ sqrt(x)、x)
IN:在: inte(f(x)/(x^2), x)希尔(f(x)/(x ^ 2)、x)
OUT: -f(x)/x + si(x)出:发送(x)/ x + si(x)
You supply a simple indefinite integral, and in return, SymbMath will perform the related complicated integrals.你提供一个简单的不定积分,作为回报,SymbMath将履行相关的复杂积分。
Example:例如:
Check whether SymbMath has already known the following integrals or not.检查是否SymbMath已经知道下面的积分。
IN:在: inte(f(x), x)希尔(f(x)、x)
OUT: inte(f(x), x)出:强烈的(f(x)、x)
IN:在: inte((2*f(x)+x), x)希尔(2 * f(x)+ x)、x)
OUT: inte((2*f(x)+x), x)出:强烈的(2 * f(x)+ x)、x)
IN:在: inte(inte(f(x)+y), x), y)希尔(交互(f(x + y)、x、y)
OUT: inte(inte(f(x)+y), x), y)出:强烈的(交互(f(x + y)、x、y)
Supply, like in the previous examples, the information: integral of f(x) is f(x) - x; then ask the indefinite integral of 2*f(x)+x, and a double indefinite integral of 2*f(x) + x, and a double indefinite integral of respect to both x and y. Change the first line, and then run the program again.供应,跟过去的例子,信息:整体的f(x)是f(x)- x,然后问的不定积分2 * f(x)+ x,双不定积分的2 * f(x)+ x,对双不定积分两个x和y。改变第一线,然后运行节目了。
IN:在: inte(f(x_), x_) := f(x) - x希尔(f(x_),x_):= f(x)- x
IN:在: inte(2*f(x)+x, x)希尔(2 * f(x)+ x、x)
OUT: 2*f(x) - 2*x + 1/2*x^2出:2 * f(x)- 2 * x + 1/2 * x ^ 2
IN:在: inte(inte(f(x)+y, x), y)希尔(交互(f(x + y,x,y)
OUT: f(x)*y - x*y + x*y^2出:f(x)性感- x性感+ x性感^ 2
You can also ask SymbMath to perform the following integrals:你还可以请求SymbMath履行下列积分。
inte(inte(f(x)+y^2, x), y),希尔(交互(f(x + y ^ 2、x,y),
inte(inte(f(x)*y, x), y),希尔(交互(f(x)性感,x),y),
inte(x*f(x), x),强烈的(* * f(x)、x),
triple integral of f(x)-y+z, or others.三重积分的f(x)消息+ z和其他项目。
You continue to ask indefinite integral.你继续问不定积分。
IN:在: inte(inte(f(x)+y, x from 0 to 1), y from 0 to 2)希尔(交互(f(x + y,x从0到1),y从0到2)
OUT: 2 f(1)出:2 f(1)
SymbMath can learn complicated derivatives from a simple derivative, even though the function to be differentiated is an unknown function, instead of standard function.SymbMath可以学习复杂的衍生工具已从一个简单的衍生,虽然功能分化是一种未知函数,而不是标准功能。
Example :例如:
Differentiate f(x^2)^6, where f(x) is an unknown function.区分f(x ^ 2)^ 6,在f(x)是一个未知的功能。
IN:在: d(f(x^2)^6, x)d(f(x ^ 2)^ 6,x)
OUT: 12 x f(x^2)^5 f'(x^2)出:12倍f(x ^ 2)^ 5 f '(x ^ 2)
Output is only the part derivative. 输出只有部分衍生工具。f'(x^2) in the output suggest that you should teach SymbMath f'(x_). f '(x ^ 2)在输出建议你应该教SymbMath f '(x_)。e.g. the derivative of f(x) is another unknown function df(x), i.e. f'(x_) = df(x), assign f'(x_) with df(x) and run it again.例如导数,f(x)是另一个未知函数df(x),即f '(x_)= df(x),分配f '(x_)与df(x)并运行它了。
IN:在: f'(x_) := df(x)f '(x_):= df(x)
IN:在: d(f(x^2)^6, x)d(f(x ^ 2)^ 6,x)
OUT: 12 x f(x^2)^5 df(x^2)出:12倍f(x ^ 2)^ 5 df(x ^ 2)
This time you get the complete derivative.这回你得到完整的衍生工具。
If you show SymbMath algebra, SymbMath can learn integrals from that algebra.如果你表现出SymbMath代数、SymbMath积分,可以学习代数。
Example :例如:
Input f(x)^2=1/2-1/2*cos(2*x), then ask for the integral of f(x)^2.输入f(x)^ 2 = 1/2-1/2 *因为(2 * x),然后请求积分的f(x)^ 2。
IN:在: f(x)^2 := 1/2-1/2*cos(2*x)f(x)^ 2 = 1/2-1/2 *因为(2 * x)
IN:在: inte(f(x)^2, x)希尔(f(x)^ 2、x)
OUT: 1/2 x - 1/4 sin(2 x)出:1/2 x - 1/4罪(2 x)
SymbMath is very flexible. SymbMath非常灵活。It learned to solve these problems, even though the types of problems are different, e.g. learning integrals from derivatives or algebra.学会解决这些问题,即使是不同类型的问题,例如学习积分或金融衍生代数。
SymbMath has the ability to learn complicated algebra from simple algebra.SymbMath具有学习的能力,从简单的代数复杂的代数。
Example:例如:
Transform sin(x)/cos(x) into tan(x) in an expression.变换(x)/因为罪(x)成褐色(x)在一个表达式。
IN:在: sin(x)/cos(x) := tan(x)因为罪(x)/(x):=褐色(x)
IN:在: x+sin(x)/cos(x)+ax +罪(x)/因为(x)+一
OUT: a + x + tan(x):一个+ x +褐色(x)
The difference between learning and programming is as follows: the learning process of SymbMath is very similar to the way human beings learn, and that is accomplished by knowing certain rule that can be applied to several problems. 学习和编程的区别如下:SymbMath的学习过程非常类似于人类学习的方式,那就是知道一定规律来完成,可以应用于几个问题。Programming is different in the way that the programmer have to accomplish many tasks before he can begin to solve a problem. 规划是不同的,必须完成许多任务程序员才能开始解决问题。First, the programmer defines many subroutines for the individual integrands (e.g. f(x), f(x)+y^2, 2*f(x)+x, x*f(x), etc.), and for individual integrals (e.g. the indefinite integral, definite integral, the indefinite double integrals, indefinite triple integrals, definite double integrals, definite triple integrals, etc.), second, write many lines of program for the individual subroutines, (i.e. to tell the computer how to calculate these integrals), third, load these subroutines, finally, call these subroutines. 首先,程序员定义为个人integrands许多子程序(如f(x),f(x + y ^ 2、2 * f(x)+ x、x * f(x)等),并为个人积分(如不定积分、定积分、不确定性双积分,长三重积分,确定双积分,明确的三重积分等),第二,写了许多行程序为个人子程序,(即告诉计算机如何计算这些积分),第三,负荷这些子程序,最后,称这些子程序。That is precisely what SymbMath do not ask you to do.那正是SymbMath不要求你去做的事。
In one word, programming means that programmers must provide step-by-step procedures telling the computer how to solve each problems. 一个字,编程意味着程序员们必须提供程序告诉计算机如何一步一步的来解决每一个问题。By contrast, learning means that you need only supply the necessary facts (usually one f'(x) and/or one integral of f(x)), SymbMath will determine how to go about solutions of many problems.相比之下,学习意味着你只需要提供必要的事实(通常是一个f '(x)和/或一个积分的f(x)),SymbMath决定怎样去解决许多问题。
If the learning is saved as a library, then you do not need to teach SymbMath again when you run SymbMath next time.学习被存储为一个图书馆,那么你不需要再教SymbMath当你运行SymbMath下次吧。
SymbMath is an interpreter, and runs a SymbMath program in the Input window, which is written by any editor in the text (ASCII) file format.SymbMath是翻译,并运行一个SymbMath输入窗口的计划,这是任何编辑写的ASCII文本文件格式。
SymbMath language is a procedure language, which is executed from top to bottom in a program, like BASIC, FORTRAN, or PACSAL. SymbMath语言是一种程序语言,实行从上到下一个程序中,如基本、FORTRAN,或PACSAL。It also is an expression-oriented language and functional language.它也是一个expression-oriented语言和功能的语言。
The SymbMath program consists of a number of statements. 这SymbMath程序由一批报表。The most useful statement contains expressions, the expression includes data, and the most important data is functions.最有用的声明包含表达式,表达式包括数据,而且最重要的数据的功能。
The structure of SymbMath language is:SymbMath语言的结构是:
data -> expression -> statement -> program数据- - - - - - - > >表达陈述——>程序
Note that upper and lower case letters are different in SymbMath language, (e.g. abc is different from ABC) until the switch lowercase := on.注意,上部和小写字母不同语言SymbMath,(例如abc不同于abc)直到开关小写:=。
In the following examples, a line of "IN: " means input, which you type in the Input window, then leave the Input window by <Esc>, finally run the program by the command "Run"; while a line of "OUT:" means output. 在以下的例子,一行“:”是指输入,输入窗口类型,然后让输入窗口在< Esc >,最后由命令运行该程序“跑”;而行":"是指输出。You will see both input and output are displayed on two lines with beginning of "IN: " and "OUT: " in the Output window. 你将会看到两个输入和输出显示在两线开始“:”和“道:“在输出窗口。You should not type the word "IN: ". 你不应该类型单词“:”。Some outputs may be omit on the examples.一些输出可以省略的例子。
# is a comment statement.号是一个评论的声明。
You can split a line of command into multi-lines of command by the comma ,. 你可以将一条指令为命令multi-lines由逗号。The comma without any blank space must be the last character in the line.逗号没有任何空格必须在最后一个字就行了。
The data types in SymbMath language is the numbers, constants, variables, functions, equations, arrays, array index, lists, list index, and strings. 数据类型在SymbMath语言是数字,常数、变量、函数、方程、数组,数组,列表,列出指标和字符串。All data can be operated. 所有的数据可操作性强的设想。It is not necessary to declare data to be which type, as SymbMath can recognise it.这是没有必要申报数据是哪个类型,如SymbMath能够识别它。
The types of numbers are integer, rational, real (floating-point), and complex numbers in the range from -infinity to infinity.数字的整数的类型,理性的,真正的(浮点数),而复杂的数字范围从-infinity无限膨胀。
In fact, the range of the input real numbers is事实上,这个范围的输入实数
-inf, -(10^300)^(10^300) to -10^(-300), 0, 10^(-300) to (10^300)^(10^300), inf.-inf,(10 ^ 300)^(10 ^ 300)到-10 ^(-300)、0、10 ^(-300年)至(10 ^ 300)^(10 ^ 300),无穷大。
The range of the output real numbers is the same as input when the switch numeric := off, but when the switch numeric := on, it is范围的实数输出是一样的开关输入端时,流数值:=掉,但当开关数字:=,它是
-inf, -1.-inf(1)。E300 to -1.E300为1。E-300, 0, 1.E - 300,0,- 1。E-300 to 1.E - 300比1。E300, inf.E300,无穷大。
It means that the number larger than 1.那意味着数字大于1。e300 is converted automatically to inf, the absolute values of the number less than 1.e300自动转换为无穷大,数字的绝对值小于1。e-300 is converted to 0, and the number less than -1e300 is converted to -inf.e - 300是转化为0,而且这个数目小于1 e300转化为-inf。
For examples:例如:
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Numbers编号 Type类型
2323 integer整数
2/32/3 rational理性
0.230.23 real真正
2.3E22.3 E2 real真正
2+3*i2 + 3 *我 complex复杂
2.3+i2.3 +我 complex复杂
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That "a" and "b" are the same means a-b = 0, while that they are different means a-b <> 0.“a”和“b”意味着couple一样= 0,而他们是不同的手段故< > 0。
For the real numbers, the upper and lower case letters E and e in exponent are the same, e.g. 1e2 is the same as 1E2.因为真实的编号,上部大、小写字母E和E指数都是相同的,例如1 e2 1 e2是一样的。
The constants are the unchangeable values. 一个自然常数是不变的价值观。There are some built-in constants. 有一些内置的常量。The name of these built-in constants should be avoided in the user-defined constants.这些内置常数的名字应该避免在用户定义的常量。
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Built-in Constants内置常数 Meanings意义
pi:=3.1415926536农夫:= 3.1415926536 the circular constant.圆形的常数。
e:=2.7182818285艾凡:= 2.7182818285 the base of the natural logarithms.基地的自然对数。
i:=sqrt(-1)我:= sqrt(1) the imaginary sign of complex numbers.想象复杂的标志数字。
infinf infinity.无限。
-inf-inf negative infinity.负无限。
c_infc_inf complex infinity, both real and imaginary parts无限复杂,无论是真实和想象的部分
of complex numbers are infinity. 复杂的数字是无限。e.g. inf+inf*i.如步+ inf *我。
constant不断 the integral constant.积分常数。
discontdiscont discontinuity, e.g. 1/0. 不连续性、例句。1/0。(You can evaluate the one-sided value(你可以评估片面的价值 by x=x0+zero or x0-zero if the value of expression is discont).x = x0 +零或x0-zero的价值表现为discont)。
x0-zerox0-zero to evaluate left-sided value when x approach x0左值评价方法x0当x
from negative (-inf) direction, as zero -> 0.从负(-inf)的方向,因为零- > 0。
x0+zerox0 +零 to evaluate right-sided value when x approach x0价值评价方法x0右侧x
from positive (+inf) direction, as zero -> 0.从正(+ inf)的方向,因为零- > 0。
undefined未定义 the undefined value, e.g. indeterminate forms:无形价值,如不确定的形式。
0/0, inf/inf, 0*inf, 0^0, etc.0/0,步/无穷大,0 *步,0 ^ 0等)。
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Zero is the positive-directed 0, as the built-in constant. 零是positive-directed 0,内置的常数。f(x0+zero) is the right-hand sided function value when x approaches to x0 from the positive direction, i.e. x = x0+. f(x0 + 0)是右边站函数值的方法从当x x0正方向,即x = x0 +。f(x0-zero) is the left-sided function value when x approaches to x0 from the negative direction, i.e. x = x0-. f(x0-zero)是左功能价值当x方法从反方向x0,即x = x0 -。e.g. f(1+zero) is the right-hand sided function value when x approaches to 1 from the positive (+infinity) direction, i.e. x = 1+, f(1-zero) is the left-hand sided function value when x approaches to 1 from the negative (-infinity) direction, i.e. x = 1-; exp(1/(0+zero)) gives inf, exp(1/(0-zero)) gives 0.如f(1 + 0)是右边站函数值x的方法时,从积极的1(+无限)方向,即x = 1 + f(1-zero)是左手面函数值x的方法时一号从负(-infinity)方向,即x = 1 -;实验(1 /(0 + 0)给步、exp(1 /(0-zero)给0。
The inf, discont and undefined can be computed as if numbers.这步,就可以计算和未定义discont好像编号。
Example:例如:
IN:在: inf+2, discont+2, undefined+2步+ 2,discont + 2,+ 2定义
OUT: inf, discont, undefined出:无穷大,discont、不可解释的
Notice that the discont and undefined constants are different. 注意到discont和未定义常量是不同的。If the value of an expression at x=x0 is discont, the expression only has the one-sided value at x=x0 and this one-sided value is evaluated by x=x0+zero or x=x0-zero. 一个表达式的值是否在x = x0是discont,表达的只有片面的价值在x = x0片面的价值,这是评估x = x0 +零或x = x0-zero。If the value of an expression at x=x0 is undefined, the expression may be evaluated by the function lim().一个表达式的值是否在x = x0是未定义的,表达可能是由评价函数小林()。
Example: evaluate exp(1/x) and sin(x)/x at x=0.例如:评估经验(1 / x)和赎罪(x)/ x在x = 0。
IN:在: f(x_) := exp(1/x)f(x_):=经验(1 / x)
OUT: f(x_) := exp(1/x)出:f(x_):=经验(1 / x)
IN:在: f(0)f(0)
OUT: discont出:discont # f(0) is discontinuity, only has one sided value# f(0)是不连续的,只有单方面的价值
IN:在: f(0+zero)f(0 + 0) # right-sided value#右值
OUT: inf出:步
IN:在: f(0-zero)f(0-zero) # left-sided value#左值
OUT: 0出:0
IN:在: subs(sin(x)/x, x = 0)替补(罪(x)、x / x = 0)
OUT: undefined出:未定义
IN:在: lim(sin(x)/x, x = 0)小林(罪(x)、x / x = 0) # it is evaluated by lim()它是由评价# l()
OUT: 1出:1 .
The sequence of characters is used as the name of variables. 这一连串的字符被用来作为变量的名字。Variable names can be up to 128 characters long. 变量名称可达到128个字符长。They must begin with a letter and use only letters and digits.他们必须以字母开头字母和字母和数字仅使用。 SymbMath knows upper and lower case distinctions in variable names, so AB, ab, Ab and aB are the different variables. SymbMath知道上部和下部情况区别,在变量名,所以AB、AB、AB和AB型都是不同的变量。They are case sensitive until the switch lowercase is set to on (i.e. lowercase := on).他们都是大小写敏感的,直到将开关小写(即小写:=。
Variables can be used to store the results of calculations. 变量可以用来存储结果的计算。Once a variable is defined, it can be used in another formula. 一旦一个变量的定义是,它可以用来在另一个公式。Having defined X as above, you could define Y := ASIN(X). 有确定的X以上,你可以定义杨:= ASIN(X)。You can also redefine a variable by storing a new value in it.你也能重新定义一个变量通过保存一个新值。 If you do this, you will lose the original value entirely.如果你这样做,你将丢失完全的原有价值。
Assign a result to a variable, just put给一个变量分配结果,就把
<var-name> :=< var-name >:= expression表达
e.g.例句。 x := 2 + 3谢:= 2 + 3 # assign value to x#分配价值x
Variables can be used like constants in expressions.变量可以当作常数表达式。
For example:例如:
a := 2 + 3答:= 2 + 3
b := a*4乙:= * 4
If an undefined variable is used in an expression, then the expression returns a symbolic result (which may be stored in another variable).如果一个未定义的变量是用于一个表达式,然后返回一个象征性表达结果(它可以被存储在另一个变量)。 Pick an undefined variable name, say x, and enter:选择一个未定义的变量的名字时,请说x,进入:
y := 3 + x杨:= 3 + x # formula results since x undefined结果自#公式x未定义的
x := 4谢:= 4 # Now x is defined现在x是#定义
yy # y returns 7, but its value is still the formula 3 + x7 # y回报,但其价值仍然是3 + x的公式
x := 7谢:= 7 # revalue x#人民币升值x
yy # new value for y#新价值y
Note that in symbolic computation, the variable has not only a numeric value but also a symbolic value.值得注意的是,在符号计算,变不仅数值也是一种象征性的价值。
Symbolic values for variables are useful mostly for viewing the definitions of functions and symbolic differentiation and integration.象征价值是有用的大多为变量的定义和浏览功能分化和整合。象征
Watch out for infinite recursion here.小心无穷递归在这里。 Defining定义
x := x+3谢:= x + 3
when x has no initial value, it will not cause an immediate problem, but any future reference to x当x没有初始值,它不会立即产生一个问题,但是未来的参考x will result in an infinite recursion !将导致一个无穷递归!
A value can be assigned to the variable, by one of three methods:一个值可以被指定给变量,通过三种方法:
(1) the assignment :=,(1)作业:=,
(2) the user-defined function f(),(2)用户自定义函数f(),
(3) subs(y, x = x0).(3)替补(y,x = x0)。
e.g.例句。
y:=x^2杨:= x ^ 2
x:=2谢:= 2 # assignment#作业
yy
f(2)外(2) # if f(x) has been defined, e.g. f(x_):=x^2.#如果f(x)已被定义,如f(x_):= x ^ 2。
subs(x^2, x = 2)替补(x ^ 2、x = 2) # evaluate x^2 when x = 2.评估x ^ 2 #当x = 2。
The variable named last is the built-in as the variable last is always automatically assigned the value of the last output result.最后的变量称为内置当作变量最后总是会自动设置的价值,最后输出结果。
The usual used independent variable is x.通常使用独立变量是x。
By default, |x| < inf and all variables are complex, except that variables in inequalities are real, as usual only real numbers can be compared. 默认情况下,| | < inf和x��量是复杂的,除了变量不等式是很实际的,像往常一样唯一真正的编号可比的。e.g. x is complex in sin(x), but y is real in y > 1.如x是复杂的罪(x),但y是真实的y > 1。
You can restrict the domain of a variable by assuming the variable is even, odd, integer, real number, positive or negative (see Chapter Simplification and Assumption).你可以限制一个变量的领域通过假设变量为均匀,奇怪,整数,实数、正面或负面的(请看简化与假设章)。
Patterns stand for classes of expressions.站在课程模式的表情。
__ any expression.任何表达式。
x_x_ any expression, given the name x.任何表达式,给出了名字x。
Patterns should appear on the left-hand side of the assignment only, not on the right-hand side of the assignment. 模式应该出现在左手边的任务仅仅,不是右侧的任务。Patterns are only used in definition of functions, procedures and rules.只用于定义模式的功能、程序和规则。
Patterns are used to define functions and rules for pattern match.模式用于定义功能和模式匹配规则。
These are two types of functions: internal and external. 这些是两种类型的功能:内部和外部的。The internal function is compiled into the SymbMath system. 内部功能是编译成SymbMath系统。The external function is the library written in SymbMath language, which is automatically loaded when it is needed. 外部功能是图书馆SymbMath语言写的,必要时自动加载。(See Chapter Library and Package). (见章节图书馆和包装)。The usage of both types are the same. 使用两种类型是相同的。You can change the property or name of the external function by modifying its library file, or you add a new external function by creating its library file, but you cannot change the internal function.你能改变自己的财产或名称的外部功能通过修改库文件,或者你添加一个新的外部功能的创造出自己的库文件,但是你不能改变内部功能。
Different versions of SymbMath have different number of standard mathematical functions. 不同版本的SymbMath有不同数量的标准数学函数。The Advanced Version C has all of them. 新版本的C具有他们所有的人。See the following table in detail for other versions. 看下面的表格的详细其他版本。All below standard functions, (except for random(x), n!所有低于标准功能,(除了随机(x)、n !, fac(n) and atan2(x,y)), can be differentiated and integrated symbolically.,前沿空中管制官(n)和atan2(x,y),可以分化和综合象征性地。
Table 17.1.5.1表17.1.5.1 Standard Mathematical Functions标准数学函数
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Functions功能 Meanings意义
random(x)随机(x) generate a random number.产生一个随机数。
n!护士! factorial of n.n阶乘矩。
fac(n)前沿空中管制官(n) the same as n!.一样的n。
sqrt(x)sqrt(x) square root, the same as x^0.5.平方根,与x ^ 0.5。
root(x,n)根(x,n) all n'th root of x.所有的'th根氮x。
exp(x)实验(x) the same as e^x.同e ^ x。
sign(x)签署(x) 1 when re(x) > 0, or both re(x) = 0 and im(x) > 0; 0 whenx=0;当你(x)> 0,或者两者都是(x)= 0的时候,我(x)> 0;0 whenx = 0;
-1 otherwise.1不然。
abs(x)abs(x) absolute value of x.绝对值x。
ln(x)淋巴结(x) natural logarithmic function of x, based on e.自然对数函数x,基于e。
log10(x)t(x)
sin(x)罪(x) sine function of x.正弦函数x。
cos(x)因为(x)
............................... above functions in Shareware Version A ...............以上的功能在一个............... Shareware版本
tan(x)褐色(x)
csc(x)csc(x)
sec(x)秒(x)
cot(x)cot(x)
asin(x)asin(x) arc sine function of x, the inverse of sin(x).电弧x的正弦函数,推导了罪(x)。
acos(x)函数(x)
atan(x)atan(x)
acot(x)acot(x)
asec(x)了一类正则(x)
acsc(x)研究会(x)
atan2(x,y)atan2(x,y)
............................. .............................above functions in Student Version B .................以上的功能.................学生版本B
sinh(x)sinh(x) hyperbolic sine function of x.双曲正弦函数x。
cosh(x)事业(x)
tanh(x)tanh(x)
csch(x)csch(x)
sech(x)sech(x)
coth(x)coth(x)
asinh(x)作用(x) arc hyperbolic sine function of x, the inverse of sinh(x).电弧双曲正弦函数x,反过来的sinh(x)。
acosh(x)函数(x)
atanh(x)函数(x)
acoth(x)acoth(x)
asech(x)asech(x)
acsch(x)acsch(x)
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Calculus functions are for calculus calculation. 微积分法计算功能。The first argument of the function is for evaluation, and the second argument is a variable that is with respect to.第一个参数是评价中的作用,第二个参数是一个变量,以尊重。
Table 17.1.5.2表17.1.5.2 Calculus Functions微积分功能
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Functions功能 Meanings意义
subs(y, x = x0)替补(y,x = x0) evaluates y when x = x0.当x = x0 y评价。
lim(y, x = x0)小林(y,x = x0) gives the limit of y when x approaches x0. 给出了极限当x方法x0 y。Note that the correct answers注意正确的答案 usually for the indeterminate forms: 0/0, inf/inf, 0*inf, 0^0, inf^0.通常为不确定的形式:0/0,步/无穷大,0 *步,0 ^ 0,inf ^ 0。
d(y, x)d(y,x) differentiate y with respect to x.区分y就x。
d(y, x, order)d(x,y,顺序) gives the nth order derivative of y with respect to an undefined variable x.给出了第n次阶导数的y就一个未定义的变量x。
d(y)d(y) implicit differentiation.隐含的分化。
inte(y, x)希尔(y,x) find the indefinite integral of y with respect to an undefined variable x.找到的不定积分y就一个未定义的变量x。
inte(y,x,a,b)希尔(y,x,a,b) find the definite integral of y with respect to an undefined variable x taken找到了定积分的y就一个未定义的变量x缠住了 from x=a to x=b.从x =一个x = b。
inte(y,x,a,b,c)希尔(y,x,a,b,c) find the definite integral of y with respect to an undefined variable x taken找到了定积分的y就一个未定义的变量x缠住了 from x=a to x=b, then to x=c, where b is singularity.从x =一个x = b,然后对x = c,在b是奇异点。
inte(y, x from a to b)希尔(y,x从a到b) the same as inte(y,x,a,b).强烈的一样(y,x,a,b)。
inte(y)交互(y) implicit integration, used to integrate the differential equations.隐式集成,用来整合微分方程组。
dsolve(y'(x)=f(x,y), y(x), x)dsolve(y”(x)= f(x,y),y(x)、x) solve differential equations.求解微分方程。
sum(y, x from xmin to xmax)和(y,从x xmin到xmax) sum of y step=1.笔y = 1步。
sum(y, x from xmin to xmax step dx)和(y,从x xmin xmax一步,dx) sum of y.笔y。
prod(y, x from xmin to xmax)促进(y,从x xmin到xmax) product of y step=1.y一步产品= 1。
prod(y, x from xmin to xmax step dx)促进(y,从x xmin xmax一步,dx) product of y.产品的y。
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If a second argument x is omitted in the functions d(y) and inte(y), they are implicit derivatives and integrals. 如果x是省略了第二个参数的功能d(y)和希尔(y),他们是隐含的金融衍生品和积分。If f(x) is undefined, d(f(x), x) is differentiation of f(x). 如果f(x)是未定义的,d(f(x)、x)是分化的f(x)。These are useful in the differential and integral equations. 这些都是有用的在微分形式和积分方程。(see later chapters).(见后面的章节)。
For examples:例如:
inte(inte(F,x), y) is double integral of F with respect to both variables x and y.希尔(交互(F,x,y)是二重积分的两个变量F对x和y。
d(d(y,x),t) is the mixed derivative of y with respect to x and t.d(d(y,x),t)是混合的衍生物x和y就t。
The keywords "from" "to" "step" "," are the same as separators in multi-argument functions. 关键字“从”、“至”“步”、“同分离器在multi-argument功能。e.g. inte(f(x), x, 0, 1) are the same as inte(f(x), x from 0 to 1).例如交互(f(x)、x,0,1)是一样的交互(f(x)、x从0到1)。
Examples:例子:
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differentiation分化 d()d() d(x^2,x)d(x ^ 2、x)
integration整合 inte()交互() inte(x^2,x)强烈的(x ^ 2、x)
limit限制 lim()小林() lim(sin(x)/x, x = 0)小林(罪(x)、x / x = 0)
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Table 17.1.5.3.1表17.1.5.3.1 The is*(x) Functions这是*(x)功能
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Function功能 Meaning意义
isodd(x)isodd(x) test if x is an odd number.测试如果x是奇数。
iseven(x)iseven(x) test if x is an even number.如果x是测试一个偶数。
isinteger(x)isinteger(x) test if x is an integer number.测试如果x是一个整数。
isratio(x)isratio(x) test if x is a rational number.如果x是一种合理的测试号码。
isreal(x)(x)来 test if x is a real number.如果x是一个真正测试号码。
iscomplex(x)iscomplex(x) test if x is a complex number.如果x是一种复杂的测试号码。
isnumber(x)isnumber(x) test if x is a number.如果x是测试一个数字。
islist(x)islist(x) test if x is a list.如果x是测试一个列表。
isfree(y,x)isfree(y,x) test if y is free of x.测试如果y是免费的x。
issame(a,b)issame(a,b) test if a is the same as b.测试是否有相同的b。
islarger(a,b)islarger(a,b) test if a is larger than b.测试是否有高于b。
isless(a,b)isless(a,b) test if a is less than b.测试是否有少于b。
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All of the is* functions give either 1 if it is true or 0 otherwise.所有的是*功能给他们任何一方如果它是真实的或0聪明。
The type(x) gives the type of x. Its value is a string.类型(x)给出了x型。它的值是一个字符串。
Table 17.1.5.3.2表17.1.5.3.2 The type(x) functions功能类型(x)
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xx type(x)类型(x)
11 integer整数
1.11.1 real真正
2/32/3 ratio比
1+i1 +我 complex复杂
sin(x)罪(x) sin()罪()
[1,2][1,2] []
a一个 symbol象征
"a"“a” string字符串
a+b+ b ++
a*b一个* b *
a^b一个^ b ^
a=b一个= b ==
a==b一个= = b === =
a>b一个> b >
a>=b一个> = b >=> =
a<b一个< b <
a<=b一个< = b <=< =
a<>b一个< > b <>
a,ba、b ,
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You also can test x, e.g. if x is type of real number, by你也可以测试x,如果x是类型的实数、
type(x)=="real"式(x)= = "真正的"
Table 17.1.5.4.1表17.1.5.4.1 Algebra Functions代数函数
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expand(F)扩大(F) expand (a+b)^2 to a^2 + 2*a*b + b^2.扩大a + b)2 ^ ^ 2 + 2,* * ^ 2 b + b。
factor(F)因子(F) factorise a^2 + 2*a*b + b^2 to (a+b)^2.一个factorise ^ 2 + 2 b + b * * ^ 2 a + b)^ 2。
solve(f(x)=0, x)解决(f(x)= 0,x) solve polynomial and systems of linear equations求解多项式和系统的线性方程组
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Note: the Shareware Version has not solve().注:该Shareware版本还没有解决()。
For example:例如:
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solving解决 solve()解决() solve(x^2+1 = 0, x)解决(x ^ 2 + 1 = 0,x)
expanding扩大 expand()扩大() expand((a+b)^2)扩大(a + b)^ 2)
factoring保理 factor()因子() factor(a*c+b*c)因子(a * c + b * c)
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Conversion functions convert a type of data to another type of data.转换函数转换一种类型的数据,另一种类型的数据。
Table 17.1.5.4.2表17.1.5.4.2 Conversion Functions转换功能
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listsum([a,b])listsum([a、b]) convert list to sum.转换表的数目。
coef(expr, x^2)系数(expr、x ^ 2) gives the coefficient of x^2 in expr.给出了x ^ 2系数expr。
left(x^2=b)左(x ^ 2 = b) left hand side of an equation.左手边的一个等式。
right(x^2=b)正确的(x ^ 2 = b) right hand side of an equation.右手边的一个等式。
re(x)稀土(x) real part of complex numbers.真正的一部分。复数
im(x)我(x) imaginative part of complex numbers.想象力的一部分复数。
num(x)胡(x) convert x to the floating-point number.转换x的浮点数。
ratio(x)比(x) convert x to the rational number.转换x理性号码。
round(x)圆(x) convert x to the rounded integer.转换x形圆整数。
trunc(x)trunc(x) convert x to the truncated integer.转换x的截断整数。
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Table 17.1.5.4.3表17.1.5.4.3 The List and Table Functions这张清单,表功能
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list(f(x), x from xmin to xmax step dx)列表(f(x),从x xmin xmax一步,dx) lists of f(x).名单的f(x)。
table(f(x), x from xmin to xmax step dx)表(f(x),从x xmin xmax一步,dx) data table of function values.数据表的功能价值。
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Above functions can be operated and chained, like the standard functions.以上功能操作和锁住,标准一样的功能。
You can define the new functions, which include the standard functions, calculus functions, and algebraic operators.你可以定义的新功能,包括标准功能,微积分功能,代数运算符。
Define a new function f(x) by定义一个新的函数f(x)
f(x_) := x^2f(x_):= x ^ 2
and then call f(x) as the standard functions. 就叫f(x)为标准的功能。The function name can be any name, except for some keywords. 函数的名称可以是任何名字,除了一些关键词。(for the maximum number of arguments, see Chapter(最大数目的参数,看一章 System Limits).系统限制)。
Clears a variable or function from assignment by清除变量或函数从分配
clear(x)清晰的(x) # clear x from assignment.明确的任务。从x号
clear(f(x))清楚(f(x)) # clear f(x) from assignment.#清楚f(x)从任务。
clear(a>0)清楚(> 0) # clear a>0 from assignment.从一个> 0 #明确的任务。
Variables can be used in function definitions. 变量可以用在函数定义。It leads to an important difference between functions and variables.这导致一个非常重要的区别函数和变量。 When a variable is defined, all terms of the definition are evaluated.当一个变量的定义是,所有的术语的定义进行了评估。 When a function is defined, its terms are not evaluated; they are evaluated when the function is evaluated. 当一个函数的定义,其条件没有评价;他们正在评估当函数进行了评价。That means that if a component of the function definition is changed, that change will be reflected the next time the function is evaluated.这意味着如果一个组件的功能定义也发生了变化,这变化可反映下次功能进行了评价。
A procedure is similar to a function, but the right side of assignment in its definition is multi statements grouped by block(). 一个程序类似作用,但右侧作业多报表它的定义是按区块()。The block(a,b,c) groups a,b,c and only returns the last argument as its value, or returns the second last argument as its value if the last argument is local(). 块(a,b,c)集团a、b、c和只返回最后一个参数为价值,或者返回倒数第二个参数为价值如果最后的论点是当地()。It is used as grouper in definition of a procedure. 作为一个程序的定义上。All variables in block are global, except for variables declared by local().所有变量的块都是全球性的,除了变量声明当地()。
e.g. f(x_):=block(p:=x^6,p,local(p))如f(x_):=区块(p = x ^:6、磷、当地(p))
Remember that you can split a line of program into multi-lines program at comma ,.记住,你可以将一行程序程序multi-lines逗号。
A rule is similar to a function. 一条规则是类似的功能。In definition of function, all arguments of function are simple variables, but in definition of rules, the first argument may be a complicated expression.在定义的功能,都是简单的变量参数的功能,但在定义的规则,第一个观点是一个复杂的表达式。
e.g.例句。
f(x_,y_) := x^2+y^2f(x_,y_):= x + y ^ 2 ^ 2 # defining function#定义功能
f(x_,y_) := block(a:=2, a+x^2+y)f(x_,y_):=区块(答:= 2,一个+ x ^ 2 + y) # defining procedure#定义程序
log(x_ * y_) := log(x)+ log(y)日志(x_ * y_):=日志(x)+日志(y) # defining rule#定义规则
An equation is an equality of two sides linked by an equation sign =, e.g. x^2+p = 0, where the symbol = stands for an equation. 一个方程是一个平等两面相连方程签署=,例如x ^ 2 + p = 0,那里的符号=代表一个等式。Note that the symbols "=", "==" and ":=" are different: ":=" is the assignment, "==" is the equal sign, but "=" is the equation sign.注意符号“=”、“= = "和":= "是不同的:“:= "是你的任务,”= = "就是平等的标志,但“=”是方程标志。
Example:例如:
IN:在: 2 = 22 = 2
OUT: 2 = 2出:2 = 2 # unevaluated# unevaluated
IN:在: 2 == 22 = = 2
OUT: 1出:1 . # evaluated to 1 (true)1 #评估(正确的)
Systems of equations are a list of equations, e.g.方程系统是一个方程中,举例说明。
[a1*x+a2*y=a3, b1*x+b2*y=b3].[a1 a2 * * x + y = a3,b1 * x + y = b3 b2 *]。
e.g.例句。
a < b一个< b less than少于
a <= b一个< = b less than or equal to小于或等于一
a > b一个> b greater than大于
a >= b一个> = b greater than or equal to大于或等于
a == b一个= = b equal to等于
a <> b一个< > b not equals不等于
Lists are similar to lists in such language as PROLOG.列出清单类似这样PROLOG语言。
[a, b, c] is a list.[a、b、c)是一个列表。
[a, b, [c1, c2]] is a list of lists.[a,b,(c1,c2]]是一个列表的列表。
The list index is the index for n-th element in a list. 名单上的指标指数的形式元素在一个列表。e.g. b[2] indicates the second element in the list b.如b[2]表明第二元素在表b。
The built-in list index is last[number]. 内置的列表索引是最后一次(数值)。The name of last output list is last, e.g. last[1] is the first element in the last output list.最后输出的名字列表上,例如去年[1]是第一个元素在最后输出名单。
Arrays are the same as those in such language as PASCAL and FORTRAN. 数组是一样在这样的语言,就像帕斯卡,FORTRAN语言。But you can use arrays without declaring arrays, unlike in PASCAL and FORTRAN.但你可以使用数组没有宣布数组,不像帕斯卡,FORTRAN语言。
e.g.例句。
a[1]:=1一个[1]:= 1
a[2]:=4一个[2]:= 4
The array index is the index for n-th element in an array. 数组的索引数组中的元素的形式。e.g. a[2] indicates the second element in the array a.例如一个[2]表示数组的第二个因素。
A string is a sequence of characters between two quotation marks. 一个字符串是一连串的字符在两个引号。e.g. 例句。"1234567890". “1234567890”。Note that 1234 is number but "1234" is string. 注意,1234号码,但“1234”,是字符串。The number can be calculated and only has 11 of max digits, while string cannot be calculated and has 64000 of max characters long.能计算和数量只有11 max位数,而不能计算字符串有64000个马克斯字符渴望。
Note that the output of strings in SymbMath is without two quotation marks. 需要注意的是,在SymbMath输出串无两个引号。This makes text output to graph and database more readable.这使得文本输出图和数据库更易读。
Strings can be stored in variables, concatenated, broken, lengthen, and converted to numbers if possible.字符串可以被存储在变量、接、破碎、加长,并转换为数字,如果可能的话。
e.g.例句。
IN:在: p := "abc"警:=“abc” # "abc" is stored in variable p“abc”号被储存在可变p
OUT: p := abc出:p:= abc
IN:在: concat("s","t")concat(“s”,“t”) # concatenate "s" and "t"#连结" s "和" t "
OUT: st出:圣
IN:在: length("abc")长度(“abc”) # count length of "abc"#计数长度的“abc”
OUT: 3出:3
IN:在: number("123")数字(“123”) # convert string "123" into number 123转换串号“123”到123号
OUT: 123出:123
IN:在: type(a), type("a")(a)型、类型(“a”)
OUT: symbol, string出:符号,字符串
The expressions (i.e. expr) are made up of operators and operands. 表达式(即expr)是由运算符和操作数。Most operator are binary, that is, they take two operands; the rest are unitary and take only one operand. 大多数经营者都是二进制的,也就是说,他们把两个操作数,其他的都是统一的,只带一个操作数。Binary operators use the usual algebraic form, e.g. a+b.二元操作符通常的代数形式使用,如+ b。
There are two kinds of expressions: numeric and Boolean. 有两种表现:数字和布尔。The numeric expression is combination of data and algebraic operators while the Boolean expression is combination of data and relational operators and logic operators. 这个数字表达相结合的数据和代数算子组合在布尔表达式的数据和关系运算符和逻辑运算符。These two kinds of expressions can be mixed, but the numeric expression has higher priority than Boolean operators. 这两种表达式是可以混合,但数字表示有更高优先级的布尔运算符。x*(x>0) is different from x*x>0. * *(x > 0)不同于* * x > 0。x*x>0 is the same as (x*x)>0.* * x > 0是一样的(x * x)> 0。
e.g.例句。
a+b+3+ b + 3 numeric expression,数字表达,
a>0一个> 0 Boolean expression布尔表达式
a>0 and b>0一个> 0和b > 0 Boolean expression布尔表达式
(x>0)*x(x > 0)* x mixed numeric and Boolean expression混合的数字和布尔表达式
Table 17.2.1表17.2.1 Operators运营商
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Operation操作 Operators运营商 Examples实例 Order秩序
comma逗号 , a:=2, b:=3答:= 2。b:= 3 11
assignment作业 :=:= p:=2+3警:= 2 + 3 22
and和 and和 a>2 and a<8一个>和< 8 2 22
or或 or或 a>2 or b>2一个> 2或b > 2 22
equation方程 == x^2+x+1 = 0x ^ 2 + x + 1 = 0 33
equal平等 === = a==2一个= = 2 33
larger than大于 > a>2一个> 2 33
larger and equal更大的平等>=> = a>=2一个> = 2 33
less than少于 < a<2一个< 2 33
less and equal越来越平等 <=< = a<=2一个< = 2 33
unequal不平等 <> a<>2一个< > 2 33
plus加上 ++ a+b+ b 44
minus减去 -- a-bcouple 44
mutilation损毁 * a*b一个* b 55
division分工 / a/ba / b 55
power权力 ^ a^b一个^ b 66
power权力 ** a**b一个* * b 66
factorial阶乘 ! n!护士! 66
positive积极 ++ +a+一 77
negative负面 -- -a- 77
function功能 f()f() sin(x)罪(x) 77
list index列表索引 f[]f[] f[1]f[1] 77
parentheses括号 () (a+b)*c(a + b)度) 77
list列表 [] [a,b](a,b) 77
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All functions have the same 7th order.所有功能有相同的7th秩序。
Operations with higher order precede, otherwise operations with equal precedence are performed from left to right.高阶前作业,否则相同优先级业务执行从左向右。 These are the usual algebraic conventions.这是通常的代数公约。
a^b^c is the same as (a^b)^c.一个c ^ ^ b是一样的(^ b)c ^。
You can get operators by type(x).你可以通过类型运营商(x)。
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plus加上 ++ a+b+ b 44
minus减去 -- a-bcouple 44
mutilation损毁 * a*b一个* b 55
division分工 / a/ba / b 55
power权力 ^ a^b一个^ b 66
power权力 ** a**b一个* * b 66
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Before you can write loops, you must be able to write statements that evaluate to 1 or 0, and before you can do that, you must be able to write useful statements with logical values. 你可以写循环之前,您必须能够写评估声明1或0,之前,你可以做到这一点,你必须能够写有用的报表和逻辑值。In mathematics, these are relational statements.在数学中,这些都是关系陈述。
SymbMath allows you to compare numbers six ways:SymbMath允许你比较编号六个方法:
a < b一个< b less than少于
a <= b一个< = b less than or equal to小于或等于一
a > b一个> b greater than大于
a >= b一个> = b greater than or equal to大于或等于
a == b一个= = b equal to等于
a <> b一个< > b not equals不等于
SymbMath uses the double equals sign == (like C language) for "is equal to" to distinguish this operator from the equation =.采用双SymbMath等号= =(如C语言)为“等于“鉴别该算子方程的=。
The result of a comparison of two real numbers is either 1 or 0. 结果的比较两个实数要么是1或0。If the comparison is not both real numbers, it left unevaluated.如果类比并不涉及不动产编号,留下unevaluated。
SymbMath uses the logical operators:SymbMath采用逻辑运算符。 AND, and OR.,或。 You can combine comparison operators with them to any level of complexity. 你可以将比较运算符和他们有任何程度的复杂性。In contrast to Pascal, logical operators in SymbMath have a lower order or precedence than the comparisons, so a < b相比之下,帕斯卡尔,逻辑运算符在SymbMath有较低的优先级顺序或比比较,所以< b and和 c > d works as expected.c > d作品与预期相符。 The result of combining logical values with结果相结合的逻辑值
logical operators is another logical value (1 or 0).逻辑运算符是另一个逻辑值(1 - 0)。 Bit operations on integers can be performed using the same operations, but result is integers.整数位操作可以进行使用相同的手术,但是结果是整数。
SymbMath uses the "short-circuit" definition of AND and OR when the arguments are Boolean.SymbMath用“短路”的定义,或当参数和布尔。 Here are tables that show how AND and OR are defined:这里有表显示,或被定义:
a AND ba和b
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bb 11 00
a一个
11 11 00
00 00 00
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a OR ba或b
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bb 11 00
a一个
11 11 11
00 11 00
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Short-circuit evaluation is used because often one condition must be tested before another is meaningful.采用短路评价因为往往一个条件必须被测试在一个很有意义的。
The result of Boolean expression with logic operators is either 1 or 0. 布尔表达式的结果与逻辑操作要么是1或0。Boolean expression like (1 < 3 or 1 > 4) return a real value 1 or 0.像布尔表达式(1 < 3或1 > 4)返回一个真正的价值1或0。 Numeric expressions can replace Boolean ones, provided they evaluate to 1 or 0.布尔的数字表达式可以取代,只要他们评估以1或0。 The advantage here is that you can define the step function that is 0 for x < a and 1 for x > a by entering:这里的优势在于,你可以定义步骤功能,是0 x(x和1 >一个进入:
step(x_, a_) := x > a步骤(,已x_):= x >
To define the function:定义的功能有:
f(x) = x-1f(x)= x-1 if x < 1如果x < 1
= x^2-x= x ^ 2-x if x >= 1如果x > = 1
enter:进入:
f(x_) := (x-1)*(x < 1) + (x^2-x)*(x >= 1)f(x_):=(x-1)* < 1 + x(x ^ 2-x)*(x > = 1)
These functions can be differentiated and integrated symbolically.这些功能可以分化和综合象征性地。
A function call activates the function specified by the function name. 一个函数调用激活函数指定的函数名。The function call must have a list of actual parameters if the corresponding function declaration contains a list of formal parameters. 这个函数必须有一个列表实际参数对应的函数声明包含了一串的形式参数。Each parameter takes the place of the corresponding formal parameter. 每一个参数代替了相应的正式的参数。If the function is external, the function call will automatically load the library specified by its function name plus extension .如果功能外,这个函数将自动载入图书馆功能的名字加上规定延长。LI when needed.李需要时。
Some examples of the function calls follow:函数调用一些例子如下:
sin(x)罪(x) # load the library sin.#负荷图书馆的罪。li when needed李在需要的时候
inte(x^2, x)强烈的(x ^ 2、x) # load the library inte.图书馆#负载密集。li when needed李在需要的时候
# is the comment statement sign.号是评论声明标志。
You can add comments into a line, or even produce a single line which is entirely a comment, by preceding the comment sign with #.你可以添加评论到一条线,甚至产生一个单一的流水线,完全是一个注释,签约前的评论#。
For example:例如:
# This is my program这是我的计划。#
3 + 43 + 4 # My first calculation#我第一次计算
Comments make your calculations more understandable, whether you are making a printed record of what you are doing or if you just want to jot some notes to yourself while you are working.让你的计算评价更易于理解,你是否正在打印记录你正在做的,或者如果你只想要写一些笔记给自己当你工作。
The evaluation statement has the format:评价声明已格式:
expression表达
SymbMath evaluates any expression which in a line and gives the value of the expression. 任何SymbMath评价对一条直线上的表达,并给出了价值的表达方式。e.g.例句。
IN:在: 3 + 43 + 4
OUT: 7出:7 # the value of 3+4# 3 + 4的价值
IN:在: d(x^6, x)d(x ^ 6,x)
OUT: 6 x^5出:6 x ^ 5 # the value of d(x^6, x)号d的价值(x ^ 6,x)
IN:在: subs(last, x = 1)替补(最后,x = 1) # evaluate the last output when x = 1.评估最后输出时# x = 1。
OUT: 6出:6
The last output can be saved to a variable for the later use by the built-in variable "last", e.g. f :=last.最后的输出可以保存到一个变量备用的“最后一次”的内部变量,例如福:=持久。
The assignment in SymbMath language is similar to assignment in such language as PASCAL.在SymbMath语言任务分派到类似这样的语言,就像帕斯卡。
An assignment operator is一个赋值运算符是 :=:=
The assignment statement specifies that a new value of expr2 be assigned to expr1, and saved into memory. 声明指定作业,一个新的价值被指定给expr1 expr2,留到内存中。The form of the assignment statements is赋值语句的形式
expr1 := expr2expr1:= expr2
You can use assignment for storing result.你可以使用分配存储的结果。
You can assign the result of calculation or any formula to a variable with a command like:你可以指定或任何公式计算结果与一个命令给一个变量,例如: X := SIN(4.2).谢:=罪(4.2)。
The assignments are useful for long calculations.作业是非常有用的,长时间的计算。 You can save yourself a lot of recalculations by always storing the results of your calculations in your own variables instead of leaving them in the default variable last.你可以为自己省下不少recalculations总是将结果储存你的计算在自己的变量,而不是让他们在默认的变量的最后一次。
You can destroy the assignment to X with the command clear(X). 你可以摧毁分配给该命令清楚X(X)。If X stored a large list, you could regain a considerable amount of memory by clearing X. Also, since a variable and a function can have the same name, you can clear a variable p, not a function p(x).如果X储存一大名单,你可以重获相当数量的内存净化X。同时,由于变量和一个函数具有相同的名字,你可以专门清理一个变量p,而不是一个函数p(X)。
The assignment operator is also used in the definition of a function or procedure.在赋值运算符也被用于定义一个函数或过程。
Variables can be used in function definitions, and that leads to an important difference between functions and variables.变量可以用在函数定义,这导致一种非常重要的区别函数和变量。 When a variable is defined, all terms of the definition are evaluated.当一个变量的定义是,所有的术语的定义进行了评估。 When a function is defined, its terms are not evaluated; they are evaluated when the function is evaluated.当一个函数的定义,其条件没有评价;他们正在评估当函数进行了评价。 That means that if a component of the function definition is changed, that change will be reflected the next time the function is evaluated.这意味着如果一个组件的功能定义也发生了变化,这变化可反映下次功能进行了评价。
e.g.例句。
IN:在: p:=2+3警:= 2 + 3 # 2+3 is evaluated at the time of assignment, p is assigned with 5.# 2 + 3评估转让时,p被指派5。
OUT: p := 5出:p:= 5
IN:在: p(x):=2+3p(x):= 2 + 3 # 2+3 is evaluated when the value of p(x) is requested,# 2 + 3评估价值时p(x)请求,
# p(x) is assigned with 2+3.# p(x)被指派2 + 3。
OUT: p(x) := 2+3出:p(x):= 2 + 3
If the left hand side of the assignment is a variable, it is the immediate assignment (i.e. expr2 is evaluated at the time of assignment); if the left hand side is a function, it is the delayed assignment (i.e. expr2 is evaluated when the value of expr1 is requested).如果左边的作业是一个变量,这是直接的任务(即expr2评估转让时);如果左边是一个函数,它是推迟任务(即expr2评估价值时的要求expr1)。
You can force all the components of a function to be evaluated when the function is defined by preceding the function with the command eval():你可以迫使所有的组件功能评估当函数被定义为之前的命令:功能():
f(x_) := eval(2+3)f(x_):=(2 + 3): # f(x_) is assigned with 5# f(x_)被指派5
Note that not only a variable but also any expression can be assigned. 注意:不是只有一个变量也是任何一个表述都可以转让。e.g. x := 2, sin(x)/cos(x) := tan(x), a>0 := 1.如x:= 2,罪(x)/因为(x):=褐色(x),一个> 0:= 1。
Clear a variable, function or expression from assignment by清理一个变量、函数或表现出让
clear(x)清晰的(x) # clear x from assignment.明确的任务。从x号
clear(f(x))清楚(f(x)) # clear f(x) from assignment.#清楚f(x)从任务。
clear(a>0)清楚(> 0) # clear a>0 from assume(a>0).从一个> 0 #清楚假设(> 0)。
There are two conditional functions:有两个条件功能:
if(test then x)如果(测试然后x)
if(test then x else y)如果(测试然后x别的y)
if(condition then x) gives x if condition evaluates to 1, or no output otherwise.如果情况。然后x)给x如果条件评估为1,或没有输出不然。
if(condition then x else y) gives x if condition evaluates to 1, y if it evaluates to 0, or no output if it evaluates to neither 1 or 0. 如果其他条件然后x y)给x如果条件对1,y如果它对0,或者没有输出如果它对没有1或0。The 2 words (then and else) can be replaced by comma ,.二字(然后和其他)可以被逗号。
It is useful in definition of the use-defined function to left the function unevaluated if the argument of the function is not number. 适用于定义的函数功能use-defined离开unevaluated如果参数的功能不号码。e.g. define f(x_) := if(isnumber(x), 1), then call f(x), f(10) gives 1, and f(a) gives f(a).例如定义f(x_):要是(isnumber(x),1),然后叫f(x)、f(10)给1,f(一个)给f(a)。
You can use two kinds of loops in SymbMath, fixed length loops controlled by do() and variable-length loops controlled by repeat(). 你可以使用两种循环在SymbMath、固定长度控制回路做的()和可变长循环重复控制()。The do() loop is similar to the FOR loop in BASIC language.做的()的循环是类似于循环的基本语言。
The control variable in the do() loops is not limited to integer values. 控制变量的做的()循环并不局限于整数的价值观。You can say:你可以说:
do(f:=f+1, x from xmin to xmax step dx)(女:= f + 1,从x xmin xmax一步,dx)
It is similar to它与
FOR x := xmin TO xmax STEP dx在x:= xmin xmax一步,__
f:=f+1女:= f + 1
NEXT x下一个x
where xmin, xmax, and dx are real values.在xmin,xmax,dx是真实的价值。 If STEP dx is omitted, it defaults to 1.如果步骤dx被忽略,它默认值为1。
e.g.例句。
IN:在: x:=0谢:= 0
OUT: x := 0出:谢:= 0
IN:在: do(x:=x+1, j from 1 to 5 step 1)(= x + 1 x:[j].从1到5步1)
OUT: x := 5出:谢:= 5
The conditional loops are probably more useful than the do() loops if a number of iteration is unknown. 有可能是更有用的循环比做的()循环如果一些迭代是未知的。It is这是
repeat(y until test)重复(y,直到试验)
repeat(y, test)重复(y,测试)
The word (until) can be replaced by comma ,. 一个词(直到)可以被逗号。The repeat() repeats to evaluate f until the test is true (i.e. the result of the test is 1).重复()重复直到测试来评估f是真实的(即测验的结果是1)。
Example:例如:
IN:在: x:=1谢:= 1
OUT: x := 1出:谢:= 1
IN:在: repeat(x:=x+1 until x>5)重复(x:= x + 1直到x > 5)
OUT: x := 6出:谢:= 6
The switch sets or changes the switch status. 开关设置或更改开关状态。The switch status is unchanged in memory until the switch is assigned by the new value.开关状态不变直到开关在内存中分配的新的价值。
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Switch开关 Action行动
output := math输出:=数学 output form is math symbol notation, this is default.输出形式是数学的象征符号,这是默认值。
output := basic输出:=基本 output form is BASIC format.输出形式基本格式。
output := fortran输出:= fortran output form is FORTRAN format.输出形式是FORTRAN格式。
output := prolog输出:= prolog output form is PROLOG format (internal form).输出形式是PROLOG格式(内部形式)。
output := off输出:=了 not display output.不显示输出。
output := on输出:=在 the same as output := basic一样的输出:=基础
lowercase := on小写:=在 convert letters into the lower-case letters.小写字母转换成文字转化成的。
lowercase := off小写:=了 not convert letters into the lower-case letters, this is default.小写字母转换的不信,这是默认值。
numeric := on数字:=在 convert numbers to floating-point numbers.转换为浮点数数字。
numeric := off数字:=了 not convert numbers to floating-point numbers, this is default.数字不转换浮点数,这是默认值。
expand := on拓展:=在 expansion. 扩张。e.g. c*(a+b) to c*a+c*b.如c * a + b)c * + c * b。
expand := off拓展:=了 disable expansion, this is default.禁用扩张,这是默认值。
expandexp := onexpandexp:=在 expand exponent. 扩大指数的增大而减小。e.g. c^(a+b) to c^a*c^b.如c ^(a + b)c ^ ^一个度b。
expandexp := offexpandexp:=了 disable exponent expansion, this is default.伤残指数扩张,这是默认值。
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When the switch output := math, the output displays the math symbol notation.当水开关输出:=数学,数学符号输出显示符号。
When the switch output := basic, the output form is the BASIC language format.当水开关输出:=基本,输出形式语言的基本格式。
When the switch output := fortran, the output form is the FORTRAN language format.当水开关输出:= fortran,fortran语言形式输出格式。
The default switch is output := math.默认的开关输出:=数学。
The output switch only changes the output format, neither affects the internal format nor the calculation.唯一的改变输出开关输出格式,也不影响内部格式计算。
When the switch lowercase := on, all letters are converted into the lower-case letters so the upper- and lower- case letters are the same, e.g. EXP(x) is the same as exp(x).当水开关小写:=,所有的信件都转化成小写字母所以上- - - - - - - - - - - -字母和较低的情况下,都是一样的,例句。经验(x)是一样的经验(x)。
Example:例如:
IN:在: 1/21/2
OUT: ½出:½
IN:在: numeric := on数字:=在
IN:在: 1/21/2
OUT: 0.5出:1 .
Example:例如:
IN:在: a*(b+c)一个*(b + c)
OUT: a (b + c):一个(b + c)
IN:在: expand := on拓展:=在
IN:在: a*(b+c)一个*(b + c)
OUT: a b + a c:一个b + c
Example:例如:
IN:在: exp(a+b)实验a + b)
OUT: e^(a + b)出:e ^(a + b)
IN:在: expandexp := onexpandexp:=在
IN:在: exp(a+b)实验a + b)
OUT: e^a e^b出:e ^ ^一个e b
The format of the readfile statement is格式的声明是readfile
readfile("filename")readfile(“文件名”)
The filename is any MS-DOS file name. 文件名是任何ms - dos文件名。If the file is not in the current directory, the filename should include the directory. 如果文件不在当前的目录中,这个文件应包括目录。e.g.例句。
readfile("directory\filename")readfile(“目录\文件名”)
e.g. read a file named "inte.sm":如读文件命名为" inte.sm”:
readfile("inte.sm")readfile(“inte.sm”)
It seems to copy the file into the user program.这似乎把这个文件复制到用户程序。
After a file is read, you can call any part of this package from a second package, as it seems the part of the first program has already been in the second program. 一个文件阅读后,你可以叫这个包的任何部分从一个包裹,好像第一个程序的一部分已经在第二计划。you can read many files into the SymbMath program at a time. 你可以阅读许多文件到SymbMath程序的一段时间。However, all names of the variables are public and name conflicts must be avoided.然而,所有名字的变量名必须公开和避免冲突。
Write a file to disk by写一个文件到磁盘
openfile("file")一个打开文件(“文件”)
do something做一些
closefile("file")closefile(“文件”)
Table 17.3.7.17.3.7表。 Reading and Writing Statements阅读和写作报表
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readcharreadchar read a character from读一个字符 keyboard.键盘。
readlinereadline read a line of strings from keyboard.读一行字符串从键盘。
readfile("file")readfile(“档案”) read (run or include) the file named "file".读(运行或包括)文件命名为"文件"。
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openfile("file")一个打开文件(“文件”) open the disk file "file" for writing.打开磁盘文件"文件"的写作。
closedfile("file")closedfile(“文件”) closed the file "file".关闭文件"文件"。
writes(s)写(s) write s on screen, only on graphics mode.在屏幕上写的年代,只是对图形模式。
newline换行符 write next text on a new line.在写新的一行下一篇课文。
null空 not write.不写。
block(a,b)块(a,b) write the value of the last argument, b.写的最后一个参数值,b。
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where the filename is any MS-DOS filename.在ms - dos文件名是任何文件名。
Note that the file must be closed by the closefile() command when writing a file with the openfile() command, but the file is automatically closed after reading the file. 注意文件都必须关闭的closefile()指令当写一份文件与一个打开文件()指令,但文件后自动关闭阅读文件。There must be the end statement at the end of file for reading.必须在最后声明的文件结束阅读。
SymbMath can read expressions from a disk file, then manipulate the expression, and finally write the result into another disk file.能读懂表达SymbMath从一个磁盘文件,然后操纵表达式,最后写结果到另一个磁盘文件。
Example: an expression y:=x^6 is already in the file "y.in",例如:一个表达式杨:= x ^ 6已经在文件”y.in”,
The contents of the file "y.in":文件的内容”y.in”:
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y:=x^6杨:= x ^ 6
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Run this SymbMath program运行这个程序SymbMath
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readfile("y.in")readfile(“y.in”) # read the expression y:=x^6 from the file "y.in"#阅读表达杨:= x ^ 6从文件”y.in”
openfile("y.out")一个打开文件(“y.out”) # open a disk file "y.out" for writing打开一个磁盘文件号”y.out”的写作
d(y,x)d(y,x) # differentiate y and write the result to the file分化并写# y结果文件
closefile("y.out")closefile(“y.out”)# close the file and return output to SymbMath#关闭文件和回报SymbMath输出
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The contents of the file "y.out":文件的内容”y.out”:
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6*x^56 * x ^ 5
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In this way you can interface to other software (see 3.7. 这样,你就接口,与其他软件(见3.7。Interface with Other Software).协同其他软件)。
These outputs in the disk file can be edited in the Edit window or the Aux Edit window.这些输出在磁盘文件会被编辑在编辑窗口或辅助编辑窗口。
It is recommended to use the BASIC output format by setting the switch output := basic when you write the output into the disk file. 建议在使用基本的输出格式设置开关输出:=基本当你写输出到磁盘文件。The default switch is output := math.默认的开关输出:=数学。
You can executes a DOS command in SymbMath language by你可以执行一个DOS命令语言在SymbMath
system("dir")系统(“目录”)
The all above statements are simple statements. 上述声明是简单的语句。The sequence statement specifies that its component statements are to be executed in the same sequence as they are written. 声明指出序列组成它的语句是实行同样的顺序都写。They are separated by the separators (comma ","). 他们分隔开来分离器(逗号”、“)。e.g.例句。
a+b, 2+3+ b,2 + 3
A library is a file of an external function, which filename is its function name within 8 letters plus extension .li. 图书馆是一个外部功能的一个文件,文件名是它的函数的名字加上延伸在8字母来将您引见给李先生。e.g. the library named sin.如图书馆命名的罪。li is a file of the sin(x) function definition.李是一个文件的罪(x)函数定义。
The library (the *.图书馆(*。LI file) is similar to the MS-DOS *.李的文件)类似的ms - dos *。BAT file. 蝙蝠的文件。You do not need to load or read the library by any command. 你不需要下载或读取任何命令的图书馆。SymbMath automatically load the library when it is needed. SymbMath自动载入图书馆当它是必要的。For example, when you use the sin(x) function first time, the library sin.例如,当你使用罪(x)功能的第一次,图书馆的罪。li will be auto-loaded. 李将auto-loaded。The library must be in the default directory, otherwise the library is not loaded and the function is not working. 图书馆必须是默认目录,否则装载并不是图书馆功能不工作。Only the assignments in the library can be loaded, and others in the library will be omitted, but all of these assignments will be not evaluated when they are loaded. 在图书馆里只有作业能够被加载,及其他图书馆将会被忽略掉,但是所有的这些作业将不被计算当他们装载。You can clear the library sin.你可以用来清除图书馆的罪。li from memory by clear(sin(x)).李从记忆清晰(罪(x))。
You can have libraries (external functions) as many as your disk space available. 你可以有图书馆(外部功能)多达你的磁盘的可用空间。You should use the "one function per file" convenience.你应该用“一个功能每一文件“便利。
Note that all names of the variables in libraries and packages are public (global) except for those declared by local() and name conflicts must be avoided.注意所有的变量名和包在图书馆公共(全球),除了那些宣布由当地(),必须避免命名冲突。
A package is the SymbMath program file which filename has not包裹,SymbMath程序文件的文件名 extension .LI. 扩展来将您引见给李先生。It is recommended that its filename has the extension .SM.建议其文件名已经扩展.SM。
A package is similar to a library, but the package must be read by a command一个包裹类似于一个图书馆,但方案必须阅读的命令
readfile("filename")readfile(“文件名”)
The filename can be any MS-DOS filename. 文件名可以是任何ms - dos文件名。It is recommended that the filename is same function name used in your program, plus the extension .sm. 建议文件名是相同的函数名在你的程序里使用,再加上.sm延伸。e.g. inte.例如交互。sm is the filename of the integral package as the name of integral function is inte(). sm是文件名的整体包装看作积分函数的名字是强烈的()。If the file is not in the current directory, the filename should include the directory. 如果文件不在当前的目录中,这个文件应包括目录。e.g.例句。
readfile("directory\filename")readfile(“目录\文件名”)
After reading the package, you can call the commands in the package from your program.读完包裹,你可以打电话到命令你的程序在寄来的包裹。
The readfile() command must be in a single line anywhere.readfile()的命令都必须在一个单独的一行代码到任何地方。
Many packages can be read at a time.许多软件包可以读一次。
You can convert a package of f.sm into a library by renaming f.sm to f.li for auto loading, or a library f.li to a package by renaming f.li to f.sm for not auto loading.你可以把包f.sm成一个图书馆,重命名f.sm f.li汽车荷载作用下,f.li或图书馆对一个包裹,重命名f.li f.sm不自动加料。
You can get help for all libraries by the library Index command in the Help menu. 你可以得到帮助,为所有图书馆的指挥,在图书馆指标帮助菜单中。You first open the library index window by this command, then open a library by selecting its library name in the library index window.你第一次打开窗户图书馆指数这个命令,然后打开一个图书馆,图书馆的名字选择在图书馆指标的窗口。
There are many libraries and packages. 有许多可用,包装。The following are some of them.以下是其中的一些。
Table 17.4.1表17.4.1 Libraries图书馆
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File Name档案名称 Function功能
plot.liplot.li plotting functions.绘图功能。
d.lid.li derivatives.衍生品。
inte.liinte.li integrals.积分。
sin.lisin.li sin(x) function.罪(x)的功能。
cos.licos.li cos(x) function.因为(x)的功能。
fac.lifac.li n!.n。
sign.lisign.li sign(x) function.签署(x)的功能。
abs.liabs.li abs(x) function.abs(x)的功能。
arg.liarg.li arg(x) function.高温(x)的功能。
sum.lisum.li sum function.sum函数。
NInte.liNInte.li numeric integration.数字集成。
NSolve.liNSolve.li numeric solver of equation.方程的数值求解。
DSolve.liDSolve.li differential equation solver.微分方程求解器进行求解。
gamma.ligamma.li gamma function.伽玛函数。
ei.liei.li exponential integral function.指数积分函数。
series.liseries.li Taylor series.泰勒级数。
partSum.lipartSum.li partial sum.部分之和。
infSum.liinfSum.li infinite sum.无限的总和。
sinh.lisinh.li sinh(x) function.sinh(x)的功能。
cosh.licosh.li cosh(x) function.事业(x)的功能。
average.liaverage.li average([x]) function.平均(x)的功能。
listSum.lilistSum.li sum of list of data.笔列表的数据。
react.lireact.li chemical reactions database.化学反应的数据库。
phoneNo.liphoneNo.li phone No. 电话号码。database.数据库。
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Table 17.4.2表17.4.2 Packages包
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init.sminit.sm initial package when running the program in当初始包装运行程序
the Input window. 输入窗口。It contains switches on the default status.它包含缺省状态开关。
chemical.smchemical.sm the atomic weight of chemical elements.化学元素的原子的重量。
ExpandTr.smExpandTr.sm expansion of trig functions.扩大三角法的功能。
expandLn.smexpandLn.sm expand ln(x*y).扩大淋巴结(x性感)。
ExpandGa.smExpandGa.sm expand gamma(n,x).扩大伽玛(氮、x)。
ExpandEi.smExpandEi.sm expand ei(n,x).扩大ei(氮、x)。
units.smunits.sm an units conversion.一个单位的转换。
listPlot.smlistPlot.sm plotting a list of data.策划一个列表的数据。
plotData.smplotData.sm interfacing software PlotData.PlotData接口软件。
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When a program is run in the Input window, SymbMath first automatically reads (or runs) the initial package "init.sm". 当一个程序运行在输入窗口,SymbMath第一自动读(或跑)初始包装”init.sm”。The commands in the "init.在“初始的命令。sm" package seems to be the SymbMath system commands. sm“一揽子似乎是SymbMath系统命令。You can read other packages (e.g. f.sm) in the initial package "init.你可以阅读其他软件(如f.sm)在初始包装”的初始化。sm", so the commands in the package "f.sm" seems to be in SymbMath system. sm”,因而在命令在包”f.sm”似乎都在SymbMath系统。You do this by adding the readfile("f.sm") into the init.你这样做,通过增加readfile(“f.sm”的初始。sm file:sm文件:
readfile("f.sm")readfile(“f.sm”)
The lnexpand.lnexpand的。sm package does the logarithmic expansion. 包装是否sm对数扩张。e.g. ln(a*b) is expanded into ln(a)+ ln(b).例如淋巴结(* b)是扩展到淋巴结(a)+淋巴结(b)。
SymbMath recognises 100 symbols of chemical elements and converts them into their atomic weights after the chemical package of "Chemical.100个符号识别SymbMath化学元素的原子的重量将他们转换成在化学包"的化学物质。sm" is read.sm”是阅读。
Example:例如:
Calculate the weight percentage of the element C in the molecule CH4.重量的百分比计算元素的CH4分子C。
IN:在: readfile("chemical.sm")readfile(“chemical.sm”)
IN:在: numeric := on数字:=在
IN:在: C/(C+H*4)*100*%C / C + H * 4)* 100 * %
OUT: 74.868 %出:74.868%
Example:例如:
Calculate the molar concentration of CuO when 3 gram of CuO is in 0.5 litre of a solution.摩尔浓度计算时的3克措措在0.5公升的解决办法。
IN:在: readfile("chemical.sm")readfile(“chemical.sm”)
IN:在: numeric := on数字:=在
IN:在: g:=1/(Cu+O)*mol宾客:= 1 /(铜+ O)*组分
IN:在: 3*g/(0.5*l)3 * g /(0.5 * l)
OUT: 0.07543 mol/l出:0.07543水解/ l)
You can run SymbMath from another software as a engine. 你能跑的SymbMath从另一个软件作为一个引擎。Anthoer software sends a text file to SymbMath, then run SymbMath in background, get result back from SymbMath.Anthoer软件发送一个文本文件去SymbMath,然后运行SymbMath背景,得到的结果SymbMath回来。
Interface with other software, (e.g. CurFit, Lotus 123) is similar to interface with the software PlotData in the plotdata package "plotdata.sm".与其它的软件接口,(例句。CurFit”、“荷花123)也类似与接口软件PlotData在PlotData包”plotdata.sm”。
After load the file "plotdata.在“plotdata装载文件。sm", the functionssm”,功能
plotdata(y, x)plotdata(y,x)
plotdata(y, x from xmin to xmax)plotdata(y,从x xmin到xmax)
plotdata(y, x from xmin to xmax step dx)plotdata(y,从x xmin xmax一步,dx)
plot a function of y by mean of the software PlotData. 地块功能的软件的y用均值PlotData。The plotdata() first opens a file "SymbMath.plotdata()的第一次打开一个文件”SymbMath。Out" for writing, then write the data table of the y function into the file "SymbMath.出去”写作,然后写数据表的功能到文件y”SymbMath。Out", then close the file, and finally call the software PlotData to plot. 出去”,然后关闭该文件,最后打电话给软件PlotData策划。These are done automatically by plotdata(). 这些做了自动plotdata()。After it exits from PlotData, it automatically return to SymbMath.出口PlotData后,它将自动返回SymbMath。
When SymbMath is interfaced with the software PlotData, SymbMath produces the data table of functions, and PlotData plots from the table. 当SymbMath是软件PlotData曼德拉,SymbMath生产数据表的功能,PlotData小块从桌子上。So SymbMath seems to plot the function. 所以SymbMath似乎情节的作用。This interface can be used to solve equations graphically.这个接口可以用来解决方程图。
Example:例如:
plot x^2 by interfacing software PlotData.情节x ^ 2 PlotData接口软件。
IN:在: readfile("plotdata.sm")readfile(“plotdata.sm”)
IN:在: plotdata(x^2, x)plotdata(x ^ 2、x)
in the software PlotData, you just select the option to read the file "SymbMath.在软件PlotData,你只要选择以“SymbMath阅读文件。Out" and to plot. “和阴谋。PlotData reads the data in the SymbMath format without any modification (and in many data format).PlotData读取数据在SymbMath格式不作任何修改(在许多数据格式)。
In PlotData,在PlotData,
in the main menu:在主菜单中。
1 <Enter>1 <进入>
in the read menu:在看菜单:
2 <Enter><进入> 2
<Enter><进入>
in the main menu:在主菜单中。
2 <Enter><进入> 2
in the graph menu:在图菜单:
1 <Enter>1 <进入>
where <Enter> is the <Enter> key. 在<进入> <进入>是关键。Refer to PlotData for detail.指PlotData细节。
SymbMath includes extensive facilities for graphing. SymbMath广泛的设施包括图。It supports BGI graphics, which graphics commands are the same as those in Borland Turbo Pascal and Turbo C, except for:它支持开的图形,图形命令是一样的那些火鸟帕斯卡,涡轮增压C,除了:
different graphics commands不同的图表命令
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SymbMathSymbMath Turbo Pascal or C涡轮Pascal或C
graph图 initgraph(drive,mode,path)initgraph(驾车、模式、路径)
text文本 closegraphclosegraph
writes(x)写(x) outtext(x)outtext(x)
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Note that if your monitor is Hercules, you must load the MSHERC.注意,如果你的显示器是海格力斯,你必须装载MSHERC。COM program as a TRS program before you run PlotData. COM程序作为地球跑之前先PlotData程序。Otherwise you will get Error when you plot.否则你将会得到错误当你的情节。
Before graphing (drawing or plotting), you must initialize the graphics system and puts the computer hardware into graphics mode by the command:在图(图纸或策划),那么你必须初始化图形系统,把计算机硬件到图形模式由命令:
graph图
then you can draw a line by然后你可以画了一条线
line(x1,y1,x2,y2)线(x1,x2,y2,日元)
lineto(x2,y2)lineto(x2,y2)
linerel(dx,dy)linerel(dx,去世)
draw a circular arc by画一个圆弧
arc(x,y,angle1,angle2,radius)弧(x,y,angle1,angle2、半径)
draw an elliptical arc by画了一个椭圆弧形
ellipse(x,y,angle1,angle2,XRadius,YRadius)椭圆(x,y,angle1,angle2,XRadius,YRadius)
put a pixel by把一个像素的
putpixel(x,y,color)putpixel(x,y,颜色)
you can move a pointer by你可以移动一个指针
moveto(x,y)moveto(x,y)
moverel(dx,dy)moverel(dx,去世)
A upper left corner on your graphics screen coordinates is (0,0).一个在你的图片左上角屏幕坐标是(0,0)。
The style of the line can be set by线的风格,可以设置
setlinestyle()setlinestyle()
You can set screen colors. 你可以设置屏幕颜色。If you are using a color system, you can set the color of the next line or graph or text with the command:如果你正在使用一种颜色系统,你可以设置你的颜色的下一行或图形或文本的命令:
setcolor(color)setcolor(颜色)
where color is color number (i.e. an integer in the range 0..15), or one在颜色的色号(即一个整数范围0 . . 15),或者一个吗 of the colorno(x) function value.colorno(x)的功能价值。
You can set the background color for your graphs with the command你可以设置背景颜色为你的图形和命令
setbkcolor(color)setbkcolor(颜色)
where color is color number (i.e. an integer in the range 0..15), or one在颜色的色号(即一个整数范围0 . . 15),或者一个吗 of the colorno(x) function value.colorno(x)的功能价值。
Table 18.1表18.1 ColorNo(x) function in the colorno.ColorNo(x)函数在ColorNo。li library李图书馆
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xx value价值
black黑色 00
blue蓝色 11
green绿色 22
cyan青色 33
red红 44
magenta洋红 55
brown布朗 66
lightgraylightgray 77
gray灰色 88
lightbluelightblue 99
lightgreenlightgreen 1010
lightcyanlightcyan 1111
lightredlightred 1212
lightmagentalightmagenta 1313
yellow黄色 1414
white白色 1515
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You can set line styles.你可以设置线的风格。
On both monochrome and color systems, you can draw lines and graphs with different line styles.两个单色和颜色系统,你可以画线和图线与不同风格。 (Since the line segments used to draw graphs are usually very short, different line styles may not be distinguished in graphs, but they will be distinguished on long lines.)(因为线提取图通常是用来画线很短,不同风格不得分为图,但是,他们都可以在漫长的杰出线。) Linestyles are indicated by integers in the range 0..Linestyles标于整数范围0 . .3, and are set by the command:(三)、设置由命令:
setlinestyle(style,u,thickness)setlinestyle(款式、u型、厚度)
where style, u and thickness are integers.在风格,你和厚度是整数。
You can set the text style by你可以设置文本风格
settextstyle(font,direction,size)settextstyle(字体、方向、大小)
where font, direction and size are integers.当字体、方向和大小是整数。
You can add labels to your graphs by你可以添加标签以你的图形
writes(s)写(s)
You can put alphanumeric labels anywhere on your graphic screens. 你可以把字母数字标签的任何你的图形屏幕。They can be horizontal or vertical, and they can be printed in various sizes. 他们可以是水平或垂直的,而且他们可以打印在各种尺寸。To print a string打印字符串 s年代 horizontally on the screen with the lower-left corner at the screen coordinates (x,y), use two commands:屏幕上的水平与lower-left街角的屏幕坐标(x,y),用两个命令:
moveto(x,y), writes(s)moveto(x,y),写(s)
To write vertically bottom to top, use two commands:写垂直底部向顶部,用两个命令:
settextstyle(1,2,2), writes(s)settextstyle(1、2、2),写(s)
If SymbMath attempts to graph a point (x,y) which is outside the the screen coordinate, it ignores the point and continues.如果SymbMath试图图点(x,y)外的屏幕坐标,而忽视了这一点并继续。 No error message is generated, and even functions which are undefined on part of the graphing domain can be graphed.没有错误讯息产生,甚至部分的功能都是未定义的域名可以图图标表示。
You can get the max x and max y on your graphics screen你能得到的最大的x和y在你最大的图形屏幕
coordinates by坐标系中通过
getmaxxgetmaxx
getmaxygetmaxy
You can get the current point(x, y) on your graphics screen coordinates by你可以得到当前点(x,y)在你的图形屏幕坐标
getxgetx
getygety
You can get the background color and foregroud color on your graphics screen by你能得到的背景颜色和foregroud你的图形屏幕颜色
getbkcolorgetbkcolor
getcolorgetcolor
You can read a character from the keyboard or pause by the command:你能读到一个角色从键盘或者暂停由命令:
readcharreadchar
You can clear graph by你可以清晰的图
cleardevicecleardevice
SymbMath auto goes back the text mode at the end of run. SymbMath汽车回到文本模式的尽头的运行。You can force it goes back the text mode by the command:你可以迫使它回到文本��式由命令:
text文本
Example:例如:
# drawing a group of circles and ovals.图一群圆形和椭圆形。
# Circles are 9 planets around sun.行星绕著太阳怪圈是9。
graph图 # graph mode#图形模式
do(circle(getmaxx*0.5+2.5*x,getmaxy*0.5,5), x,0,90,10)做的(圆(* * getmaxx 0.5 + 2.5 * 0.5 x,getmaxy,5)、x,0,- 90 10)
do(oval(getmaxx*0.5,getmaxy*0.5,2.5*x,x), x,10,90,10)做的(椭圆形(getmaxx getmaxy * * 0.5,0.5,2.5 * x,x)、x、10日、10)
readcharreadchar # pause graph by read a char通过阅读#停顿图进行计算
text文本 # back text mode#回到文本模式
You can plot a function of y = f(x) on the xy-plane by external function:你可以绘制功能的y = f(x)由外部初步评估一般航测作业功能:
plot(f(x),x)情节(f(x)、x)
plot(f(x),x,xmin,xmax)情节(f(x)、x、xmin,xmax)
plot(f(x),x,xmin,xmax,ymin,ymax)情节(f(x)、x、xmin,xmax,ymin,ymax)
plot(f(x),x,xmin,xmax,ymin,ymax,color)情节(f(x)、x、xmin,xmax,ymin,ymax,颜色)
f(x) can be either a functionf(x)可以当一个功能 with bound variable x or an expression involving x.有界变量x或表达式包括x。 For example, you could graph the parabola with the command plot(x^2,x).例如,你可以图抛物线的命令情节(x ^ 2、x)。
The xmin and xmax are range of x-axis, the ymin and ymax are range of y-axis. 这是xmin和xmax x的范围,ymin范围和ymax是���动。The default values are xmin=-5, xmax=5, ymin=-5, and ymax=5. 默认值是xmin = 5,xmax = 5,ymin = 5、ymax = 5。The values of xmin, xmax, ymin, ymax are real numbers, such thatxmin的价值,xmax,ymin,ymax是真实的编号,这样 xmin < xmaxxmin < xmax and和 ymin < ymax.ymin < ymax。 Thses values tell SymbMath that the visible screen corresponds to a portion of the xy-plane withThses价值观告诉SymbMath可见光屏幕对应一个部分的初步评估一般航测作业 xmin <= x <= xmaxxmin < = x < = xmax and和 ymin <= y <= ymax.ymin < < = = ymax y。
The operator plot() plots one point (x,f(x)) for each pixel on the x-axis, and connects successive points.接线员阴谋策划一个点()(x,f(x)),为每一个像素在x轴,连接连续分。 To omit the connections and just plot the points, use the command:省连接就绘制分,使用命令:
dotplot(f(x),x)dotplot(f(x)、x)
To plot only every 20th point, which is useful for rapidly graphing complicated functions, use20th策划只是点,有利于快速图复杂函数,使用
sketch(f(x),x)素描(f(x)、x)
If you want your circles and squares to look correct --that is, if you want one vertical unit to be really the same distance as one horizontal unit--you should select window parameters so that the horizontal axis is 1.4 times as long as the vertical axis.如果你想让你的圆圈和方框看上去正确的——也就是说,如果你想要一幢单位真的相同距离一横单位,你应该选择窗口参数使水平轴为1.4倍长垂直轴上。
Example 5.2:范例5.2:
plot x^3 and sin(x).x ^ 3罪情节(x)。
IN:在: graph图
IN:在: plot(x^3,x)情节(x ^ 3、x)
IN:在: plot(sin(x),x)情节(罪(x)、x)
You can plot the parametric functions of x=x(t) and y=y(t) by你可以绘制参数功能= x(t)x和y = y(t)
paraplot(x(t),y(t),t)paraplot(x(t),y(t),t)
paraplot(x(t),y(t),t,tmin,tmax)paraplot(x(t),y(t),t tmin,tmax)
paraplot(x(t),y(t),t,tmin,tmax,ymin,ymax)paraplot(x(t),y(t),t tmin,tmax,ymin,ymax)
Example:例如:
IN:在: graph图
IN:在: paraplot(sin(t),sin(2*t),t)paraplot(罪(t)、罪(2 * t),t)
You can graph the portion of a polar curve你可以图的一部分性能曲线 r = f(t) that lies in the window with external function:r = f(t),位于窗口的外部功能:
polaplot(f(t),t)polaplot(f(t),t)
polaplot(r, t,tmin,tmax)polaplot(r,t tmin,tmax)
polaplot(r, t,tmin,tmax,rmin,rmax)polaplot(r,t tmin,tmax,rmin,拒绝)
f(t) can be a function with bound variable t or an expression involving t.f(t)可以是一个函数有界变量t或表达式包括t。
Example:例如:
Plot a circle地块圈 r = 1 in polar coordinates.在极坐标r = 1。
IN:在: graph图
IN:在: polaplot(1,t)polaplot(1,t)
The variable t covers the domain (0, 2*pi); you can change this default by specifying a range for t:不包括域变量(0、2 * pi),你可以改变这个默认的指定范围内进行t:
polaplot(1, t,0,pi)polaplot(1,t 0,pi)
You can plot data by你可以阴谋数据
dataplot([x1,x2,...dataplot x1,x2([…], [y1,y2,...])]、[1,y2,……)
dataplot([x1,x2,...dataplot x1,x2([…], [y1,y2,...]、[1,y2,……], xmin,max)],xmin,马克斯)
dataplot([x1,x2,...dataplot x1,x2([…], [y1,y2,...]、[1,y2,……], xmin,xmax,ymin,ymax)],xmin,xmax,ymin,ymax)
dataplot([x1,x2,...dataplot x1,x2([…], [y1,y2,...]、[1,y2,……], xmin,xmax,ymin,ymax,link)],xmin,xmax,ymin,ymax,链接)
Example:例如:
IN:在: graph图
IN:在: dataplot([1,2,3], [1,4,9])dataplot([1、2、3]、[1,4,9])
You can plot a list of data by你可以绘制列表的数据
listplot([y1,y2,...])listplot([1,y2,……)
for x1=1, x2=2, x3=3, ....为x1 = 1、2 = 2 x3 = 3,....
Example:例如:
IN:在: graph图
IN:在: listplot([1,4,9])listplot([1,4,9])
You can fit a set of data into a function x^2你可以把一套数据到一个函数x ^ 2
Example 5.7.范例5.7。
IN:在: graph图
IN:在: dataplot([1,2,3,4],[1,4,9,16],0,5,0,20)dataplot([1、2、3、4]、[1、4号、9号,16],0、5 - 20)
IN:在: plot(x^2,x,0,5,0,20)情节(x ^ 2、x、0、5 - 20)
1. 1。Load the Graphics.载入图片。EXE file into memory in the DOS prompt byEXE文件到内存在DOS提示
c:\DOS\graphicsc:\ \图形DOS
2. 2。Run SymbMath, then display a graph on screen.SymbMath跑,然后在屏幕上显示一个图。
3. 3。Print Screen by pressing the <Print Screen> key on keyboard.打印屏幕按<打印屏幕>键键盘。
Note that you must load the Graphics.注意你必须装载图形。EXE file before you run SymbMath.你跑SymbMath EXE文件之前。
SymbMath is a multi-windowed editor in which you can copy-and-paste anywhere in a file and between files, even from the Help window.SymbMath是一个multi-windowed编辑器中,你可以拷贝和粘贴任何地方之间的一个文件时,文件,甚至从帮助窗口。
When you start SymbMath, the computer screen looks like:当你开始SymbMath,计算机的屏幕看起来像:
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| File|文件 Input输入 Run跑 Output输出 Color颜色 Help帮助 Example Keyword例如关键字 ||
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---------------------------------- Output ---------------------------------------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -输出- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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SymbMathSymbMath | Arrow keys and <Enter>, Highlight or first capital letter|箭头键和<进入>,突出或第一个字母
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The screen is divided into four areas: a menu line, an input window, an output window, and a status line.屏幕上分为四个方面的工作:一个菜单线、一个输入窗口,一个输出窗口,状态栏上。
The menu line is the main menu and locates in the top of the screen.菜单线主菜单和位于屏幕顶端。
The input window is a multi-windowed text editor for input.窗户是一个multi-windowed输入的文本编辑器,用于输入。
The output window is a multi-windowed text editor for output.窗户是一个multi-windowed输出的文本编辑器,用于输出。
The status line indicates the current status or which key to be active. 显示当前的状态行的地位或关键活泼。It places in the bottom of the screen. 它的地方,在底部的屏幕上。The content of the status line will be changed according to which active window.状态栏上的内容将会改变,根据该活动窗口。
In the menu line, the File, Color, and Help commands have its pull-down menus.在菜单线,文件,颜色,帮助命令有其拉菜单。
Select the menu by the arrow keys and <Enter>, or the first capital letter. 选择菜单箭头键和<进入>,或第一大写字母。The <Esc> key always escape from the current window and return to the previous window.《Esc >关键总是逃避当前窗口,回到以前的窗口。
A pop-up menu is the Edit Help menu.一个弹出菜单编辑帮助菜单中。
The File menu has 5 choices in the pull-down menu:有五种选择“文件”菜单中的“在拉菜单:
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| Open|开放 ||
| New|新 ||
| Save|拯救 ||
| DOS shell| DOS壳 ||
| Exit|出口 ||
----------------------- - - - - - - - - - - - - - - - - - - - - - - - - - -
The Open command opens a file for edit in the Input window. 打开命令打开一个文件对编辑输入窗口。This command first opens a Directory window to choose a file for edit. 这个命令首先打开一个目录窗口选择一个文件的编辑。In the Directory window, the following commands are available.在该目录下的窗口,下面的指令是很有用的。
Table 2.1表2.1 Commands in the Directory Window命令在该目录下的窗口
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Action行动 Keystrokes按键
file mask文件面具 <F4>, *.sm< F4 >,* .sm e.g. *.sm例句。* .sm
zoom window缩放窗口 <F5>< F5 >
zoom back变焦回来 <F5>< F5 >
resize window调整窗口 <Shift><F10>, then the -><- keys, <F10><转变> < F10 >,那么- - - - - - - - - - - - > < < F10 >键,
select选择 the arrow keys键盘上的方向键
page up页面 <Pg Up>< Pg起来>
page down页数下 <Pg Dn>< Pg Dn >
accept接受 <Enter><进入>
abort流产 <Esc>< Esc >
go to the x filename去x文件名 xx (where x is any single letter.)(在x是任何一个信。)
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You select a file from the Directory window to open for edit in the Input window.你选择一个文件目录窗口打开编辑输入窗口。
The New command creates a new file and clears the Input window.新命令创建一个新的文件和清除输入窗口。
The "Save Input" command saves the file in the Input window into disk under a different name or in a different directory.“拯救输入"的命令的文件保存到磁盘下输入窗口的一个不同的名称或在一个不同的目录。
The "Save Output" command saves the file in the Output window into disk under a different name or in a different directory.“拯救输出”命令节省文件窗口向外输出一个不同的名称或磁盘下在一个不同的目录。
The "DOS shell" command executes a DOS command and automatically returns to the SymbMath system if you provide a DOS command on the command window, otherwise it goes to the DOS shell, the control must be returned to the resident SymbMath system with the EXIT command on the DOS shell.“DOS壳”命令执行一个DOS命令和自动返回SymbMath系统提供一个DOS命令如果你命令窗,否则就会一直持续到DOS壳,控制必须回到居民SymbMath系统与出口的DOS命令外壳。
The Exit command exits from SymbMath.出口出口SymbMath命令。
The Input menu lets the control goes into the Input window. 输入菜单让控制进入输入窗口。To enter text (e.g. math expressions), type as though you were using a typewriter.进入文本(如数学表达式),键入好像你用打字机。
The Run menu executes the user program in the Input window, outputs the results in the Output window, and saves the output into the file named "output".运行菜单执行用户程序输入窗口,输出的结果,在输出窗口,节省输出到文件命名为“输出”。
Notice that it clears memory and executes the initial package "init.注意它清理记忆和执行初始包装”的初始化。sm" before it interprets the users program in the Input window.阐明了sm之前用户输入窗口的计划。
The Output command goes into the Output window.输出命令进入输出窗口。
The Output window is similar to the Input window, where you can edit any text. 输出窗口输入窗口相似,在那里你可以编辑任何文本。You can copy the output into your document by the block copy command in the editor.你可以复制输出到你的文档副本由块指挥,在编辑器。
In the Output window, the line with beginning of IN: is content of input, and the line with beginning of OUT: is the output.在输出的窗口,在符合开始:内容的输入,以及符合的开始:输出。
The output in the Output window is always saved into the "output" file输出在输出窗口总是保存在“输出”文件
The Color menu has 6 choices:颜色的菜单有6个选择:
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| Menu line线|菜单 ||
I Input window我输入窗口 ||
| input Border|输入边境 ||
| output Window|输出窗口||
| Output border|输出边境 ||
| Status line|状态行 ||
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When you choose one of them, a color pattern will come up. 当你选择其中一个,颜色模式将出现。There are 126 colours in the color pattern. 有126种颜色的颜色模式。Select your favour color by the arrow keys and <Enter>.选择你的忙颜色由键盘上的方向键和<进入>。
It is to change the menu line's color.这是改变菜单线的颜色。
It is to change the input window's color.这是改变输入窗口的颜色。
It is to change the input window border's color.这是改变输入窗口的边界的颜色。
It is to change the output window's color.这是改变输出窗口的颜色。
It is to change the output window border's color.这是改变输出窗边的颜色。
It is to change the status line's color.这是改变状态栏上的颜色。
The Help menu displays the syntax of SymbMath language.在帮助菜单中显示的SymbMath语法的语言。
In the Help menu, Each command has its own Help window and help file. 在帮助菜单,每条指令都有它自己的帮助窗口和帮助文件。The on-line help files are text (ASCII) files.在线帮助文件都是文本的ASCII文件。
In the Help window, to search for a special word, you first press <Ctrl><F3>, then type the word you want to search, finally press <Ctrl><F3> again. 在帮助窗口,寻找一个特别的词,你先按< Ctrl > < F3 >,然后输入您想要寻找的这个词,最后按< Ctrl > < F3 >了。e.g. if you want to search for the word "help", you first press <Ctrl><F3>, then type "help", finally press <Ctrl><F3> again. 如果你想寻找的那声“救命”,你先按< Ctrl > < F3 >,然后输入“帮助”,最后按< Ctrl > < F3 >了。The cursor will go to the word "help". 光标会去的那声“救命”。You press <Shift><F3> to repeat the last find.你按<转变> < F3 >重复过去的发现。
The commands in the Help window are the same as that in the Edit window, except that text is unable to be changed, (see Chapter 2.9 Editor).在帮助窗口的命令是一样的,在编辑窗口,除了文字无法改变,(见章节2.9编辑)。
Table 19.6表19.6 Commands in the Help window命令的帮助窗口
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Action行动 Keystrokes按键
move the cursor移动光标 the arrow keys键盘上的方向键
zoom in window放大窗口 <F5>< F5 >
zoom out window缩小窗口 <F5>< F5 >
exit from the window出口从窗户 <Esc> or <F10>< Esc >或< F10 >
go to the beginning of the line去开始的线 <Home><回家>
go to the end of the line走到生命的尽头 <End><结束>
page up页面 <Pg Up>< Pg起来>
page down页数下 <Pg Dn>< Pg Dn >
go to the beginning of window去开始的窗户 <Ctrl><Home>< Ctrl > <回家>
go to the end of the window走到天涯的窗口 <Ctrl><End>< Ctrl > <结束>
go to the beginning of the file去文件的开头 <Ctrl><Pg Up>< Ctrl > < Pg起来>
go to the end of the file去文件的末尾 <Ctrl><Pg Dn>< Ctrl > < Pg Dn >
go to nth line去第n次线 <Crtl><F2>, No.< Crtl > < F2 >,没有。, <Crtl><F2>,< Crtl > < F2 >
find the special word找到特别的词 <Ctrl><F3>, "word", <Ctrl><F3>< Ctrl > < F3 >,“字”,< Ctrl > < F3 >
repeat last find重复上找到 <Shift><F3><转变> < F3 >
re-size windowre-size窗口 <Shift><F10>, the arrow keys, <F10><转变> < F10 >,键盘上的方向键,< F10 >
go to x去x xx
(where x is the first letter of filename)(在x是第一个字母文件名)
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In the Input, Output and Aux Edit windows, press <F1> to pop-up the Edit Help menu.在输入、输出和辅助编辑窗口,按< F1 >,编辑帮助菜单弹出。
The Example menu shows examples in the SymbMath language.这个例子菜单显示的例子SymbMath语言。
The Keyword menu shows keyword in the SymbMath language.关键词菜单显示SymbMath语言中的关键词。
The Topic command opens a help window for the keywords in topic order.这个话题命令打开帮助窗口的关键词主题秩序。
The Alphabetical order command opens a help window for the keywords in alphabetical order.字母顺序命令打开帮助窗口的关键词按字母顺序排列的。
The Index command opens an index window, where you can select a keyword (file *.key) to open a help window for its file. 索引命令窗口打开一个指标,在那里你可以选择一个关键字(文件* .key)来打开一个窗口,它帮助文件。e.g. if you want to help for the keyword d, you press d and <Enter> to open the help file d.key.如果你想要帮助,为关键词d,你按d和<进入>打开d.key的帮助文件。 If the keyword is longer than 8 letters, its filename is the first 8 letters plus extension .key.如果关键词是超过8字母,它的文件名是第一个字母加上扩展.key 8。
The Library index command is similar to the Index command, but it opens a library index window for library (external function file *.li).图书馆索引命令相似指数的命令,但它会打开一个图书馆,图书馆指标窗口(外部功能文件*来将您引见给李先生)。
SymbMath includes a multi-windowed text editor for creating and modifying program files. SymbMath包括一个multi-windowed文本编辑器来创建和修改程序文件。Usage of the editor is similar to WordStar in non document mode, to Borland's SideKick, or to Borland's C compiler.使用的编辑是类似于用非WordStar文件方式,宝兰的伙伴,或火鸟的C编译器。
You can execute the edit commands either by selecting the edit commands in the Edit Help menu or by keystrokes.你可以执行编辑命令要么通过选择编辑在编辑帮助菜单命令或按键。
Open the Edit Help menu by pressing <F1> within the Input window, the Aux Edit window, or the Help window.在帮助菜单中打开编辑按< F1 >输入窗口内,辅助编辑窗口,或者帮助窗口。
This menu has 11 choices:这个菜单拥有11个选择:
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| Show help file|显示帮助文件 ||
| Cursor movement|光标移动 ||
| Insert & Delete|插入和删除||
| Searching|搜索 ||
| Block functions|块函数 ||
| Special block functions|特殊块函数||
| File functions|文件功能 ||
| Application keys|应用键 ||
| Miscellaneous|杂 ||
| Global functions|全球功能 ||
| Hot keys|热键 ||
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Except for the first choice of the "Show help file", others have their own sub-menu. 除了第一选择“显示帮助文件”,其他都有自己的子项目中。You can select the edit command in the sub-menu by the up or down key and <Enter>.你可以选择编辑命令在子项目向上或向下的关键和<进入>。
This command opens a help window to show a help file.这个命令打开一个帮助窗口来显示一个帮助文件。
This command opens a menu for the cursor movement commands.这个命令打开一个菜单中光标移动命令。The functionality of most of the cursor-movement commands is straight forward. 大部分的功能指令cursor-movement俱各直往前行。In this section, only the "non-obvious" commands will be explained.在本节中,只有“明显的”命令会解释说。
Scroll Up向上滚动
The text scrolls one line up. 一行文本卷轴。The cursor will be at same physical line on the computer-screen光标将在同一物理computer-screen路线上
Scroll Down向下滚动
The text scrolls one line down. 一行文本卷轴下来。The cursor will be at the same physical line on the computer-screen.光标将在相同的物理computer-screen路线上。
Previous Position先前位置
Moves the cursor to its position just prior to the last command. 的光标位置,就在最后的命令。For instance, if you inadvertently press Goto Text start, moving your cursor to the top of the file, you can press Previous Position to get back to where you were.例如,如果你不经意的新闻到文本开始,你移动光标到上面的文件,你可以按先前位置回到你上哪儿去了。
Goto Line线扫描
Moves the cursor to the line number you specify.移动光标移到你指定的行数。
Goto Position岛的位置
The position is the number of characters from the text start. 这个职位是文本的数量的字符开始。New lines and tabs are both counted as one character.新的生产线和制表符都算作一个字符。
Goto Blockstart到Blockstart
Moves the cursor to the block-begin marker that you already have set with Mark blockstart. 移动光标移到block-begin标记,你已经设定马克blockstart。The command works even if the block is not displayed (see "Hide/display block" under "Block Commands"), or if the block-end marker is not set.指挥工作就是块是不显示(参见“隐藏/显示块”,在“块命令”),或者如果block-end标记是不确定的。
Goto Blockend到Blockend
Moves the cursor to the block-end marker that you have already set with Mark Blockend. 移动光标移到block-end标记,你已经设定马克Blockend。The command works even if the block is not displayed (see "Hide/display block") or the block-begin marker is not set.指挥工作就是块是不显示(参见“隐藏/显示块”)或block-begin标记是不确定的。
To write a program, you need to know more than just how to move the cursor around. 编写一个程序,你需要了解更多的只是如何移动光标。You also need to be able to insert and delete text. 你也必须能够进行插入和删除的文本。The following commands insert and delete characters, words, and lines.下列命令插入和删除字符、词和线路。You can also insert blocks of text from other files - refer to "The Auxiliary Editor" later in this chapter.你也可以插入块的文本,从其他的文件-指的"辅助编辑器”在本章后面。
Insert Line插入线
Inserts a line break at the cursor position.插入一个换行游标目前的位置。
Delete character left of cursor删除字符剩下的游标
Moves one character to the left and deletes the character positioned there by backspace. 一个字符移动到左边和删除角色定位在退格。Any characters to the right of the cursor move one position to the left. 对任何字符位置的光标移动到左边。You can use this command to remove line breaks.你可以使用这个命令删除换行符。
Delete character under cursor删除字符下,光标
Deletes the character under the cursor and moves any characters to the right of cursor one position to the left. 删除性状在移动光标和字符右边的光标一个位置移动到左边。This command works across line breaks, and can be used to remove them.这个命令的作品在换行符,并可以用来移除他们。
Delete word right of cursor删除的话对光标的
Deletes the word to the right of the cursor. 删除了词的权利,光标。A word is defined as a sequence of characters delimited by one of the following characters:一个词被定义为一种字符序列组成的一个划如下特征:
space < > , ; . 空间< >,。( ) [ ] ^^()[] ' * + - / $" * + - /美元
This command does not work across line breaks.这条命令不会工作中遇到换行符。 Press Paste to undo a deleted word.按粘贴到撤销删除的话。
Delete from cursor to start of line从开始删除指针的线
Seletes all text from the cursor position to the beginning of the line. 从Seletes所有文本光标位置开始就行了。To undo this command press Paste.解除这个命令按粘贴。
Delete from cursor to end of line从指针删除结束的线
Selects all text from the cursor position to the end of the line. 选中所有文本,从光标位置到生命的尽头。To undo this command press Paste.解除这个命令按粘贴。
Delete line删除线
Deletes the line containing the cursor and moves any lines below one line up. 删除线移动光标,包含任何线条下一排好队。To undo a line delete, use Paste.为代价的一行删除,使用粘贴。
The editor supports search and replace commands that let you search for strings in the text and replace them with other strings. 编辑支持搜索和替换的命令,让你搜索和替换字符串文本中他们和其他的字符串。Replacement can optionally be prompted (ask yes/no at each replacement).更换可以随意地促使(要求是/否在每个置换)。
Search搜索
Lets you search for a string of up to 45 characters. 让你寻找一个字符串高达45字符。When you enter this command, the status line is cleared, and the prompt当你进入这个命令,状态栏上清理,提示
search text, text:搜索文本,文本:
appears at the bottom of the Edit window. 出现在编辑窗口的底部。Enter the string you are looking for and then press Search again. 输入字符串你正在寻找,然后按下再重新搜索。The search string can contain any characters, including control characters. 搜索字符串可以包含任何字符,包括控制字符。To quit the search operation, use the abort command <Esc>.放弃搜索操作,使用终止命令< Esc >。
Search again再重新搜索
Moves the cursor to the next occurrence of the last used search-string.移动光标到下一个出现的最后一search-string使用。
Replace取代
This operation works identically to the Find command, except that you can replace the "found" string with any other string of up to 45characters. 这个手术的作品同发现指令,但有一点除外,即你可以替换字符串“发现”与其他串高达45字符。First, enter the search string and press Replace, the editor prompts you for the string that will replace the search string. 首先,进入搜索字符串和按下更换,编辑提示你的字符串,它将取代搜索字符串。Enter up to 45 characters, press Replace again.进入到45特点,按更换一次。
The next prompt (prompt before replacing (y/n)) can be answered Yes or No: y means you decide whether an occurrence of the string will be replaced, while n means the editor will replace it automatically.下一个提示(迅速取代之前(y / n))可以回答“是”或“否”:y意味着你决定是否发生的字符串将被取代,而n意味着编辑将取代,它会自动。
When the editor finds the items--and of the N option is not specified-it then positions the cursor at the start of the item, and asks当编辑发现项目和N选项——不是specified-it然后光标位置,在开始一个道具,问道
Replace Yes/No/Rest (y/n/r) ?取代是的/没有/休息(y / n/r)?
in the prompt line. 在迅速的线。You can abort the Find/Replace operation at this point with the Abort command <Esc>. 你可以放弃的查找替换操作在这一点上与终止命令< Esc >。Press the Y-key and the word at the cursor will be replaced with the replace-string, and the cursor moves to the next occurrence of the search string. 按Y-key道在光标会被替换replace-string,光标就会移动到下一个出现的搜索字符串。Press the R-key and this and all subsequent of the search-string on replaced automatically.按R-key这及随后的search-string取代自动。在
Replace Again取代又
Finds the next occurrence of the last used search string and prompts for replacement with the last used replace-string.发现未来发生的最后使用搜索字符串替换和提示,与去年replace-string使用。
Wordstar Search and Replace commendsWordstar搜索和替换的任务吧
These four commands is almost identical to the four described above. 这四个命令是几乎相同的四个以上所描述的。The only difference is that the user input is terminated with <Enter> and not the commandkeystroke. 唯一的区别是终止用户输入与<进入>而不是commandkeystroke。This means that it's not possible to search for new lines.这意味着不可能寻找新的生产线。
A block of text is any amount of text, from a single character to hundreds of lines, that has been surrounded with special block-marker characters. 一块文本是任何数额的文本,从单一字符几百行的,已经被包围了特殊block-marker字符。You can only mark one block in a source text at a time.你只能标记一个块在源文本的一段时间。
Three different kinds of block-marking commands can be used in the editor, and the commands are: WordStar-like block commands, MultiMate-like block commands and Sprint-like block commands. 有三种不同的block-marking命令可以用于编辑,命令是:WordStar-like块的命令,命令和Sprint-like MultiMate-like块街区的命令。The overall concept for each of the three command-categories can be summarised as follows:整体的概念,每一种都有command-categories可以归纳如下:
Sprint like commands冲刺喜欢命令
Place the cursor at the beginning at the block - press Block select. 将光标在块开始-压块选择。Now move the cursor to the blockend (the block will be highlighted as you go). 现在移动光标移到blockend(块将突出你去)。When at the blockend, select a function to be performed of the block.blockend时,选择一个功能进行一个街区。 The block can be either moved or copied to the paste buffer. 区块可以移动或复制到糊缓冲区。Later the content of the paste buffer can be pasted into the text with the Paste command.后来糊的内容缓存可以贴在该文本粘贴命令。
WordStar like commandsWordStar喜欢命令
You mark a block by placing a block-begin marker before the first character and a block-end marker after the last character of the desired portion of text. 你标记一个街区由把一个block-begin标记的品格,在第一block-end标记后的最后一个字所需的部分文本。Once the block is marked, you can copy, move, or delete it, or write it to a file.一旦块标记,您可以复制、移动或删除它,或把它写一个文件。
MultiMate like commandsMultiMate喜欢命令
These commands works on the principle that you use the same key to begin and end a given operation. 这些指令的运作原则,使用相同的钥匙你开始和结束一个给定的操作。To abort any block command before it's completed (when it's waiting for input), just press Esc. 任何阻止终止命令之前完成。(当它等待输入),只需按下Esc。For instance, to copy a block using the block commands, you press MultiMate copy to start the process (mark the block begin), use the arrow keys to highlight the block, then press MultiMate copy again to mark the block end. 例如,复制一个块采用次命令,你按下MultiMate复制启动这个过程(马克区块开始)使用箭头键来突出的街区,然后再按MultiMate复制纪念块结束。After that, you move the cursor to the position where the copy. 在那之后,你移动光标位置的文本。If you want to insert multiple copies of the marked block, you simply move the cursor with arrowkeys to the new location(s), then press Paste.如果你想要插入的多个副本的标记的街区,你只需将鼠标移动到新的位置与arrowkeys(s),然后按下粘贴。
Block select块选择
When pressing the Block select command, you enter block marking mode. 当按区块选择命令,你进入块标识模式。The block will be highlighted as you move (ahead or back from the starting position). 那块一样,当你移动会高亮(提前或回起始位置)。In block marking mode, no characters can be inserted. 标识块模式,没有字符可以插入。Pressing a character key causes the cursor to move to the next occurrence of that character, Quit block marking mode by pressing <Esc> of Block select again.按字符键引起光标移动到下一个出现的人物,放弃压块标识模式< Esc >块选择了。
Copy block to paste buffer复制粘贴缓冲块
The currently marked block is copied to the paste buffer. 当前标志着块拷贝到糊缓冲区。The command terminates block marking mode, and the previous content of the paste buffer are overwritten.命令终止模式块标记,保持原有的内容是糊缓冲覆盖。
Move block to paste buffer移动块粘贴缓冲区
The currently marked block is deleted from the text and moved to the paste buffer. 当前标志着块删除文本和搬到浆料的缓冲区。the command terminate block marking mode, and the previous contents of the paste buffer are overwritten.命令终止模式块标记,保持原有的内容的缓冲被覆盖粘贴。
Paste粘贴
The contents of the paste buffer are inserted in the text at the current cursor position. 粘贴缓冲区的内容被插入文本在当前光标位置。The paste buffer itself is not affected by the command.糊缓冲本身就是不受命令。
Mark Blockstart马克Blockstart
Marks the beginning of a block. 新年的开始一个街区。The marker itself is not visible, and the block itself only becomes visible when the block-end marker is set. The marked text (a block) is displayed with a different attribute than theunmarked text (you can choose the attribute for unmarked text with the menu item.本身是不可见的标记,朽木本身只能是可见当年block-end标记被设置。,有记号的文本(一块)显示有不同的属性比theunmarked文字(你可以选择的属性为文本标记菜单项目。
Mark Blockend马克Blockend
Marks the end of a block. 标志着结束的一个街区。The marker itself is invisible, and the block itself becomes visible only when the block-begin marker is also set. Pressing Mark Blockend in block marking mode exit this mode. 标志本身是无形的,朽木本身变得可见只有当block-begin标记还确定。压马克Blockend块标记模式退出此模式。The block isstill highlighted.区块依然突出了。
WordStar show/hide block显示/隐藏WordStar块
Causes the visual marking of a block to be alternately switched off and on. 使视觉标记的一个街区,关掉。交替The block manipulation commands copy, move, delete, and write to a file work only when the block is displayed. 块操作命令复制、移动、删除和写一个文件的工作,只有当块是显示。Block-related cursor movements jump to beginning/end of block works both when the block is hidden and displayed.Block-related光标移动跳开始/结束工作时块两块是隐藏和显示。
WordStar copy blockWordStar复制块
Copies the currently marked block to the paste buffer and thenpastes the contents of the paste buffer at the current cursor position.拷贝当前明显妨碍粘贴缓冲区和thenpastes粘贴缓冲区的内容在当前光标位置。
MultiMate copy blockMultiMate复制块
Press MultiMate copy block to start the process mark the block begin, use the arrow keys to highlight the block, then press MultiMatecopy block again to mark the block end. 按MultiMate复制块启动这个过程马克区块开始,使用箭头键来突出的街区,然后再按MultiMatecopy块马克块结束。After that, you move the cursor tothe position where the copy is to be inserted,then press MultiMate copy block once more to insert the copy. 在那之后,你将鼠标移动到位置需要插入的拷贝,再按MultiMate复制块再次插入副本。If you want toinsert multiple copies of the marked block, you simply move the cursor with arrow keys to the new locations, then press Paste.如果你想要toinsert标记块的多个拷贝,你只需用箭头键移动光标到新的位置,然后按下粘贴。
MultiMate move blockMultiMate移动块
Press MultiMate move block to start the process mark the block beginning, use the arrow keys to highlight the block, then press MultiMate move block again to mark the block end. 按MultiMate移动块启动这个过程马克区块开始,使用箭头键来突出的街区,然后再按MultiMate移动块马克块结束。After that, you press MultiMate move block once more to move the block.在那之后,你按下MultiMate移动块再一次移动块。
MultiMate delete blockMultiMate删除块
Press MultiMate delete block to start the process mark the block beginning, use the arrow keys to highlight the block, then press MultiMate delete block again to delete the block.按MultiMate删除块启动这个过程马克区块开始,使用箭头键来突出街区,然后按删除MultiMate块再删除一个街区。
Copy block to printer复制块到打印机
Writes previously marked block to the printer. 写以前明显妨碍打印机。The block is left unchanged in the current file, and the markers remain in place. 块是左不变在当前文件,这些标记继续存在。If no block is marked, nothing happens.如果无阻塞醒目,什么也没发生。
Copy block to file拷贝文件块
Writes a previously marked block to a file. 写一个先前标记块到一个文件。the block is left unchanged in the current file, and the markers remain in place. 块是左不变在当前文件,这些标记继续存在。If no block is marked, nothing happens.如果无阻塞醒目,什么也没发生。
When you issue this command, the editor prompts you for the mane of the file. 当你发行这个命令,促使你编辑文件的鬃毛。To select an existing file to overwrite, use DOS wildcards. 选择将会覆盖现有的一个文件,使用DOS通配符。A directory appears in a small window on screen, and you can select a file name from this directory. 一个目录出现在屏幕上的一个小窗口,你可以选择一个文件的名字从这个目录。If you type the file name yourself and the file specified already exists, the editor issues a warning and prompts for verification before overwriting the existing file. 如果你输入文件名自己和指定的文件已经存在,编辑警告,提示问题进行验证之前,已有的文件覆盖。If you don't give an extension for the file name, the system automatically appends the extension for the current file mask. 如果你不给延期文件名,系统会自动列表之后添加的拓展当前文件的面具。To specify a file name with no extension, follow the name with a dot.指定一个文件名没有扩展,遵循名字和一个点。
Change case for a block改变情况一个街区
Changes case for the currently marked block. 案例明显改变目前阻碍。Three selections is offered:提供三个选择:
Upper/Lower or Reverse case (u/l/r):上层/降低或反例(u / l / r):
Type u for Upper (all letters in the block is changed to upper case), l for Lower (all letters changed to lower case) or r for Reverse (all letters shift case from lower to upper or from upper to lower).u型上(所有字母的大写挡了),我对于较低的(改为小写字母)或r逆序(所有的信件转变,以较低的箱子上或从上到下)。
Copy block from file块从文件副本
Invokes the auxiliary editor in Xcopy mode and pops up the Pick list (a list of the files most recently loaded into the editor, up to seven files). 调用辅助编辑Xcopy中挑一的模式和弹出列表(一个列表文件最近装入编辑,到七文件)。You can select the file to read from this list, or choose..你可以选择文件读取这个列表,或选择. .load file.. 装载文件…which will pop up the File name input box.这将弹出文件名输入框。
You can type in an explicit file name, or use DOS wildcards to form a file mask. 你可以输入一个很明显的文件名,或者使用DOS通配符,形成一个文件的面具。If you type in a name, you can specify any legal file name. 如果你输入一个名称,你可以指定任何法律文件的名字。If you specify no file extension (.如果你没有指定文件扩展名。PRO, .箴。TXT, .TXT文件,。BAK, etc.) the editor assumes you want the extension for the current file mask. 不,等等)。假设你想要编辑的拓展当前文件的面具。To read a file that lacks an extension, append a period to the file name.阅读文件,缺乏一个扩展,附加一个时期到文件的名字。
Aux edit辅助编辑
You are asked to enter a filename. 你被要求输入一个文件名。This done in the same way as described under Load file. 这样在同样的方式描述在荷载作用下的文件。An auxiliary editor pops up a new window with the selected file. 一个辅助的弹出一个新窗口编辑与选中的文件。After editing the file, press Esc or F10 to return to the original editor. 修订后的文件,按Esc或F10回到原来的编辑器。If the file is changed you are asked for a filename (Just press return to save with the same filename) or asked "Are you sure"如果文件是改变了你要求一个文件名(只需按下回到相同的文件名保存)或问道:"你肯定”
(if Esc was pressed).(如果被按下Esc)。
Pop-up help menu弹出帮助菜单
Shows the key-sequences for all commands. 显示key-sequences所有的命令。A command can be activated from the help menu simply by pressing return with the cursor on the command. 一个命令可以被激活的帮助菜单只要按还和光标的命令。The first entry in the help menu is show help file. 第一个进入帮助菜单显示帮助文件。If this entry is selected the help file is displayed.如果该条目被选中的帮助文件被显示。
Show Help file显示帮助文件
Displays the help file (if a help file is present) in a separate window.显示帮助文件(如果一个帮助文件存在)在一个单独的窗口。
Auto indentation自动缩进
Provides automatic indentation of successive lines.提供自动缩进连续的线。 When auto indentation is active, the cursor does not return to column one when you press Enter. 当汽车凹坑是活跃的时,光标不返回列人,当你按回车。Instead, it returns to the starting column of the line you just left.相反,它返回到柱线开始你就离开了。
When auto indentation is On, the message indent shows up on the status line; when it's Off, the message disappears. 当汽车凹坑,缩进显示的信息在状态栏上,当它是关闭的,信息就消失了。Auto indent is On by default.自动缩进在默认。
Insert mode插入模态
When entering text, you can choose between two basic entry modes: Insert and Overwrite. 当进入文本,您可以选择两种基本的进入模式之间:插入和覆盖。You can switch between these modes with the Insert mode toggle, (Ctrl-V or Ins). 你可以用这些模式之间切换插入模态切换,(Ctrl-V或Ins)。The current mode is displayed in the status line at the top of the screen.当前的模式将显示在状态栏上在屏幕顶端。
Insert mode is the editor's default; this lets you insert new characters into old text. 插入模式是编辑默认的,这让你插入新的角色到旧的文本。Text to the right of the cursor simply moves to the right as you enter new text.文本光标的权利仅仅移动到就像你输入一个新的文本。
Use Overwrite mode to replace old text with new. 使用覆盖模式来代替原来的文本,以新的。Any characters entered will replace existing characters under the cursor.字符将取代现有的角色进入在光标。
Text mode文本模式
Use this command to toggle word wrapping between on and off.使用此命令词之间切换包装和关闭。
Lower/Upper/Reverse case word放下/上层/反例词
Use these three commands to change case for a single word.使用这三个命令来改变案例为一个字。
Exit editor退出编辑
The command that exits the editor.命令退出编辑器。
Resize window调整窗口
Move the window to a new position by holding down the <Shift> key and pressing the appropriate arrow key in the numeric keypad without Caps Lock.移动窗口到一个新的位置通过��低人民币<转变>键和箭头键按下相应的数字键没有大写锁定。
Change the size of a window by the arrow keys.改变大小,一个窗口在键盘上的方向键。
Zoom window缩放窗口
The window is zoomed out to the screen-size. 窗子是放大到screen-size。Press Zoom window again to return to original size.按缩放窗口回原来的大小。
Previous line前一条线
When the editor prompts for a string (as in Search), pressing Previous line causes the most recently entered string to be shown.当编辑提示找一个字符串(搜索),按前一条线使最近进入字符串被显示。
File mask文件面具
Press this command when the filename browser in the file-name input box is active. 当按下这个命令浏览器在file-name文件名输入框是积极的。You can then enter the file-mask (e.g. *.sm).然后你可以进入file-mask(例如。* .sm)。
Terminate input终止输入
The key to use to terminate user input.使用的关键终止用户输入的信息。
The Edit Window Status line编辑窗口状态栏上
The status line in the top bar of the Edit window gives you information about the source text you are editing, where in the text the cursor is located, and which editing modes are activated:在状态行的顶栏编辑窗口的信息给你正在编辑的源文本,在文本光标位于,编辑模式就会被激活。
Line线 Col西 X:FILENAME.TYP谢:FILENAME.TYP Insert插入 Indent缩进 Text mode文本模式
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Status地位 Description描述
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Line线 Shows which line number contains the cursor.显示出所包含的行数游标。
Col西 Shows which column number contains the cursor.显示出所包含的列数游标。
X:FILENAME.TYP谢:FILENAME.TYP Indicates the drive (x:), name (FILENAME), and extension显示驱动器(x),名字(文件名),与推广
(.TYP) of the text you are editing.(.TYP)正在编辑的文本。
Insert插入 Tells you that the editor is in Insert mode: Characters entered on the告诉你,编辑是在插入模态:字符后 keyboard are inserted at the cursor position, and text in front of the cursor键盘是插入游标目前的位置,和文本在前面的游标 moves to the right.移到右边去。
Use the Ins key or Ctrl-V to toggle the editor between insert mode and使用Ins键或Ctrl-V之间切换编辑模式和插入 Overwrite mode.覆盖模式。
In Overwrite mode, text entered at the keyboard overwrites characters under在覆盖模式,文本输入下的人物得以在键盘的覆盖 the cursor, instead of inserting them before existing text.光标,而不是插入现有文本之前。
Indent缩进 Indicates that the auto indent feature is set to On. 表明,特点是将汽车缩进。You toggle it on and off在你切换和关闭 with the command Auto indentation.该命令自动缩进。
Text mode文本模式 Indicates whether text mode (word-wrap mode) is on. 显示文本模式是否(word-wrap模式)。You toggle it on and off在你切换和关闭 with the command Text mode.该命令文本模式。
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Within the Input window, press <F8> to open another window, called the Aux Edit window. 输入窗口内,按< F8 >打开另一个窗口,叫做辅助编辑窗口。In the Aux Edit window, press <F8> again to open another Aux Edit window. 在辅助编辑窗口,按< F8 >再次打开另一个辅助编辑窗口。So you can open many the Aux Edit windows to edit many files.所以你可以打开许多辅助编辑窗口编辑许多文件。
Text in the Input window always be saved after exit by pressing <Esc>. 文本输入窗口总得救出境后按< Esc >。The Aux Edit window is closed with saving by pressing <F10>, or without saving by pressing <Esc>.辅助编辑窗口关闭拯救按< F10 >,或不保存按< Esc >。
In the Input window or the Aux Edit window, press <F1> to pop-up the Edit Help menu (see 19.9.1 Edit Help Menu), or <Shift><F1> to see the manual, and <F7> to copy block from the an Aux Edit window into the main editor or into the last Aux Edit window.在输入窗口或辅助编辑窗口,按< F1 >编辑帮助菜单,弹出(见19.9.1编辑帮助菜单),或<转变> < F1 >去看手册,并< F7 >复制状况,从一个辅助编辑窗口的主要编辑或最后一辅助编辑窗口。
Move the cursor around in the editor with the arrow keys, <Page Up>, <Page Down>, and some other keys listed below.移动光标在编辑器与键盘上的方向键,<页面>,<页数下>,以及其他一些键列在了下面。 The editor has two typing modes: Insert and Overwrite.编辑模式有两个输入:插入和覆盖。 In Insert mode, anything you type is inserted at the cursor position. 在插入模态的时候,你的任何类型的插入游标目前的位置。In Overwrite mode, pressing a key replaces the current character at the cursor position with the new typed character. 在覆盖模式,按一个键替换当前光标位置字符与新型的性格。Initially, the editor operates in Insert mode, to switch modes, press the <Insert> key or <Ctrl>V.最初,编辑操作在插入模式、开关模式,按<插入>键或< Ctrl > V。 (<Ctrl>V means to hold down the <Ctrl> key on your keyboard while you press V.(< Ctrl > V意味着按住< Ctrl >键,你的键盘当你按下伏。 The V need not be in upper case.)不需要的“V”以大写字母。)
Unlike a more standard word processing program, the editor does not have word-wrap. 不像一个更标准字处理程序,编辑没有word-wrap。You must press <Enter> at the end of each line.你必须按<进入>每年年底的一线。
The editor has an auto indent feature that allows subsequent lines to automatically indent.编辑有一个自动缩进线功能,允许随后自动缩进。 If you leave several spaces at the start of a line, use <Ctrl>OI to indent subsequent lines the same amount.如果你离开几个空间开始的一条线,使用< Ctrl >无知后续线路缩相同的数量。 The command sequence is a toggle, so you need only press <Ctrl>OI again to stop indenting.命令序列是一个触发器,所以你只需要按< Ctrl >无知缩来制止。
Sometimes you may want to see more than the area covered by the current window.有时你可能想看到更多覆盖的面积比当前窗口。 You can zoom the window, expanding it to the size of the entire screen, by pressing <F5>.您可以缩放窗口,扩大到整个屏幕的大小,按< F5 >。 To return the window to its usual size, press <F5> again.返回窗口,其通常的大小,按< F5 >了。 For other window commands, such as moving and resizing a window, see the window command table, below.其他窗口的命令,例如移动和尺寸的一个窗口,看到窗户指挥桌子,下面。
The editor uses approximately 70 commands, which can be grouped into 6 main categories:编辑用大约70的命令。这命令素来是可以划分为6个主要类别有:
1. 1。cursor movement commands光标移动命令
2. 2。insert and delete commands插入和删除命令
3. 3。search and replace commands搜索和替换的命令
4. 4。file commands文件的命令
5. 5。block commands块命令
6. 6。miscellaneous commands杂命令
Table 19.9.1表19.9.1 Editor commands.编辑器命令。
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Cursor Movement Commands (move cursor to):光标移动命令(移动光标到):
.............................................................................
Line up排队 <Ctrl>E< Ctrl > E or Up arrow或箭
Line down线,把 <Ctrl>X< Ctrl > X or Down arrow下箭头
Character left人物离开 <Ctrl>S< Ctrl >年代 or Left arrow <-或左箭头处< -
Character right性格对 <Ctrl>D< Ctrl > D or Right arrow或右箭头 ->- >
Word left词离开 <Ctrl>A< Ctrl >一个 or <Ctrl> <-或< Ctrl > < -
Word right的话对 <Ctrl>F< Ctrl > F or <Ctrl> ->>或< Ctrl > - - - - - -
Beginning of line线开始 <Ctrl>QS or <Home>< Ctrl >或<回家> QS
End of line行的未端 <Ctrl>QD or <End>< Ctrl >或<结束> QD
Page up页面 <Ctrl>R< Ctrl > R or <Pg Up>或< Pg起来>
Page down页数下 <Ctrl>C< Ctrl > C or <Pg Dn>或< Pg Dn >
Scroll up向上滚动 <Ctrl>W< Ctrl > W
Scroll down向下滚动 <Ctrl>Z< Ctrl > Z
Top of screen屏幕的顶部 <Ctrl>QE or <Ctrl><Home>< Ctrl > QE或< Ctrl > <回家>
Bottom of screen底部的屏幕 <Ctrl>QX or <Ctrl><End>QX < Ctrl >或< Ctrl > <结束>
Top of file顶级的文件 <Ctrl>QR or <Ctrl><Pg Up>QR < Ctrl >或< Ctrl > < Pg起来>
Bottom of file底部的文件 <Ctrl>QC or <Ctrl><Pg Dn>QC < Ctrl >或< Ctrl > < Pg Dn >
Beginning of block开始块 <Ctrl>QB< Ctrl > QB
End of block块结束 <Ctrl>QK< Ctrl > QK
Previous point上一点 <Ctrl>QP< Ctrl > QP
Goto line线扫描 <Ctrl>F2< Ctrl > F2
Goto position岛的位置 <Shiift>F2< Shiift > F2
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Insert & Delete Commands:插入和删除命令:
...........................................................
Insert mode on/off插入模态开/关 <Ctrl>V or <Ins>< Ctrl >或< Ins > V
Insert line插入线 <Ctrl>N< Ctrl > N
Delete line删除线 <Ctrl>Y< Ctrl > Y
Delete to end of line删除结束的线 <Ctrl>QY< Ctrl >探明
Delete left character删除左特征 <Ctrl>H or <Backspace>< Ctrl >或<退格> H
Delete character under cursor删除字符下,光标 <Ctrl>G or <Del>< Ctrl >或< Del > G
Delete right word删除的权利的话 <Ctrl>T< Ctrl > T
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Block commands:块命令:
............................................................
Block select块选择 <Ctrl>KM< Ctrl >公里
Copy block to paste buffer复制粘贴缓冲块 <Ctrl>KI< Ctrl >亲吻
Move block to paste buffer移动块粘贴缓冲区 <Ctrl>KY< Ctrl >“
Paste粘贴 <Ctrl>U or <Ctrl><F7>你< Ctrl >或< Ctrl > < F7 >
Mark block begin马克块开始 <Ctrl>KB< Ctrl > KB
Mark block end马克块结束 <Ctrl>KK< Ctrl > KK
Mark word马克的话 <Ctrl>KT< Ctrl > KT
WordStar show/hide block显示/隐藏WordStar块 <Ctrl>KH< Ctrl > KH
WordStar copy blockWordStar复制块 <Ctrl>KC or <Ctrl><F5>KC < Ctrl >或< Ctrl > < F5 >
Repeat the last copy重复最后复制 <Shift><F5><转变> < F5 >
WordStar move blockWordStar移动块 <Ctrl>KV or <Alt><F6>< Ctrl >或< Alt > KV < F6 >
MultiMate copy blockMultiMate复制块 <Ctrl><F5>< Ctrl > < F5 >
MultiMate move blockMultiMate移动块 <Alt><F6>< Alt > < F6 >
MultiMate delete blockMultiMate删除块 <Alt><F7>< Alt > < F7 >
Delete block删除块 <Ctrl>KY< Ctrl >“
Read block读块 <Ctrl>KR or <F7>< Ctrl >或< F7 >基米-雷克南
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Special Block functions特殊块函数
....................................................................
Copy block to printer复制块到打印机 <Ctrl>KP or <Alt><F8>KP < Ctrl >或< Alt > < F8 >
Copy block to file拷贝文件块 <Ctrl>KW or <Alt><F5>< Ctrl >千瓦或< Alt > < F5 >
Copy block from file块从文件副本 <Ctrl>KR or <F7>< Ctrl >或< F7 >基米-雷克南
Change case for block变化情况下建立了分段 <Ctrl>KE or <Ctrl><F6>《< Ctrl >或< Ctrl > < F6 >
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Miscellaneous Commands:杂命令:
.....................................................................
Quit edit退出编辑 <Esc>, <F10>, <Ctrl>KD, or <Ctrl>KQ< Esc >,< F10 >,< Ctrl > KD,KQ或< Ctrl >
Call the auxiliary editor叫辅助编辑 <F8>< F8 >
Tab标签 <Ctrl>I< Ctrl >我 or <Tab>或<”选项卡>
Tab mode toggle标签模式切换 <Ctrl>OT< Ctrl >不
Auto indent on/off自动缩进开/关 <Ctrl>OI< Ctrl >无知
Restore line恢复线 <Ctrl>QL< Ctrl >各项目功能显而易见,
Find找到 <Ctrl>QF or <Ctrl><F3>《< Ctrl >或< Ctrl > < F3 >
Repeat last find重复上找到 <Ctrl>L< Ctrl >我 or <Shift><F3>或<转变> < F3 >
Find & replace发现和取代 <Ctrl>QA or <Ctrl><F4>< Ctrl > QA或< Ctrl > < F4 >
Repeat last find & replace重复上发现和替代 <Ctrl>L< Ctrl >我 or <Shift><F4>或<转变> < F4 >
Control key prefix控制关键的前缀 <Ctrl>P< Ctrl > P
Abort operation流产手术 <Ctrl>U< Ctrl >你
Restore error message恢复错误信息<Ctrl>QW< Ctrl > QW
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Global Commands全球命令
...................................................................
Resize window调整窗口 <Shift><F10><转变> < F10 >
Zoom window缩放窗口 <F5>< F5 >
Previous line前一条线 <F8>< F8 >
File mask文件面具 <F4>< F4 >
Terminate input终止输入 <F10>< F10 >
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Table 19.9.2表19.9.2 Edit window commands编辑窗口的命令
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Action行动 Keystrokes按键
help帮助 <F1>< F1 >
zoom in window放大窗口 <F5>< F5 >
zoom out window缩小窗口 <F5>< F5 >
resize window调整窗口 <Shift><F10>, the arrow keys, <F10><转变> < F10 >,键盘上的方向键,< F10 >
move window移动窗口 <Shift><F10>, <Shift> and the arrow key in numeric<转变> < F10 >,<转变>,箭头键在数字
keypad without Caps Lock没有大写锁定键盘
open an Aux Edit window打开一个辅助编辑窗口 <F8>< F8 >
close the Aux Edit window with saving关闭辅助编辑窗口的拯救 <F10>< F10 >
close the Aux Edit window without saving关闭辅助编辑窗口没有保存<Esc>< Esc >
copy block from an Aux Edit window复制一个辅助编辑窗口区 <F7>< F7 >
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You can copy-and-paste text anywhere in a file and between files, even from the Help window. 你可以在任何地方粘贴文本之间的一个文件时,文件,甚至从帮助窗口。In this way you do not need to remember syntax of the SymbMath commands.以这个方式,你不需要记住语法的SymbMath命令。
You move the cursor to the beginning of text you want to copy, press <F1>, select the Block Function menu and press <Enter>, select the Block Select command and press <Enter>, move the cursor to the end of text you want to copy, press <F1>, select the Copy Block To Paste buffer command and press <Enter>, press <Esc>, go into the Input window, move the cursor to a place where you want to paste, press <F1>, select the Paste command and <Enter>.你移动光标的开始你��要复制的文本,按< F1 >,选择块函数的菜单和按<进入>,选择区块选择指挥和按<进入>,移动光标到最后的文本您想要复制的,按< F1 >,选择复制粘贴缓冲块指挥和按<进入>,按< Esc >,进入输入窗口、移动光标移到一个地方,你要粘贴,按< F1 >,选择粘贴命令和<进入>。
As an expert system, SymbMath consists of three major components: a knowledge base, an inference engine, and a global database. 作为一个专家系统,SymbMath由三个主要组成部分:一个知识库、推理机、以及全球性的数据库。The knowledge base is a set of rules, the inference engine is a rule interpreter for utilising the knowledge base in the solution of the problem, and the global data base is a working memory for keeping track of the problem status, the data from the data file for the particular problem, and the solution of sub-problems. 知识库是一套规则,推理机采用的翻译是一个规则的知识库,以解决这个问题,而这个全球数据为基础是工作记忆跟踪问题的现状,提出了数据从数据文件为一个特定的问题,解决问题。In addition, it contains a natural language interface for input and output natural languages (e.g. mathematical formulas, chemical reactions).此外,它包含了自然语言界面为输入和输出自然语言(如数学公式、化学反应)。
User用户 Library图书馆 disk磁盘
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| Natural Language Interface |自然语言界面| |
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------->|- - - - - - - - - - - - > | Inference Engine推理引擎 |<----------| < - - - - - - - - - - - - -
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| Knowledge Base || |知识库 | Global Data Base |全局数据基地| |
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|| Data File数据文件 ||
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Figure 20.1图20.1 Structure of SymbMathSymbMath结构
Table 20.1表20.1 Characteristics of SymbMathSymbMath特点
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Function:功能: Symbolic computation.象征性的计算。
Domain:领域: Mathematics, chemistry.数学、化学。
Search direction:搜索方向。 Forward chaining.前锋链。
Control mechanism:控制机制。 Guessing and test, pattern match.猜测和测试、模式匹配。
Search space transformations:搜索空间转换: Break into sub-problems.闯入解析解。
Knowledge base representation: Rules.知识库表示:规则。
Developer interface:开发者接口: Learning, programming, library.学习、编程、图书馆。
User interface:用户界面: Pull-down menu, pop-up menu, multi-windowed editor, help,下拉式菜单,弹出菜单,multi-windowed编辑,帮助, windows.窗户。
System interface:系统界面: numeric computation software, graphic software, etc.数值计算软件,图形软件等等。
Input format:输入格式: Math formulas, numbers, BASIC or FORTRAN codes,数学公式、数字、基本或FORTRAN语言代码, chemical symbols and reactions.化学符号和反应。
Output format:输出格式: Math notation, BASIC or FORTRAN codes,数学符号,基本或FORTRAN语言代码,
chemical reaction equations.化学反应方程式。
Input from:输入: Keyboard, disk.键盘,磁盘。
Output to:输出: Screen, disk, printer.屏风、磁盘、打印机。
Tool language:工具语言: PROLOG.PROLOG。
Computer:计算机: IBM PC.IBM的个人电脑。
Memory:记忆功能: 400 KBytes.400 k,宽带下载1秒钟。
Operating system:操作系统: MS-DOS.ms - dos。
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You can peep at the internal format in the SymbMath system by setting output := prolog. 你可以窥视内部格式在SymbMath系统通过设置输出:= prolog。This is useful for understanding SymbMath.这是非常有用的SymbMath理解。
Example:例如:
IN:在: output := prolog输出:= prolog
IN:在: a+b+ b
OUT: plus(var("a"),var("b"))出:还有(var(“一个”),var(b)
1. 1。The maximum character of a symbol is 64000.最大的字符标志是64000。
2. 2。The maximum character of an expression is 64000.最大的字符一个表达式是64000。
3. 3。The range of the input real numbers is输入范围的实数
-inf, -(10^300)^(10^300) to -10^(-300), 0, 10^(-300) to (10^300)^(10^300), inf.-inf,(10 ^ 300)^(10 ^ 300)到-10 ^(-300)、0、10 ^(-300年)至(10 ^ 300)^(10 ^ 300),无穷大。
4. 4。The range of the output real numbers is the same as input when the switch numeric:=off, but when the switch numeric:=on, it is范围的实数输出是一样的开关输入端时,流数值:=掉,但当开关数字:=,它是
-inf, -1.-inf(1)。E300 to -1.E300为1。E-300, 0, 1.E - 300,0,- 1。E-300 to 1.E - 300比1。E300, inf.E300,无穷大。
5. 5。The maximum digit of the input numbers is 64000.最大的数字输入编号是64000。
6. 6。The maximum digit of the stored numbers is 16.最大的数字存储数字的是16岁。
7. 7。The maximum digit of the output numbers is 11.最大的数字输出编号是11分。
8. 8。The maximum digit of the rational numbers is 16.最大的数字的合理编号为16岁。
9. 9。The maximum arguments of the user-defined function with pattern is 7.最大的争论和用户自定义函数模式是7。
10. 10。The maximum arguments of the user-defined rule is 2 and the maximum pattern is 3.最大的争论用户自定义的规则是2和最大模式三个方面。
Only following rules are available:只有遵循规则可供选择:
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f(a_ + b_)f(已+ b_) f(a_ + b_, x_)f(已x_ + b_,) d(s(x_), x_)d(s(x_),x_) inte(c(x_), x_)希尔(c(x_),x_)
f(a_ - b_)f(已- b_) f(a_ - b_, x_)f - b_ x_已,) d(s(n_,x_), x_)d(s(n_,x_),x_)
f(a_ * b_)f(已* b_) f(a_ * b_, x_)f(已b_ x_ *,)
f(a_ ^ b_)f(已b_ ^) f(a_ ^ b_, x_)f(已b_ x_ ^,)
f(s(a_))f(s(已) f(c(x_), x_)f(c(x_),x_)
f(-a_)f(-a_) f(a, x_)f(a,x_)
f'(x_)f '(x_) f(a_, x)f(已、x)
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where s() is a simple function, c() is a complicated function.在s()是一个简单的函数,c()是一个复杂的功能。
SymbMath has two versions: Shareware Version A, and Advanced Version C. The Shareware version lacks the solve(), trig (except sin(x) and cos(x)), and hyperbolic functions, (lack 10% keywords). SymbMath有两个版本:Shareware版本,和先进的版本c Shareware版本缺乏解决()、三角法(除罪(x),因为(x))和双曲线函数,缺乏10%关键字)。You cannot input these lack functions in Shareware or student version.你不能输入他们的功能或学生缺乏共享软件版本。
Upper- and lower-case letters are different until the switch lowercase is set to on (i.e. lowercase := on).小写字母上,不同小写直到开关设置在(即小写:=。
All keywords are lower-case letters until the switch lowercase := on.所有小写字母关键词直到开关小写:=。
There are two types of the keywords: internal and external. 有两种类型的关键词:内部和外部的。The internal keywords have been compiled into the SymbMath system, so you cannot change them. 内部关键词被编译成SymbMath系统,所以你不能改变它。The external ones are in files, so you can change their name or property. 在外部的文件,所以你可以改变他们的名字或财产。Usages of both types are the same.使用的两种类型是相同的。
The following only includes the internal and some external keywords. 以下只包括内部和外部的关键字。You can define your own keyword and add your defined function. 你可以定义自己的关键字,加上你的定义的功能。If some keywords do not work, you should check whether or not the libraries are in the default library directory.如果几个关键词不工作,你应该检查是否在默认的图书馆是图书馆目录。
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Arithmetic operators:算术操作符:
+, -, *, /+,-,*,/ plus, minus, times, division加、减、时代、师
^, ** power权力
()
Relational operators:关系运算符。
=== = equals等于
> greater than大于
>=> = greater than or equal大于或等于
< less than少于
<=< = less than or equal小于或等于
<> not equal不平等
Assignments:作业:
:=:=
Equation:公式:
==
solve(x^2=1,x)解决(x ^ 2 = 1,x) solve x^2=1 for x解决^ 2 x = 1 x
solve([x+y=b,x-y=c], [x,y])解决([x + y = b,x - y = c]、[x,y]) solve解决 x+y=b and x-y=c for x and yx + y = b和x - y = c为x和y
psolve(f(x),x)psolve(f(x)、x) solve f(x)=0 for x解决f(x)= 0 x
nsolve(cos(x)=x,x)nsolve(因为(x)= x,x) numerically solve f(x)=0 for x with initial x0=1进行数值求解f(x)= 0具有初始x0 x = 1
nsolve(f(x)=0,x,x0)nsolve(f(x)= 0,x,x0) numerically solve f(x)=0 for x with initial x0进行数值求解f(x)= 0 x初x0
dsolve(y'(x)=f(x,y), y(x),x)dsolve(y”(x)= f(x,y),y(x)、x) solve differential eq y’=f(x,y) for y(x)求解微分eq y”= f(x,y)为y(x)
Comment:评论:
#
Built-in constants:内置的常量:
i, e, pi, inf, zero, constant, discont, c_inf, undefined.我,呃,圆周率,无穷大,零、持续、discont,c_inf,未定义的。
Built-in variables:内置的变量:
last最后
Logic operators:逻辑操作符:
and, or, not(x)和/或,而不是(x)
Algebraic functions:代数功能:
-x-x minus x减去x
sqrt(x)sqrt(x) sqare root of xsqare根x
n!护士! factorial of nn阶乘
fac(n)前沿空中管制官(n) faction of n派系n
mod(x,y)国防部(x,y) reminder on division of x by y在这个由分工x y
div(x,y),师(x,y), integer divide x by y整数分由y x
random随机 random number 0<= x<1随机数字0 < = x < 1
random(x)随机(x) random number <= x随机数< = x
expand(x)扩大(x) expand x扩展x
factor(x)因子(x) factor x因子x
factor(y,x)因子(y,x)
root(x,n)根(x,n) all n-th roots of x所有类型的根x
Complex to real:复杂的现实:
re(x)稀土(x) real part of the complex number x真正的部分复数x
im(x)我(x) imaginative part of the complex number x想象力的部分复数x
abs(x)abs(x) absolute value of x绝对值x
|x|| | x absolute value of x绝对值x
arg(x)高温(x) argument of complex number x参数的复数x
sign(x)签署(x) sign of complex number of x复数x的迹象
Exponential functions:指数函数:
exp(x)实验(x) natual expoential of x, exp(x)=e^x自然expoential x,经验(x)= e ^ x
ln(x)淋巴结(x) natual logarithm of x自然对数x
log10(x)t(x) log of x to base 10日志x基地10
Trig functions:三角法功能:
sin(x)罪(x) sine of x正弦x
cos(x)因为(x) cosine of x余弦x
tan(x)褐色(x) tangent of x切线x
csc(x)csc(x) cosecant of xcosecant x
sec(x)秒(x) secant of x进行x
cot(x)cot(x) cotangent of xcotangent x
Inverse trig functions:逆三角法功能:
asin(x)asin(x) angle whose sine is x角的正弦是x
acos(x)函数(x) angle whose cosine is x谁的余弦角是x
atan(x)atan(x) angle whose tangent is x角的正切是x
acot(x)acot(x) angle whose cotangent is x其cotangent角度是x
asec(x)了一类正则(x) angle whose secant is x角度进行的是x
acsc(x)研究会(x) angle whose cosecant is x其cosecant角度是x
atan2(x,y)atan2(x,y) angle whose tangent is x/y是谁的切线角度x / y
Hyperbolic functions:双曲功能:
sinh(x)sinh(x) hyperbolic sine of x双曲正弦x
cosh(x)事业(x) hyperbolic cosine of x双曲余弦x
tanh(x)tanh(x) hyperbolic tangent of x双曲正切x
csch(x)csch(x) hyperbolic cosecant of x双曲cosecant x
sech(x)sech(x) hyperbolic secant of x双曲型进行了x
coth(x)coth(x) hyperbolic cotangent of x双曲cotangent x
Inverse hyperbolic functions:反双曲功能:
asinh(x)作用(x)
acosh(x)函数(x)
atanh(x)函数(x)
acoth(x)acoth(x)
acsch(x)acsch(x)
asech(x)asech(x)
Special math integral functions:特殊数学积分功能:
ei(x)ei(x) expoential integral functionexpoential积分函数
ei(n,x)美国饭店协会教育学院(氮、x) incomplete exponential integral function inte(t^n*e^t, t,-inf,x)强烈的不完整的指数积分函数(t ^ ^ n * e t,t -inf、x)
gamma(n)伽玛(n) gamma function inte(t^(n-1)*e(-t), t,0,inf)=(n-1)!强烈的伽玛函数(t ^(n-1)* e(刚),t 0,inf)=(n-1)!
gamma(n,x)伽玛(氮、x) incomplete gamma function inte(t^n*e(-t), t,0,x)强烈的不完整的伽玛函数(t ^ n * e(刚),t - x)
erf(x)(x)广泛的 error function 2/sqrt(pi)*inte(e^(-t^2),t,0,x)2 / sqrt误差函数(pi)*交互(e ^(刚^ 2),t - x)
si(x)si(x) sine integral function inte(sin(x)/x)强烈的正弦积分函数(罪(x)/ x)
ci(x)ci(x) cosine integral function inte(cos(x)/x)强烈的余弦积分函数(因为(x)/ x)
li(x)李(x) log integral function inte(1/ln(t), t,0,x)强烈的日志积分函数(1 /淋巴结(t)、t - x)
li(n,x)李(氮、x) incomplete log integral function inte(ln(t)^n, t,0,x)不完整的记录交互积分函数(淋巴结(t),t ^ n - x)
Defining functions:定义功能:
f(x_) := x^2f(x_):= x ^ 2
f(x_) := if(x>0 then x^2)f(x_):要是(x > 0然后x ^ 2)
Defining procedures:定义步骤:
f(x_) := block(p:=x^2,p,local(p))f(x_):=区块(x ^ 2 = p:、磷、当地(p))
Defining rules:定义规则:
log(x_ * y_) := log(x)+log(y)日志(x_ * y_):=日志(x)+日志(y)
f'(x_) := sin(x)f '(x_):=罪(x)
Clear:明确:
clear(x)清晰的(x) clear variable x清楚变量x
clear(f(x))清楚(f(x)) clear function f(x)清晰的函数f(x)
clear(a>0)清楚(> 0) clear unequal a>0一个清晰的不平等> 0
Calculus functions:微积分功能:
Differentiating:区分:
d(y,x)d(y,x) differentiate y with respect to x区分y就x
d(y,x,n)d(x,y,n) differentiate y with respect to x in the n-th order区分y就x在形式秩序
diff(y,x=x0)比较(y,x = x0) differentiate y with respect to x at x0区分y就在x0 x
diff(y,x=x0,n)比较(y,x = x0、n) differentiate y with respect to x at x0 in the n-th order区分y就在各种类型的x x0秩序
f'(x)f '(x) differentiate f(x) with respect to x区分f(x)关于x
Integrating:整合:
inte(y,x)希尔(y,x) integrate y with respect to x集成y就x
inte(y,x,xmin,xmax)强烈的(x,y,xmin,xmax) integrate y with respect to x from xmin to xmax集成y就从x xmin到xmax
ninte(y,x,xmin,xmax) numerically integrate y w.r.t. x from xmin to xmaxninte(x,y,xmin,xmax)数值w.r.t.整合,从x xmin y xmax
Substituting:代替:
subs(y,x=x0)替补(y,x = x0) substitute x by x0 in y代替x的x0 y
Limit:限制:
lim(y,x=x0)小林(y,x = x0) limit of y as xy为限制x -> x0- > x0
lim(y,x=x0+zero)小林(y,x = x0 + 0) limit of y as xy为限制x -> x0 from right- - - - - - > x0从右边
lim(y,x=x0-zero)小林(y,x = x0-zero) limit of y as xy为限制x -> x0 from left- - - - - - > x0从左
nlim(y, x=x0)nlim(y,x = x0) numeric limit of y as x数字限制的y为x -> x0- > x0
laplace(y,x)拉普拉斯(y,x) Laplace transform拉普拉斯变换
sum(y, x,xmin,xmax,dx)和(x,y,xmin,xmax,dx) sum of y w.r.y w.r之和。t x from xmin to xmax step dx从x xmin t,xmax dx步
partsum(y,x)partsum(y,x) partial sum of y部分和y的
infsum(y,x)infsum(y,x) infinite sum of y无限笔y
prod(y, x,xmin,xmax,dx)促进(x,y,xmin,xmax,dx) product of y w.r.y w.r产品。t x from xmin to xmax step dx从x xmin t,xmax dx步
series(y,x)系列(y,x) series of y at x=0 to order of 5一系列的y在x = 0点5
series(y,x,order)系列(x,y,顺序) series of y at x=0 to order一系列的y在x = 0秩序
Conversion functions:转换功能:
ratio(x)比(x) convert real number to ratio真正的数字转换成比例
round(x)圆(x) convert x to the rounded integer closet to x转换到圆形的整数倍橱柜x
trunc(x)trunc(x) convert x to the truncated integer closet to x转换x的橱柜截断整数x
nume(a/b)nume(a / b) numerator of a/b出a / b
deno(a/b)deno(a / b) denominator of a/b分母的a / b
number(x)号码(x) convert a string to a number将一个字符串到一个号码
string(x)字符串(x) convert a number to a string将一个数字字符串
term(a+b)术语a + b) a list of terms一个列表中的术语
multi(a*b)多(* b) a list of multipliers一个列表的乘数效应较小,
type(x)类型(x) type of x类型的x
gcd(a,b)肾小球囊性肾病(a,b) the greatest common divider of a and b最常见的分a、b
Table:表:
table(x)表(x) produce a table of the function values from x=-5 to 5 with step 1产生一个表的函数值从x = 5 - 5第一步
table(x,xmin,xmax)表(x,xmin,xmax) produce a table of the function values from x=xmin to xmax on step 1产生一个表的函数值,从x = xmin xmax在第一步
table(x,xmin,xmax,dx)表(x,xmin,xmax,dx) produce a table of the function values from x=xmin to xmax产生一个表的函数值,从x = xmin xmax with step dxdx层
Numeric computation:数值计算。
num(x)胡(x) numeric value of xx的数值
nsolve(cos(x)=x,x)nsolve(因为(x)= x,x) numerically solve cos(x)=x w.r.t. x with initial x0=1因为进行数值求解(x)= x w.r.t.具有初始x0 x = 1
nsolve(cos(x)=x,x,x0)nsolve(因为(x)= x,x,x0) numerically solve cos(x)=x w.r.t. x with initial x0因为进行数值求解(x)= x w.r.t.具有初始x0 x
ninte(y,x,xmin,xmax)ninte(x,y,xmin,xmax) numerically integrate y w.r.t. x from xmin to xmax数值计算w.r.t.整合从x,y xmin xmax
nlim(y,x=x0)nlim(y,x = x0) numerica limit of y w.r.t. x at x0numerica限制在y w.r.t. x0 x
numeric:=on数字:=在 numeric switch on数字开关
Test functions:测试功能:
isodd(x)isodd(x) test if x is odd测试如果x很奇怪
iseven(x)iseven(x) test if x is even如果x是测试均匀
isinteger(x)isinteger(x) test if x is integer测试如果x是整数
isratio(x)isratio(x) test if x is rational number如果x是有理数测试
isreal(x)(x)来 test if x is real测试如果x是真实的
iscomplex(x)iscomplex(x) test if x is complex如果x是测试复杂
isnumber(x)isnumber(x) test if x is a number如果x是测试一个数字
islist(x)islist(x) test if x is a list如果x是测试一个列表
isfree(y,x)isfree(y,x) test if y is free of x测试如果y是免费的x
issame(x,y)issame(x,y) test if x is same as y如果x是相同测试y
islarger(a,b)islarger(a,b) test if a is larger than b测试是否有高于b
isless(a,b)isless(a,b) test if a is less than b测试是否有少于b
type(x)=="real"式(x)= = "真正的" test if x is real测试如果x是真实的
Vector or list:向量或列表:
[a,b](a,b) vector or list向量或列表
[list(y,x,xmin,xmax)][表(x,y,xmin,xmax)
member([a],j)会员([a]. j) the j-th member of a list [a]j-th成员的名单[j].
last[1]最后一个[1] the first member of the last list去年的第一个成员名单
reverse([x])逆序([x]) reverse a list x逆向列表x
a[1]一个[1] list index, the first member of a list a列表指数、第一个成员名单
dottime(a,b)dottime(a,b) dot product of vectors a and b向量积的a和b
Matrix or array:矩阵或阵列。
[[a11,a12],[a21,a22]][[a11,a12]、[,38,a22]] matrix or array矩阵或阵列
a[a[1]]一个[[1]]
Statistics:统计:
average([a,b])平均([a、b]) avergae of a list of [a,b]avergae名单(a,b)
max([a,b])马克斯([a、b]) max of a list of [a,b]马克斯名单(a,b)
min([a,b])分钟([a、b]) min of a list of [a,b]分钟名单(a,b)
listsum([a,b])listsum([a、b]) convert a list of [a,b] to sum a+b转换一个列表(a、b]综+ b
length([a,b])长度([a、b]) length of a list of [a,b]一个列表的长度(a,b)
Switches:开关:
numeric数字
output输出
expand扩大
expandexpexpandexp
lowercase小写
:=:=
on在
off了
basic基本
fortranfortran
prologprolog
math数学
DOS Commands:DOS命令:
system("dir")系统(“目录”)
Comma:逗号:
,
from从
to对
step一步
then然后
else别的
until直到
Assume:假设:
assume(a>0)假设(> 0) assume a > 0假定> 0
isreal(x):=1来(x):= 1 assume x is real假设x是真正的
Conditional:条件:
if(x>0 then x)如果(x > 0然后x) if x > 0 then x如果x > 0然后x
if(x>0 then x else -x)如果(x > 0然后x别的-x) if x > 0 then x else -x如果x > 0然后-x x别的
Loop:循环:
repeat(expr until x>5)重复直到expr x > 5)repeat expr unti x>5unti expr x >重复5
do(expr, x,xmin,xmax,dx)做的(expr,x,xmin,xmax,dx) do expr w.r.t. x from xmin to xmax with step dx, last output做w.r.t. expr从x xmin层对xmax dx,最后输出
list(y,x,xmin,xmax)表(x,y,xmin,xmax) do expr w.r.t. x from xmin to xmax with step dx, all output做w.r.t. expr从x xmin层对xmax dx,所有的结果吗
Reading:阅读:
readfile("file")readfile(“档案”)read a file with filename “file”阅读文件,文件名"文件"
readcharreadchar read charactor读特征
readlinereadline read a line读一线
Writing:写:
openfile("file")一个打开文件(“文件”) open a file named “file”打开一个文件命名为"文件"
closefile("file")closefile(“文件”) close a file named “file”关闭一个文件命名为"文件"
writes(x)写(x) write text or number on graph mode写文字或数字图形模式
null空
newline换行符 write a new line写新的一行
String:弦:
"123"“123” string字符串
concat("a","b")concat(“一个”、“b”) concate “a” and “b”concate“a”和“b”
break("ab",1)休息(“ab”,1)break “ab” from the first member打破“ab”从第一个成员
length("a")长度(“一个”) length of “a”长度的“a”
string(1)字符串(1) convert a number to a string将一个数字字符串
Getting parts:得到部分:
type(x)类型(x) type of x类型的x
left(a=b)左(= b) left side of a=b左一个= b
right(a=b)正确的(= b) right side of a=b右边的= b
term(a+b)术语a + b)
multi(a*b)多(* b)
coef(y,x)系数(y,x) coefficeint of x in ycoefficeint x,y
coef(y,x,n)系数(y,x,n) coefficeint of x with the n-th order in ycoefficeint x和y的形式秩序
coefall(y,x)coefall(y,x) a list of all coefficients of x in y from low to high, order <5.列出所有系数x y由低到高,订单< 5。
power(x^n)力量(x ^ n) powe, give n鲍威,给n
base(x^n)基地(x ^ n) base, give x基地,给x
argue(x)认为(x) argument of function, argue(f(x)) gives x参数的功能,认为(f(x))给x
sequence(x)序列(x)
re(x)稀土(x) real part实部
im(x)我(x) imaginative part想象力的部分
int(x)智力(x) integer part整数部分
frac(x)数量(x) fractional part小数部分
Database:数据库:
phoneno(x)phoneno(x) phone number电话号码
colorno(x)colorno(x) color number色号
atom_wei(x)atom_wei(x) atomic weight原子的重量
Graph:图:
graph图 graph mode图形模式
text文本 text mode文本模式
cleardevicecleardevice clear graph screen清晰的图形屏幕
line(x1,y1,x2,y2)线(x1,x2,y2,日元) draw a line from point (x1,y1) to (x2,y2)画了一条线从一个点(x1,日元)到(x2,y2)
lineto(x,y)lineto(x,y) draw a line from current point to (x,y)画了一条线从目前的指(x,y)
linerel(dx,dy)linerel(dx,去世) draw a line from current point by (dx,dy)画了一条线从目前的论点(dx,去世)
arc(x,y,r,t1,t2)弧(x,y,r,t1、t2) draw arc at (x,y) with radia r from angle t1 to t2在画弧(x,y)角度,从高继发r级t2
ellipse(x,y,angle1,angle2,xRadius,yRadius)椭圆(x,y,angle1,angle2,xRadius,yRadius)
draw an ellipse arc from angle1 to angle 2 with xRadius and yRadius画了一个椭圆弧线,从angle1角度和yRadius xRadius 2例 as the horizontal and vertical axes at point (x,y)作为点的水平和垂直轴(x,y)
circle(x,y,r)圆(x,y,r) draw a circle at (x,y) with radia r画一个圈(x,y)与高继发r
oval(x,y,xr,yr)椭圆形(x,y,鑫刃,岁) draw an oval at (x,y) with x radia xr and y radia yr画了一个椭圆(x,y)x和y高继发鑫刃高继发老师/年
putpixel(x,y,color)putpixel(x,y,颜色) put pixel at (x,y) with color在把像素(x,y)和颜色
moveto(x,y)moveto(x,y) move current pointer to (x,y)当前指针移动(x,y)
moverel(dx,dy)moverel(dx,去世) move current pointer by (dx,dy)当前的移动指针(dx,去世)
setviewport(x1,y1,x2,y2,clip)setviewport(x1,x2,y2,日元,夹子) set view port from (x1,y2) to (x2,y2)设置视场港由(x1,y2)到(x2,y2)
setlinestyle(style,dir,thick)setlinestyle(风格、目录、厚) set line style风格设置线
settextstyle(font,dir,size)settextstyle(字体、目录、大小) set text style设置文本风格
settextjustify(hor,ver)settextjustify(何珥山、覆盖)
setcolor(colorno)setcolor(colorno) set color设置颜色
setbkcolor(colorno)setbkcolor(colorno) set background color设置背景颜色
getbkcolorgetbkcolor get background color得到背景颜色
getcolorgetcolor get color得到颜色
getxgetx get x of current pointer得到x的当前指针
getygety get y of current pointer得到y的电流指针
getmaxxgetmaxx get max x of screen把马克斯x的屏幕
getmaxygetmaxy get max y of screen获得最大的快乐屏幕
plot(y,x)情节(y,x) plot y w.r.t. x from x=-5 to 5, from y=-5 to 5y w.r.t.情节从x x = 5 - 5,从y = 5 - 5
plot(y,x,xmin,xmax)情节(x,y,xmin,xmax) plot y w.r.t. x from x=xmin to xmax, from y=-5 to 5从x w.r.t.情节y = xmin到xmax x,y = 5 - 5
plot(y,x,xmin,xmax,ymin,ymax)情节(x,y,xmin,xmax,ymin,ymax)
plot y w.r.t. x from x=xmin to xmax, from y=ymin to ymax从x w.r.t.情节y = xmin到xmax x,y = ymin到ymax
dotplot(x^3,x)dotplot(x ^ 3、x)
dotplot(y,x,xmin,xmax)dotplot(x,y,xmin,xmax)
dotplot(y,x,xmin,xmax,ymin,ymax)dotplot(x,y,xmin,xmax,ymin,ymax)
paraplot(x(t),y(t),t)paraplot(x(t),y(t),t) parametric plot x(t) and y(t) w.r.t. t from t=0 to 2*pi情节(t)参数x和y(t)w.r.t. t从0到2 * t = pi
paraplot(x(t),y(t),t,tmin,tmax)paraplot(x(t),y(t),t tmin,tmax) parametric plot x(t) and y(t) w.r.t. t from t=tmin to tmax情节(t)参数x和y(t)w.r.t.从t = tmin t,tmax
polaplot(r(t),t)polaplot(r(t),t) polar plot r(t) w.r.t. t from t=0 to 2*pi极地情节r(t)w.r.t. t从0到2 * t = pi
polaplot(r(t),t,tmin,tmax)polaplot(r(t),t tmin,tmax) polar plot x(t) and y(t) w.r.t. t from t=tmin to tmax极地情节x(t)和y(t)w.r.t.从t = tmin t,tmax
dataplot([x1,x2],[y1,y2])dataplot([x1,x2]、[1,y2]) plot a set of data策划组数据
dataplot([x1,x2],[y1,y2],xmin,xmax,ymin,ymax)dataplot([x1,x2]、[1,y2],xmin,xmax,ymin,ymax)
plot a set of data from xmin to xmax, from ymin to ymax情节的一组数据,从xmin xmax,从ymin到ymax
listplot([y1,y2])listplot([1,y2]) plot a list of data地块的名单数据
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acosh函数 acotacot acothacoth acsc研究会 acschacsch
and和 arc弧 arg高温 argue争论 asec了一类正则
asechasech asinasin asinh作用 assume承担 assumed假定
atanatan atan2atan2 atanh函数 atom_weiatom_wei average平均
base基地 basic基本 block块 cici circle圈
clear清楚 cleared清除 closefileclosefile coef系数 coefallcoefall
colornocolorno concatconcat constant不断 cos因为 cosh事业的
cotcot cothcoth csccsc cschcsch c_infc_inf
d维 dataplotdataplot degree程度 denodeno diff差别
discontdiscont div独特的 do做 done做 dotplotdotplot
dottimedottime dsolvedsolve e艾凡 eiei ellipse椭圆
else别的 erf广泛的 eval: exp实验 expand扩大
expandallexpandall expanddeexpandde expandexpexpandexp f'(x)f '(x) fac前沿空中管制官
factor因素 fortranfortran frac数量 from从 gamma伽玛
gcd肾小球囊性肾病 getbkcolgetbkcol getcolorgetcolor getmaxxgetmaxx getmaxygetmaxy
getxgetx getygety graph图 grid网格 i我
if如果 im我 infinf infsuminfsum int智力
inte强烈 iscomplexiscomplex iseveniseven isfreeisfree isintegerisinteger
islargerislarger islessisless islistislist isnumberisnumber isoddisodd
isratioisratio isreal来 issameissame laplace拉普拉斯 last最后
left离开 length长度 li李 lim老林 line线
linerellinerel linetolineto list列表 listplotlistplot listsumlistsum
ln淋巴结 local当地 log10t lowercase小写 math数学
max马克斯 member成员 min分钟 mod国防部 moverelmoverel
movetomoveto multmult newline换行符 ninteninte nlimnlim
not不 nsolvensolve null空 num胡 number号码
numenume numeric数字 off了 on在 openfile一个打开文件
or或 order秩序 output输出 oval椭圆形 paraplotparaplot
partsumpartsum pipi plot情节 power权力 prod促进
prologprolog psolvepsolve putpixelputpixel random随机 ratio比
re稀土 readcharreadchar readfilereadfile readlinereadline repeat重复
reverse逆向right权利 root根 round圆 sec秒
sechsech sequence序列 series系列 setbkcolorsetbkcolor setcolorsetcolor
setlinestylesetlinestyle settextjustifysettextjustify settextstylesettextstyle setviewpointsetviewpoint sisi
sign标志 sin罪 sinhsinh solve解决 sqrtsqrt
step一步 string字符串 subs替补 sum金额 system系统
table表 tan谭 tanhtanh term术语 text文本
then然后 to对 trunctrunc type类型 undefined未定义
until直到 writes写 zero零
++ -- * / ^
** () [] == :=:=
=== = > >=> = < <=< =
<> ! # , |x|| | x
"x"“x” '
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You can use library as standard functions by library name without extension. 你可以使用图书馆作为图书馆的名字没有标准功能扩展。E.g. abs, not abs.li.如abs、不abs.li。
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ABS.LIABS.LI ACOS.LIACOS.LI ACOSH.LIACOSH.LI
ACOT.LIACOT.LI ACOTH.LIACOTH.LI ACSC.LIACSC.LI ACSCH.LIACSCH.LI ARG.LIARG.LI
ASEC.LIASEC.LI ASECH.LIASECH.LI ASINH.LIASINH.LI ASSUME.LIASSUME.LI ATAN.LIATAN.LI
ATAN2.LIATAN2.LI ATANH.LIATANH.LI ATOM_WEI.LIATOM_WEI.LI AVERAGE.LIAVERAGE.LI AXIS.LIAXIS.LI
CEILING.LICEILING.LI CIRCLE.LICIRCLE.LI COEF.LICOEF.LI COLORNO.LICOLORNO.LI COS.LICOS.LI
COSH.LICOSH.LI COT.LICOT.LI COTH.LICOTH.LI CSC.LICSC.LI CSCH.LICSCH.LI
D.liD.li DATAPLOT.LIDATAPLOT.LI DENO.LIDENO.LI DET.LIDET.LI DIFF.LIDIFF.LI
DIFF2.LIDIFF2.LI DO.LIDO.LI DOTPLOT.LIDOTPLOT.LI DOTTIME.LIDOTTIME.LI DSOLVE.LIDSOLVE.LI
DT.LIDT.LI EI.LIEI.LI ERF.LIERF.LI EXPANDAL.LIEXPANDAL.LI EXPANDDE.LIEXPANDDE.LI
FAC.LIFAC.LI FACTOR.LIFACTOR.LI FIT.LIFIT.LI FITPLOT.LIFITPLOT.LI FIXAXIS.LIFIXAXIS.LI
FLOOR.LIFLOOR.LI FRAC.LIFRAC.LI GAMMA.LIGAMMA.LI GCD.LIGCD.LI GRID.LIGRID.LI
IFACTOR.LIIFACTOR.LI IM.LIIM.LI INFPROD.LIINFPROD.LI INFSUM.LIINFSUM.LI INT.LIINT.LI
Inte.liInte.li INTE.LIBINTE.LIB Inte.licInte.lic INTeger.LIINTeger.LI INTE_SUB.LIINTE_SUB.LI
INVERSE.LIINVERSE.LI ISLARGER.LIISLARGER.LI ISLESS.LIISLESS.LI ISMEMBER.LIISMEMBER.LI ISREAL.LIISREAL.LI
LAPLACE.LILAPLACE.LI LI.LILI.LI LIM.LILIM.LI LIST.LILIST.LI LISTPLOT.LILISTPLOT.LI
LISTSUM.LILISTSUM.LI LN.LILN.LI LOG10.LILOG10.LI LSOLVE.LILSOLVE.LI MAX.LIMAX.LI
MEMBER.LIMEMBER.LI MIN.LIMIN.LI MOD.LIMOD.LI MODELPLO.LIMODELPLO.LI NINTE.LININTE.LI
NLIM.LINLIM.LI NOT.LINOT.LI NSOLVE.LINSOLVE.LI NUME.LINUME.LI ORDER.LIORDER.LI
OVAL.LIOVAL.LI PARAPLOT.LIPARAPLOT.LI PARTPROD.LIPARTPROD.LI PARTSUM.LIPARTSUM.LI PHONENO.LIPHONENO.LI
PLOT.LIPLOT.LI PLOT0.LIPLOT0.LI PLOT2EQ.LIPLOT2EQ.LI PLOT2Y.LIPLOT2Y.LI PLOTEQ.LIPLOTEQ.LI
PLOTGRID.LIPLOTGRID.LI POLAPLOT.LIPOLAPLOT.LI POLYDIV.LIPOLYDIV.LI POLYDIV2.LIPOLYDIV2.LI POLYMOD.LIPOLYMOD.LI
PRIME.LIPRIME.LI PROD.LIPROD.LI PSOLVE.LIPSOLVE.LI RE.LIRE.LI REACT.LIREACT.LI
RECTANGL.LIRECTANGL.LI REVERSE.LIREVERSE.LI ROOT.LIROOT.LI SEC.LISEC.LI SECH.LISECH.LI
SERIES.LISERIES.LI SI.LISI.LI SIGN.LISIGN.LI SIN.LISIN.LI SINH.LISINH.LI
SOLVE.LISOLVE.LI STD.LISTD.LI subst.lisubst.li SUM.LISUM.LI TABLE.LITABLE.LI
TAN.LITAN.LI TANH.LITANH.LI TERM.LITERM.LI TOGETHER.LITOGETHER.LI VAR.LIVAR.LI
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The keywords indicated internal are the internal functions or constans, otherwise they are the external.关键词表明内部内部功能或constans,否则他们是外部的。
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* absabs internal+external内部+外部
abs(x) is the absolute value function of x. x can be complex numbers. abs(x)是绝对的价值功能的x是复杂的x数字。abs(x) = sqrt(re(x)^2+im(x)^2). abs(x)= sqrt(re(x)^ 2 +输入法(x)^ 2)。The results are in the range 0 to inf. abs(x) = |x|.结果在范围0到inf. abs(x)= | | x。
See also: abs, arg, sign, re, im, |x|.还看到:abs、高温、标志、稀土,im,| | x。
e.g.例句。
IN:在: abs(-1), abs(-i)abs(1),abs(-)
OUT: 1, 1出:1、1
* acos函数
acos(x) is the arc cosine function of x. The inverse function of cos(x). (x)是函数功能的弧形余弦逆函数x。因为(x)。The result is given in radians.给出结果按弧度。
See also: acos, cos.还看到:函数,因为。
* acosh函数
acosh(x) is the inverse hyperbolic cosine function of x. The inverse function of cosh(x).函数(x)是反双曲余弦函数的逆函数x。事业(x)。
See also: acosh, cosh.还看到:函数,事业。
* acotacot
acot(x) is the arc cotangent function of x. The inverse function of cot(x). acot(x)是电弧cotangent功能。反功能x(x)胶辊。The result is given in radians. 给出结果按弧度。acot(x)=pi/2-atan(x).acot(x)= pi / 2-atan(x)。
See also: acot, cot.还看到:acot、胶辊。
* acothacoth
acoth(x) is the inverse hyperbolic cotangent function of x. The inverse function of coth(x). acoth(x)是cotangent所对应的反双曲函数的逆函数x。coth(x)。acoth(x)=atanh(1/x).acoth(x)=函数(1 / x)。
See also: acoth, coth.还看到:acoth,coth。
* acsc研究会
acsc(x) is the arc cosecant function of x. The inverse function of csc(x). 研究会(x)是电弧cosecant功能。反功能x csc(x)。The result is in radians. 结果是按弧度。acsc(x)=pi/2-asin(x).研究会(x)= pi / 2-asin(x)。
See also: acsc, csc.还看到:研究会,csc。
* acschacsch
acsch(x) is the inverse hyperbolic cosecant function of x. The inverse function of csch(x). acsch(x)是cosecant所对应的反双曲函数的逆函数x。csch(x)。acsch(x)=asinh(1/x).acsch(x)=作用(1 / x)。
See also: acsch, csch.还看到:acsch,csch。
* and和 internal内部
logic operator. 逻辑运算符。It is bitwise and. 这是位。The result is 1, 0 or unevaluated.结果是1、0或unevaluated。
See also: and, or.看也:和或。
e.g.例句。
IN:在: 1 and 1, 1 and 01和1,1和0
OUT: 1, 0出:1、0
* arc弧 internal内部
arc(x,y,angle1,angle2,radius) draws a circular arc from angle1 to angle2 with radius at point(x,y). 弧(x,y,angle1,angle2、半径)吸引一个圆弧半径,从angle1 angle2点与(x,y)。The angles are counter-clockwise with 0 degrees at o'clock, 90 degrees at 12 o'clock, and so on. 逆时针方向旋转角度的方法,是0度点,90度到12点钟,等等。It only works on graphics mode.它只适用于图形模式。
See also: arc, ellipse, line, lineto, linerel, putpixel.还看到:弧形管、椭圆管、线、lineto,linerel,putpixel。
e.g.例句。
IN:在: graph, arc(100,100,0,180,100), readchar, text图、弧形(100100—0180100),readchar、文本
* arg高温
arg(x) gives the argument (phase angle) of x in radians. 高温(x)给的论点(相位)的x的弧度。It only gives the principle value (P.V.): -pi < arg(x) <= pi. 它只给出了原理价值(P.V.):-pi <高温(x)< = pi。arg(x) = atan2(re(x),im(x)). 高温(x)= atan2(re(x),我(x))。x can be complex number. x是复杂的号码。For positive real x, arg(x)=0.为积极的真正的x,高温(x)= 0。
See also: abs, arg, sign, atan2.还看到:abs、高温、标志,atan2。
e.g. num(arg(i)) gives 1.5..如:胡(高温(我)让1.5 . .
* argue争论 internal内部
argue(f(x)) gives the argument of the function f(x). 认为(f(x))给出了参数的函数f(x)。type(f(x)) gives the function name.型(f(x))给函数的名称。
See also: type.还看到:类型。
e.g. argue(sin(x)) give x, type(sin(x)) gives "sin()".如认为(罪(x))给x,类型(罪(x))给“罪()”。
* asec了一类正则
asec(x) is the arc secant function of x. The inverse function of sec(x). 了一类正则(x)是电弧进行功能。反功能x秒(x)。The result is given in radians.给出结果按弧度。
See also: asec, sec.还看到:了一类正则,秒。
* asechasech
asech(x) is the inverse hyperbolic secant function of x. The inverse function of sech(x). asech(x)是进行反双曲函数的逆函数x。sech(x)。asech(x)=acosh(1/x).asech(x)=函数(1 / x)。
See also: asech, sech.还看到:asech,sech。
* asinasin
asin(x) is the arc sine function of x. The inverse function of sin(x). asin(x)是弧正弦函数的逆函数x。罪(x)。The result is given in radians.给出结果按弧度。
See also: asin, sin.还看到:asin,罪。
* asinh作用
asinh(x) is the inverse hyperbolic sine function of x. The inverse function of sinh(x).(x)是作用所对应的反双曲正弦函数的逆函数x。sinh(x)。
See also: asinh, sinh.还看到:作用,sinh。
* assume承担
assume(x > 1) assumes the variable x > 1 in real domain.假设(x > 1)假设变量x > 1在现实领域。
By default, |x| < inf and all variables are complex, except that variables in inequalities are real, as usual only real numbers can be compared. 默认情况下,| | < inf和x��量是复杂的,除了变量不等式是很实际的,像往常一样唯一真正的编号可比的。e.g. x is complex in sin(x), but y is real in y > 1.如x是复杂的罪(x),但y是真实的y > 1。
You can restrict the domain of a variable by assuming the variable is even, odd, integer, real number, positive or negative. 你可以限制一个变量的领域通过假设变量为均匀,奇怪,整数,实数、积极还是消极的。The assume() can be cleared by clear().这个假设()能被清理清晰()。
See also: sign, isodd, iseven, isinteger, isreal, isnumber, clear.还看到:标志,isodd,iseven,isinteger来,以色列情报机构摩萨德一直,isnumber、清楚。
e.g. assume(x>0), assume(x>0, y<0), iseven(x):=1例如假设(x > 0),假设(x > 0,y < 0),iseven(x):= 1
* assumed假定
assumed points out that the variable has been assumed.假设指出变量被假定。
See also: assume, clear.还看到:假设,清晰。
* atanatan internal + external内部+外部
atan(x) is the arc tangent function of x. The inverse function of tan(x). atan(x)是弧正切函数的逆函数x。谭(x)。The result is given in radians.给出结果按弧度。
See also: atan, tan.还看到:atan,黄褐色。
* atan2atan2 internal内部
atan2(x,y) returns the radian angle of (x,y).atan2(x,y)返回弧度角的(x,y)。
atan2(x,y)atan2(x,y) = sign(y)*pi/2符号=(y)* pi / 2 if x=0如果x = 0
= atan(y/x)= atan(y / x) if x>0如果x > 0
= atan(y/x)+pi= atan(y / x)+ pi if x<0, y>=0如果x < 0,y > = 0
= atan(y/x)-pi= atan -pi(y / x) if x<0, y<0 .如果x < 0,y < 0。
Thus atan2(x,y) takes its value of -pi < atan2(x,y) <= pi.因此atan2(x,y)以其价值,-pi < atan2(x,y)< = pi。
See also: atan, arg.还看到:atan、高温。
* atanh函数
atanh(x) is the inverse hyperbolic tangent function of x. The inverse function of tanh(x).函数(x)是相对应的x的双曲正切函数的逆的功能。tanh(x)。
See also: tanh.还看到:tanh。
* average平均
average(x) gives average of a list of data.平均(x)给平均列表的数据。
See also: max, min, length, listsum.还看到:最大、最小、长度、listsum。
e.g.例句。
IN:在: average([1,2,3]平均([1、2、3)
OUT: 2出:2
* base基地 internal内部
base(x^n) gives the base of x^n.基地(x ^ n)给x ^ n的基础。
See also: base, power, type.还看到:基地、电力、��型。
e.g. base(x^n) gives x, type(x^n) gives "^", power(x^n) gives n.例如基地(x ^ n)给x,类型(x ^ n)给“^”、权力(x ^ n)给n。
* basic基本 internal内部
basic is a value of the switch output. 基本是一个价值的开关输出。It sets output in BASIC format.它集基本格式输出。
See also: output, on, off, fortran, prolog, math.还看到:输出,上、下、fortran,prolog,数学。
e.g. output := basic.如输出:=基础。
* block块 internal内部
block(a,b,c) groups a,b,c and only returns the last argument as its value, or returns the second last argument as its value if the last argument is local(). 块(a、b、c)集团a、b、c和只返回最后一个参数为价值,或者返回倒数第二个参数为价值如果最后的论点是当地()。It is used as grouper in definition of a procedure. 作为一个程序的定义上。All variables in block are global, except for variables declared by local().所有变量的块都是全球性的,除了变量声明当地()。
See also: local.还看到:当地的市场。
e.g. f(x_):=block(p:=x^6,p, local(p))如f(x_):=区块(p = x ^:6、磷、当地(p))
* break打破 internal内部
break("ab",n) breaks a string into two strings in position of the n-th characters.休息(“ab”,n):将一个字符串以两个字符串的形式在位置的字符。
e.g. break("ab",1) gives [a,b].如休息(“ab”,1)给(a,b)。
* cici
ci(x) is cos integral, ci(x) = inte(cos(x)/x, x).ci(x)是因为积分、ci(x)=交互(因为(x)/ x,x)。
See also: si, ei, gamma, erf.还看到:是的,ei,伽马、广泛。
* circle圈
circle(x,y,radius) draws a circle at point(x,y) with radius.圆(x,y,半径画一圈点(x,y)和半径。
See also: graph, arc, oval.还看到:图形,弧,椭圆形。
e.g. graph, circle(200,200,100), readchar, text例如图,圆(200200100),readchar、文本
* clear清楚 internal内部
clear(y) clears values and definitions for the variable, function or expression y from memory.清楚(y)放行的价值观和定义的变量、函数或表达式y从记忆。
See also: assume, :=.还看到:假设,即:=。
e.g. clear(p), clear(f(x)), clear(a>0)如明显(p),明显(f(x)),清楚(> 0)
* cleared清除 internal内部
It says that the variable, function or expression has been cleared from assignment.报告说,变量、函数或表达式已经允许从任务。
See also: clear, assume, :=.还看到:明确承担,:=。
* closefileclosefile internal内部
closefile("filename") closes the file "filename" and return the output to screen. closefile(文件名)关闭文件"文件名“后输出到屏幕。The filename is any MS-DOS file name.文件名是任何ms - dos文件名。
See also: openfile, readfile.还看到:一个打开文件,readfile。
* coef系数 internal + external内部+外部
coef(y,form) gives the coefficient of form in the polynomial y. It picks only terms that contain the particular form specified. 系数(y,形成了形态系数多项式y。它撷取只有条款包含特定的形式规定。x is not considered part of x^6.x是不考虑x ^ 6。部分
See also: coefall.还看到:coefall。
e.g.例句。
IN:在: coef(2*x^6+x+4, x^6), coef(2*x^6+x+4, x)系数(2 * x ^ 6 + x + 4,x ^ 6),系数(2 * x ^ 6 + x + 4,x)
OUT: 2, 1出:2、1
coef(y, x, order) gives the coefficient of x with order in the polynomial系数(x,y,顺序)给出了x与秩序系数多项式
y.y。 order < 5.订单< 5。
e.g.例句。
IN:在: coef(x^2+x+6, x, 0)系数(x ^ 2 + x + 6,x,0)
OUT: 6出:6
* coefallcoefall internal内部
coefall(y, x) gives a list of all coefficients of x in the polynomial y. order < 5.coefall(y,x)给列出所有系数多项式与x的订单< 5。 The polynomial is in order from low to high.多项式是为了从低到高。
See also: coef.还看到:系数。
e.g.例句。
IN:在: coefall(6+5*x+x^2, x)coefall(6 + 5 * x + x ^ 2、x)
OUT: [6, 5, 1]出:[6、5,1]
* concatconcat internal内部
concat("a","b") concatenates 2 string into one string.concat(“一个”、“b”)序2串成一个字符串。
See also: remove, string.还看到:删除、字符串。
e.g. concat("a","b") gives "ab".例如concat(“一个”、“b”)给“ab”。
* constant不断 internal+external内部+外部
The indefinite integral constant. 的不定积分常数。It only appear on solving differential equation, be omitted on indefinite integral.它只出现在求解微分方程,对不定积分被忽略掉。
See also: dslove, pi, e.还看到:dslove,pi、e。
* cos因为 internal + external内部+外部
cos(x) is the cosine function of x. The angle x is measured in radians (multiply by degree to convert from degrees). 因为(x)是余弦函数x。角度弧度测量x(乘程度的转换度)。x can be complex numbers.x是复杂的数字。
See also: acos, sec.还看到:函数、秒。
* cosh事业的
cosh(x) is the hyperbolic cosine function of x. cosh(x)=(exp(x)+exp(-x))/2. (x)是事业的双曲余弦函数事业x(x)=(经验(x)+经验(-x)/ 2。x can be complex numbers.x是复杂的数字。
See also: acosh.还看到:函数。
* cotcot
cot(x) is the cotangent function of x. The angle x is measured in radians. cot(x)是cotangent功能角度x是x。以弧度。(multiply by degree to convert from degrees). (乘程度的转换度)。cot(x)=1/tan(x).cot(x)= 1 / tan(x)。
See also: acot, tan.还看到:acot,黄褐色。
* cothcoth
coth(x) is the hyperbolic cotangent function of x. coth(x)=1/tanh(x).coth(x)是cotangent双曲函数coth x(x)= 1 / tanh(x)。
See also: acoth, tanh.还看到:acoth,tanh。
* csccsc
csc (x) is the cosecant function of x. The angle x is measured in radians (multiply by degree to convert from degrees). csc(x)是cosecant功能角度x是x。以弧度(乘程度的转换度)。csc(x)=1/sin(x) x can be complex numbers.csc(x)= 1 /罪(x)x是复杂的数字。
See also: acsc, sin.还看到:研究会,罪。
* cschcsch
csch(x) is the hyperbolic cosecant function of x. csch(x)=1/sinh(x). csch(x)是cosecant双曲函数csch x(x)= 1 / sinh(x)。x can be complex numbers.x是复杂的数字。
See also: acsch, sinh.还看到:acsch,sinh。
* c_infc_inf internal内部
The complex infinite, both real and imaginary parts of complex numbers are infinity, as the built-in constant. 复杂的无限,既真实和想象的复杂的数字是无限的部分,内置的常数。complex_inf=inf+inf*i, inf-inf*i, -inf+inf*i, or -inf-inf*i.complex_inf = inf + inf *我,inf-inf *我,-inf + inf *我,或者-inf-inf *我。
See also: inf, zero.还看到:无穷大,零。
* d维 internal + external内部+外部
d() gives the partial derivative.d()给的偏导数。
d(y,x)d(y,x) internal内部
It differentiate y with respect to x.它鉴别y就x。
e.g. d(x^2,x) gives 2*x.例如d(x ^ 2、x)给2 * *。
d(f(x),x) is the same as f'(x) .d(f(x)、x)是一样的”(x)f。
e.g. d(sin(x),x) gives cos(x).例如d(罪(x)、x)给因为(x)。
d(y, x, n)d(x,y,n)
It gives the n-th order derivative of y with respect to an undefined variable x.给出了阶导数形式的y就一个未定义的变量x。
e.g. d(sin(x),x,2) gives -sin(x).例如d(罪(x)、x,2)给-sin(x)。
See also: diff, f'(x), lim, inte, ninte.还看到:比较、f '(x),ninte,强烈的涵义。
* degree程度
degree gives the number of radians in one degree. 给予数量的弧度的程度在一个学位。degree=pi/180. 学历= pi / 180。You can multiply by degree to convert from degree to radians.你可以乘程度弧度的转换程度。
See also: pi.还看到:pi。
e.g. 45*degree, sin(45*degree).例句。45度程度、罪(45度度)。
* denodeno internal内部
deno(x) gives denominator of x. It only works for rational number.deno(x)给分母x。它仅作为理性的号码。
See also: nume.还看到:nume。
e.g. deno(2/3) gives 3.例如deno(2/3)给3。
* diff差别
diff(y, x = x0) differentiates y when x = x0.比较(y,x = x0)y当x = x0辨析。
See also: d, inte, lim.还看到:d,密集,小林。
e.g. diff(x^6, x = 1) gives 6.例如差异(x ^ 6、x = 1)给6。
* div独特的 internal内部
div(a,b) divides a by b in integer.师(a,b)分为b在整数。
See also: mod.还看到:国防部。
e.g. div(5,2) gives 2, mod(5,2) gives 1.例如师(5)、2)给2、国防部(5)、2)给1。
* discontdiscont internal内部
The discontinuity. 这个城市不连续性。If f(x0) gives discont, the function has a discontinuity and only has the one-sided value at x=x0. 如果f(x0)给discont,功能有一个非连续性及价值,只有在x = x0片面。You should evaluate its left-sided or right-sided value by f(x0-zero) or f(x0+zero).你应该评估它的左侧或右侧价值f(x0-zero)或f(x0 +零)。
See also: zero, inf.还看到:零,无穷大。
e.g.例句。
IN:在: f(x_) := 1/x+1f(x_):= 1 / x + 1
IN:在: f(0)f(0)
OUT: discont出:discont
IN:在: f(0+zero)f(0 + 0)
OUT: inf出:步
* do做 internal内部
do(expr, x,xmin,xmax,dx) evaluates expr with the x looping from xmin to xmax on step dx.做的(expr,x,xmin,xmax,dx)评估expr与x,从xmin xmax环状步__。
See also: repeat, list.还看到:重复,列表。
e.g.例句。
IN:在: x:=0, do(x:=x+1, j,1,5,1)谢:= 0,(x:= x + 1,j,1、5,1)
OUT: x := 5出:谢:= 5
* done做 internal内部
It indicates that the command has been done. 它表示命令已经做到了。See also: assumed, cleared.还看到:假设,清除。
* dotplotdotplot
dotplot(y, x) plots y with dots.dotplot(y,x)情节y用点。
dotplot(y, x,xmin,xmax)dotplot(x,y,xmin,xmax)
dotplot(y, x,xmin,xmax,ymin,ymax)dotplot(x,y,xmin,xmax,ymin,ymax)
See also: plot, polaplot, paraplot.还看到:阴谋,polaplot,paraplot。
e.g. dotplot(x^3, x)例如dotplot(x ^ 3、x)
* dsolvedsolve
dsolve(y'(x)=f(x,y), y(x), x) solves the first order variables separable and linear differential equations. dsolve(y”(x)= f(x,y),y(x)、x),解决了一阶变量分离和线性微分方程。The y'(x) must be alone on the left hand side of the equations.y”(x)必须单独左侧方程。
See also: solve, nsolve.还看到:解决,nsolve。
e.g. dsolve(y'(x) = sin(x), y(x), x)例如dsolve(y”(x)=罪(x),y(x)、x)
* E艾凡 internal内部
E is the exponential part of a floating point number.E是指数部分浮点数。
See also: e, exp.还看到:e、经验。
e.g. 1.1E2 is the same as 1.1*10^2.例句。1.1 E2相当于1.1 * 10 ^ 2。
* e艾凡 internal + external内部+外部
(1) e is the exponential constant (base of natural logarithms), e=2.718...(1)e是指数常数(基地的自然对数)、e = 2.718…, the built-in constant, e is converted to 2.718... ,内置恒、e转化为2.718…when the switch numeric:=on. 当水开关数字:=。e^x is the same as exp(x).e ^ x是一样的经验(x)。
e.g. e^2, e^x.例如e ^ 2、e ^ x。
(2) e is the exponential part of a floating point number, the same as E.(2)e是指数部分浮点数,与e。
e.g. 1.1e2 is the same as 1.1E2.例句。1.1 e2相当于1.1 e2。
See also: E, exp.还看到:E、经验。
* eiei
ei(x) is the exponential integral function Ei(x), ei(x) = inte(e^t/t, t,-inf,x), ei'(x) = e^x/x.美国饭店协会教育学院(x)是生态指数积分函数(x),ei(x)=交互(e ^ t / t,t -inf、x),ei”(x)= e ^ x / x。
ei(n,x) is the incomplete exponential integral function, ei(n,x) = inte(t^n*e^t, t,-inf,x), d(ei(n,x),x) = x^n*e^x, ei(-1, x) = ei(x), ei(0,x) = e^x.美国饭店协会教育学院(n、x)是指数积分函数不完整,ei(氮、x)=交互(t ^ ^ n * e t,t -inf、x),d(ei(n、x),x)= x ^ ^ n * e x,ei(1 x)= ei(x),ei(0 x)= e ^ x。
See also: gamma, erf, ci, si, li.还看到:伽马、角度、ci、硅、李。
* ellipse椭圆 internal内部
ellipse(x,y,angle1,angle2,XRadius,YRadius) draws an elliptical arc from angle1 to angle2 with XRadius and YRadius as the horizontal and vertical axes at point(x,y). 椭圆(x,y,angle1,angle2,XRadius,YRadius)绘制了一个椭圆弧形,从angle1 angle2 XRadius和YRadius与作为点的水平和垂直轴(x,y)。The angles are counter-clockwise with 0 degrees at o'clock, 90 degrees at 12 o'clock, and so on. 逆时针方向旋转角度的方法,是0度点,90度到12点钟,等等。it only works on graphics mode.它只适用于图形模式。
See also: arc, ellipse, line, lineto, linerel, putpixel.还看到:弧形管、椭圆管、线、lineto,linerel,putpixel。
e.g.例句。
IN:在: graph, ellipse(100,100,0,180,200,100), readchar, text图,椭圆(100100—0180200100),readchar、文本
* else别的
comma. 一个逗号。The same as comma ,. 逗号一样。The 6 keywords: from, to, step, then, else, until are the same as comma ,.6关键词:从,,一步,然后,否则,直到同逗点,。
See also: from, to, step, then, until, ,.还看到:从,一步,然后,直到,。
* eval: internal内部
eval(y) evaluates y. It is only used in definition of a function.(y)评价:y。它是只用于定义的功能。
e.g.例句。
IN:在: f(x_):= eval(sin'(x))f(x_):=:'(x)(罪)
OUT: f(x_) := cos(x).出:f(x_):=因为(x)。
* erf广泛的
erf(x) is the error function of x. It is the probability integral(x)是广泛的误差函数x。它是概率积分 function or the integral of the Gaussian distribution. 函数或整体的高斯分布。erf(x) = 2/sqrt(pi)*inte(exp(-t^2),t,0,x), d(erf(x),x) = 2/sqrt(pi)*e^(-x^2).广泛的(x)= 2 / sqrt(pi)*强烈预期(刚^ 2),t - x),d(角度(x)、x)= 2 / sqrt(pi)* e ^(-x ^ 2)。
See also: ei, gamma, ci, si.还看到:ei,伽马、ci、硅。
* exp实验 internal内部
exp(x) is the exponential function of x (base of e). The same as e^x, e=2.718... (x)是经验的指数函数x(基地的e)。同e ^ x,e = 2.718…It is the inverse to ln(x). 它是相对应的,淋巴结(x)。x can be complex numbers.x是复杂的数字。
See also: e, E.还看到:e、e。
* expand扩大 internal内部
(1) expand(y)(1)膨胀(y) expands out products and positive powers in y. expand() works only on positive integer powers.扩大了产品和积极的力量扩大()与作品只有在正整数的力量。
See also: factor.还看到:因素。
e.g. expand((a+b)^2) gives a^2 + 2*a*b + b^2.例如扩大(a + b)^ 2)给^ 2 + 2 b + b * * ^ 2。
(2) the switch of expansion.(2)切换的扩张。
expand:=on拓展:=在 e.g. c*(a+b) to c*a+c*b.如c * a + b)c * + c * b。
expand:=off拓展:=了 disable expansion, this is default.禁用扩张,这是默认值。
See also: expandexp.还看到:expandexp。
* expandexpexpandexp internal内部
The switch of exponential expansion.开关指数扩张。
expandexp:=onexpandexp:=在 e.g. c^(a+b) to c^a*c^b.如c ^(a + b)c ^ ^一个度b。
expandexp:=offexpandexp:=了 disable exponential expansion, this is default.伤残指数扩张,这是默认值。
See also: expand.还看到:扩大。
* f'(x)f '(x)
f'(x) differentiates f(x) with respect to x. f'(x)=d(f(x),x). f '(x)划分f(x)关于x。f '(x)= d(f(x)、x)。f'(x0) is different from diff(f(x), x=x0): f'(x0) first evaluates f(x0), then differentiates the value of f(x0); diff(f(x), x=x0) first differentiates f(x), then replace x = x0.f '(x0)不同于差异(f(x)、x = x0):f '(x0)首先评估f(x0),然后划分价值f(x0);差异(f(x)、x = x0)首先划分f(x),然后替换x = x0。
See also: d.还看到:d。
e.g. sin'(x) gives cos(x).如罪”(x)给因为(x)。
* fac前沿空中管制官
fac(n) is the factorial function of n. The same as n!.前沿空中管制官(n)是因功能。一样的氮n。
See also: n!.还看到:n。
e.g. fac(3) gives 6.如前沿空中管制官(3)给予6。
* factor因素 internal + external内部+外部
factor(y)因子(y) internal内部
It factorises y.它factorises y。
See also: expand, expandexp.还看到:扩展,expandexp。
e.g.例句。
IN:在: factor(a^2 + 2*a*b + b^2)因子(一个^ 2 + 2 b + b * * ^ 2)
OUT: (a+b)^2出:a + b)^ 2
factor(y, x)因子(y,x)
It factorises y for x. y must be polynomial with order < 5.它factorises y为x。y必须多项式订单< 5。
e.g.例句。
IN:在: factor(x^2+5*x+6, x)因子(x ^ 2 + 5 * x + 6,x)
OUT: (2+x) (3+x)出:(2 + x)(3 + x)
* fortranfortran internal内部
fortran is the value of the switch output. fortran语言的价值开关输出。It forces the output in FORTRAN format.它迫使输出FORTRAN语言格式。
See also: output, basic, math, prolog, on, off.还看到:输出、基础、数学、prolog,上、下。
e.g. output:=fortran.如输出:= fortran语言。
* frac数量
frac(x) gives the fractional part of number x. frac(x)=x-trunc(x).(x)给数量小数部分的数字x(x)= x-trunc数量(x)。
See also: int, trunc.还看到:智力trunc。
e.g. frac(2.4) gives 0.4.例如数量让0.4(2.4)。
* from从
The comma, the same as the comma (,). 逗号,逗号的一样()。The 6 keywords: from, to, step, then, else, until are the same as comma ,.6关键词:从,,一步,然后,否则,直到同逗点,。
See also: to, step, then, else, until , ,.还看到:、步骤、然后,否则,直到,。
* gamma伽玛
gamma(n) is the gamma function _(n), gamma(n) = inte(t^(n-1)*e^(-t), t,0,inf), gamma(n) = (n-1)!.伽玛(n)是伽玛函数_(n),伽马(n)=交互(t ^ ^(n-1)* e(刚),t 0,inf),伽马(n)=(n-1)!
gamma(n,x) is the incomplete gamma function, gamma(n,x) = inte(t^n*e^(-t), t,0,x),伽玛(氮、x)是不完整的伽玛函数,伽马(氮、x)=交互(t ^ ^ n * e(刚),t - x) d(gamma(n,x),x) = x^n*e^(-x) gamma(n,0) = 0, gamma(n,inf) = gamma(n+1) = n!.d(伽玛(n、x),x)= x ^ ^ n * e(-x)伽马(n,0)= 0,伽马(氮、inf)=伽玛(n + 1)= n。
gamma(n,x) is similar to gamma(n), but its power term is t^n, instead of t^(n-1).伽玛(氮、x)类似于伽玛(n),但是它的力量术语t ^ n,而不是t ^(n-1)。
See also: ei, erf, ci, si, li.还看到:ei,广泛、ci、硅、李。
* gcd肾小球囊性肾病
gcd(a,b) gives the greatest common divider of a and b.肾小球囊性肾病(a,b)给出了常见的最大分a和b。
e.g. gcd(2,4) gives 2.如肾小球囊性肾病(2、4)给2。
* getbkcolorgetbkcolor internal内部
getbkcolor gets background color on the graph screen. 背景颜色getbkcolor得到图上的屏幕。It must be on the graph mode.它必须图上的模式。
See also: getbkcolor, getcolor, setbkcolor, setcolor.还看到:getbkcolor,getcolor,setbkcolor,setcolor。
* getcolorgetcolor internal内部
getbkcolor gets foreground color on the graph screen. getbkcolor得到景色图上的屏幕。It must be on the graph mode.它必须图上的模式。
See also: getbkcolor, getcolor, setbkcolor, setcolor.还看到:getbkcolor,getcolor,setbkcolor,setcolor。
* getmaxxgetmaxx internal内部
getmaxx gets the max x of the graphics screen (number of column of pixel). getmaxx得到最大x的图形屏幕(数量的列像素)。For EGA video, getmaxx gives 640. 法治的视频,getmaxx给640。It must be in graph mode.它必须在图形模式。
See also: getmaxx, getmaxy, getx, gety.还看到:getmaxx,getmaxy,getx,gety。
* getmaxygetmaxy internal内部
getmaxy gets the max y of the graphics screen (number of rows of pixel). getmaxy得到最大y的图形屏幕(像素的行数)。For EGA video, getmaxy gives 350. 法治的视频,getmaxy给350。It must be in graph mode.它必须在图形模式。
See also: getmaxx, getmaxy, getx, gety.还看到:getmaxx,getmaxy,getx,gety。
* getxgetx internal内部
getx gets the x of the current point(x,y) on the graphics screen (number of column of pixel). getx得到x的当前点(x,y)在图形屏幕(数量的列像素)。For EGA video, 0 <= getx < 640. 法治的视频,0 < = getx < 640。It must be in graph mode.它必须在图形模式。
See also: getmaxx, getmaxy, getx, gety.还看到:getmaxx,getmaxy,getx,gety。
* getygety internal内部
gety gets the y of the current point(x,y) on the graphics screen (number of rows of pixel). gety得到y当前点(x,y)在图形屏幕(像素的行数)。For EGA video, 0 <= gety < 350. 法治的视频,0 < = gety < 350。It must be in graph mode.它必须在图形模式。
See also: getmaxx, getmaxy, getx, gety.还看到:getmaxx,getmaxy,getx,gety。
* graph图 internal内部
graph is the graph mode. 图是图形模式。It initialises the graphics system and sets the screen to graphics mode. 它initialises图形系统和设置屏幕图形模式。You can close graphics mode and go back the text mode by the text command. 你可以关闭图形模式和回到文本模式的文本所命令。It is useful to freeze the graphics by the command readchar before back to the text mode.这是有用的冻结图形由命令readchar之前回到文本模式。
See also: text.还看到:文本。
e.g. graph, line(100,100,300,300), readchar, text例如图、线(100100300300),readchar、文本
* i我 internal内部
i represents the imaginative unit of the complex numbers, i=sqrt(-1), as the built-in constant.我代表这个富有想象力的单位的复杂数字,i = sqrt(1),作为一个内置的常数。
See also: re, im, sign, arg.还看到:是,我签署、高温。
e.g. 1+2*i.例句。1 + 2 *我。
* if如果 internal内部
if(condition,x)如果条件、x) gives x if condition evaluates to 1, or left unevaluated otherwise.如果条件评价给x为1,或左unevaluated不然。
if(condition,x,y)如果条件,x,y)
gives x if condition evaluates to 1, y if it evaluates to 0, or left unevaluated if the condition is neither 1 nor 0.如果条件评价了1 x,y如果它对0或者离开unevaluated如果条件不1和0。
Note that the words then and else can be replaced by comma ,. 注意的话还可以再被逗号。It is useful in definition of the use-defined function to left the function unevaluated if the argument of the function is not number.适用于定义的函数功能use-defined离开unevaluated如果参数的功能不号码。
See also: isnumber.还看到:isnumber。
e.g.例句。
IN:在: f(x_) := if(isnumber(x), 1)f(x_):要是(isnumber(x),1)
IN:在: f(x), f(10)f(x)、f(10)
OUT: f(x), 1出:f(x),1
* im我 internal内部
im(x) gives the imaginative part of the complex number x.我(x)给这个富有想象力的部分复数x。
See also: re, abs, sign, arg.还看到:稀土、abs、标志,高温。
e.g. im(1+2*i) gives 2.例如输入法(1 + 2 *我)给2。
* infinf internal内部
inf is a positive infinity, as the built-in constant.是一个积极的无限缝,内置的常数。
See also: c_inf, zero.还看到:c_inf、零。
e.g. inf+2*inf gives inf, 1/inf gives 0.如步+ 2 *步给无穷大,1 / inf给0。
* infsuminfsum
infsum(y,x) is infinite sum.infsum(y,x)是无限的总和。
See also: partsum, sum.还看到:partsum、金额。
* int智力
int(x) gives the integer part of number x. int(x)=trunc(x).智力(x)给整数部分的数字x。智力(x)= trunc(x)。
See also: frac, trunc.还看到:数量,trunc。
e.g. int(2.3) gives 2.如智力(2.3)给2。
* inte强烈 internal + external内部+外部
inte() is the integral function.强烈的()的整体功能。
inte(y,x)希尔(y,x) internal内部
It finds the indefinite integral of y with respect to an undefined variable x.它发现的不定积分y就一个未定义的变量x。
inte(y,x,xmin,xmax)强烈的(x,y,xmin,xmax)
It finds the definite integral of y with respect to the variable x taken from x=xmni to x=xmax.它发现定积分的y就变量x取自x = = xmax xmni为x。
inte(y,x,xmin,x1,xmax)强烈的(x,y,xmin,x1,xmax)
It finds the definite integral of y from x=xmin to x=x1, then from x=x1 to x=xmax. 它发现���积分的x = xmin y从对x = x1,然后从x = = xmax x1到x。x1 is singularity.x1是奇异点。
See also: ninte.还看到:ninte。
* iscomplexiscomplex internal内部
iscomplex(x) tests if x is complex. iscomplex x(x)测试是复杂的过程。It gives 1 if x is complex, or 0 otherwise.它给如果x是复杂的,或0聪明。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. iscomplex(i) gives 1.例如iscomplex(我)给1。
* iseveniseven internal内部
iseven(x) gives 1 if x is an even integer, or 0 otherwise. iseven(x)给如果x是一个更整数,否则返回0。You can assume x is even by iseven(x) := 1.你可以假定x是即使iseven(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. iseven(2) gives 1, iseven(3) gives 0.例如iseven(2)给1、iseven(3)给0。
* isfreeisfree internal内部
isfree(y,x) gives 1 if y is free of x, or 0 otherwise. isfree(y,x)给1如果y为自由x,否则返回0。You can assume y is free of x by iseven(y,x) := 1.你可以假定y是免费的iseven x(y,x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. isfree(a*b,x) gives 1, isfree(x*y,x) gives 0.例如isfree(* b,x)给1、isfree(x性感,x)给0。
* isintegerisinteger internal内部
isinteger(x) gives 1 if x is an integer, or 0 otherwise. isinteger(x)给如果x是一个整数,否则返回0。You can assume x is integer by isinteger(x) := 1.你可以假定是由isinteger整数x(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. isinteger(2) gives 1, isinteger(3.2) gives 0.例如isinteger(2)给1、isinteger(3.2)给0。
* islargerislarger
islarger(a,b) gives 1 if a is larger than b, or 0 otherwise. islarger(a,b)给1如果大于b,否则返回0。It is extent of operator >. 这是程度上的操作>。It can compare 2 complex number, but the operator > cannot.它可以比较两个复杂的数字,但操作员>所做不到的。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber. 还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。isless.isless。
e.g.例句。
IN:在: islarger(1+i, 1-i)islarger(1 +我,1-i) # is 1+i larger than 1-i ?号是1 +我比1-i吗?
OUT: 1出:1 . # yes#是的
* islessisless
isless(a,b) gives 1 if a is less than b, or 0 otherwise. isless(a,b)给1如果少于b,否则返回0。It is extent of operator <. 这是程度上的操作意义。It can compare 2 complex number, but the operator < cannot.它可以比较两个复杂的数字,但操作员<不能。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g.例句。
IN:在: isless(1+i, 1-i)isless(1 +我,1-i) # is 1+i less than 1-i ?号是1 +我不到1-i吗?
OUT: 0出:0 # no#不
* islistislist internal内部
islist(x) gives 1 if x is a list, or 0 otherwise. islist(x)给如果x是一个列表,或0聪明。You can assume x is a list by islist(x) := 1.你可以假定是一个表islist x(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. islist([a]) gives 1, islist(3.2) gives 0.例如islist([a])给1、islist(3.2)给0。
* isoddisodd internal内部
isodd(x) gives 1 if x is an odd integer, or 0 otherwise. isodd(x)给如果x是一个古怪的整数,否则返回0。You can assume x is odd by isodd(x) := 1.奇怪的是,你可以假定由isodd x(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. isodd(3) gives 1, isodd(2) gives 0.例如isodd(3)给1、isodd(2)给0。
* isratioisratio internal内部
isratio(x) gives 1 if x is ratio, or 0 otherwise. isratio(x)给如果x是比,否则返回0。You can assume x is ratio by isodd(x) := 1.你能承担比增加isodd x(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. isratio(2/3) gives 1, isratio(2) gives 0.例如isratio(2/3)给1、isratio(2)给0。
* isreal来 internal内部
isreal(x) gives 1 if x is real, or 0 otherwise. (x)来给如果x是真实的,否则返回0。You can assume x is real by isreal(x) := 1.你可以假定x是实际来(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. isreal(2.2) gives 1, isreal(a) gives 0.如(2.2)给1来来,以色列情报机构摩萨德一直(a)给0。
* issameissame internal内部
issame(a,b) gives 1 if a is the same as b, or 0 otherwise. issame(a,b)给1如果一个相同b,否则返回0。You can assume a is the same as b by issame(a,b) := 1. 你可以假定一个相同的issame b(a,b):= 1。It is similar to a==b, but a == b left unevaluated if a <> b.这是类似于一个= = b,而是一个= = b离开unevaluated < >如果b。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. issame(3,3) gives 1, issame(3,2) gives 0.例如issame(3,3)给1、issame(3、2)给0。
* isnumberisnumber internal内部
isnumber(x) gives 1 if x is a number, or 0 otherwise. isnumber(x)给如果x是一个号码,否则返回0。You can assume x is a number by isnumber(x) := 1.你可以假定是一个数字被isnumber x(x):= 1。
See also: iscomplex, iseven, isfree, isinteger, islarger, isless, islist, isodd, isreal, isratio, issame, isnumber.还看到:iscomplex,iseven,isfree,isinteger,islarger,isless,islist,isodd来,以色列情报机构摩萨德一直,isratio,issame,isnumber。
e.g. isnumber(2.2) gives 1, isnumber(a) gives 0.例如isnumber(2.2)给1、isnumber(一)给0。
* laplace拉普拉斯
laplace(y,x) gives Laplace transform of y.拉普拉斯(y,x)给拉普拉斯变换的y。
e.g. laplace(sin(t),t) gives 1/(1+t^2).例如拉普拉斯(罪(t)、t)给1 /(1 + t ^ 2)。
* last最后 internal内部
last最后 represents the last output, as the built-in variable.代表了最近的输出,内置的变量。
last[1]最后一个[1] the first element of the last output list.第一个元素的最后输出名单。
* left离开 internal内部
left(x=a) gives the left-hand side of an equation and inequality.左(x =)给左手边的一个等式和不等式。
See also: right.还看到:没错。
e.g. left(x+y=2) gives x+y, left(a>b) gives a.如左(x + y = 2)给x + y,左(一个> b)了。
* length长度 internal内部
length([a]) gives the length of a list and string (the number of member in the list and string).长度([a])给出了一个清单,字符串的长度(数量的成员的名单,字符串)。
See also: list, string.还看到:列表,字符串。
e.g. length([a,b]) gives 2, length("abc") gives 3.例如长度((a,b)给2、长度(“abc”)给3。
* li李
li(x) is the ln integral function, li(x) = inte(1/ln(t), t,0,x) = ei(ln(x)), li'(x)=1/ln(x).李(x)是积分函数取出,李(x)=交互(1 /淋巴结(t)、t - x)= ei(淋巴结(x)),李的(x)= 1 /淋巴结(x)。
li(n,x) is the incomplete ln integral function, li(n,x) = inte(ln(t)^n, t,0,x) = ei(n,ln(x)), d(li(n,x),x) = ln(x)^n. 李(氮、x)是不完整的;整体功能,李(氮、x)=交互(淋巴结(t),t ^ n - x)= ei(氮、淋巴结(x)),d(李(n、x),x)=淋巴结(x)^ n。li(n,0) = 0.李(n,0)= 0。
See also: ei, gamma, erf, ci, si, li.还看到:ei,伽马、角度、ci、硅、李。
* lim老林
lim(y, x = x0) finds the limiting value of y when x = x0.小林(y,x = x0)发现限值,当x = x0 y。
lim(y, x = x0+zero) finds the right-sided limit as x approaches to x0 from the positive (+inf) direction (x = x0+).小林(y,x = x0 + 0)限制发现右侧x的方法,从积极的x0(+ inf)方向(x = x0 +)。
lim(y, x = x0-zero) finds the left-sided limit as x approaches to x0 from the negative (-inf) direction (x = x0-).小林(y,x = x0-zero)发现左限制方法从x x0负(-inf)方向(x = x0 -)。
Note that the correct answers are usually for the indeterminate forms: 0/0, inf/inf, 0*inf, 0^0, inf^0.注意正确答案通常为不确定的形式:0/0,步/无穷大,0 *步,0 ^ 0,inf ^ 0。
See also: zero, replace.还看到:零,替代。
e.g. lim(sin(x)/x, x = 0) gives 1.例如小林(罪(x)、x / x = 0)给1。
* line线 internal内部
line(x1,y1,x2,y2) draws a line from point (x1,y1) to (x2,y2). 线(x1,x2,y2,日元)画一线从一个点(x1,日元)到(x2,y2)。line() is graphics function so it only works on graphics mode.线()是图形功能,它只适用于图形模式。
See also: arc, lineto, linerel, putpixel.还看到:弧形,lineto,linerel,putpixel。
e.g. graph, line(100,100,200,200), readchar, text例如图、线(100100200200),readchar、文本
* linetolineto internal内部
lineto(x2,y2) draws a line from the current point (x,y) to (x2,y2). lineto(x2,y2)画一线从目前的点(x,y)到(x2,y2)。lineto() is graphics function so it only works on graphics mode.lineto()的图形功能,它只适用于图形模式。
See also: arc, line, linerel, putpixel.还看到:弧形、线、linerel,putpixel。
e.g. graph, moveto(100,100), lineto(200,200), readchar, text例如图,moveto(100100),lineto(200200),readchar、文本
* linerellinerel internal内部
linerel(dx,dy) draws a line from the current point (x,y) to (x+dx,y+dy). linerel(dx,去世)画一线从目前的点(x,y)(x + y +秦代dx,)。linerel() is graphics function so it only works on graphics mode.linerel()的图形功能,它只适用于图形模式。
See also: arc, line, lineto, putpixel.还看到:弧形、线、lineto,putpixel。
e.g. graph, moveto(100,100), linerel(100,100), readchar, text例如图,moveto(100100),linerel(100100),readchar、文本
* list列表 internal内部
list(y,x,xmin,xmax,dx)表(x,y,xmin,xmax,dx) lists every y when x runs from xmin to xmax on step dx. 列出每一个y当x是由xmin走到xmax __。list() is similar to do(), but list() outputs every result at every step dx, and cannot accept assignment as y.列表()也类似可以做的(),但是每一个结果列表()输出,每走一步dx,而不能接受另一项任务是y。
See also: do, repeat, table.还看到:重复,桌子。
e.g. [ list(x^2, x,1,3,1) ] gives [1,4,9].例句。[列表(x ^ 2,x,第1、3、1)]给[1,4,9]。
* listsumlistsum
listsum(x) converts a list into sum.listsum列表(x)转换成的数目。
See also: average, max, min.还看到:一般,最大、最小。
e.g. listsum([a,b] gives a+b.例如listsum([a、b]给+ b。
* ln淋巴结 internal+external内部+外部
ln(x) is the natural logarithmic function of x. Its base is e. It is the inverse to exp(x). 淋巴结(x)是自然对数函数的基础是x。e。它是逆到实验(x)。Note that if it has multi-values, the ln(x) only gives a principle value (P.V.) and other values are P.V.注意,如果它有多维价值,淋巴结(x)只给一个原则的价值(P.V.)和其他值P.V.+2*k*pi*i (where k=0, 1, 2,...+ 2 k * * *我(在pi k = 0、1,2,……, -1, -2, ...). ,第1、2、…)。If x is complex number (x=A+B*i) then ln(x)=ln(abs(x))+i*atan2(A,B).如果x是复数(x = A + B *我)然后淋巴结(x)=淋巴结(abs(x))+我* atan2(A,B)。
See also: exp.还看到:经验值。
e.g. ln(e) gives 1.例如淋巴结(e)给1。
* local当地 internal内部
local(a,b) declares the variables a and b are local variables in block(). 本地(a,b)这是变量中的局部变量a和b块()。local() must be the last argument within block().本地()必须在最后一个参数块()。
See also: block还看到:分块
e.g. f(x_) := block(p:=x^2,p,local(p))如f(x_):=区块(x ^ 2 = p:、磷、当地(p))
* log10t
log10(x) is log with base of 10. t(x)都是原木基础为10。log10(x) = ln(x)/ln(10).t(x)=淋巴结(x)/淋巴结(10)。
See also: ln.还看到:淋巴结。
e.g. log10(10) gives 1.例如t(10)给1。
* lowercase小写 internal内部
The switch of the case conversion.案件的开关转换。
lowercase := on小写:=在
It converts the letters to lower-case letters.它转换为小写字母的信。
e.g. SIN(x) is converted to sin(x).例句。罪(x)转化为罪(x)。
lowercase := off小写:=了
It disables the case conversion, this is default. 它使情况下转换,这是默认值。It only effects the input.它只影响输入。
* math数学 internal内部
math is a value of the switch output. 数学是一个价值的开关输出。It forces output in math symbolic notation.它迫使数学符号输出符号。
See also: output, off, on, basic, fortran, prolog.还看到:输出了,很快,,基本,fortran语言prolog。
e.g. output:=math.如输出:=数学。
* max马克斯
max(x) gives maximum of x.马克斯(x)给予最大的x。
See also: min, average, listsum, length.还看到:具、平均,listsum、长度。
e.g. max([1,2,3]) gives 3.如马克斯([1、2、3)给3。
* member成员 internal内部
member(list,n) gives n-th member of list.会员(会员名单,n)给出的成员名单。形式
See also: length, last.还看到:长度,最后。
e.g. member([a,b,c], 2) gives b.如会员([a、b、c),2)给b。
* min分钟
min(x) gives minimum of x.分钟(x)给予最低的x。
See also: max, average, listsum, length.还看到:马克斯,平均水平,listsum、长度。
e.g. min([1,2,3]) gives 1.例如分钟([1、2、3)给1。
* mod国防部 internal内部
mod(m,n) gives the remainder on division of m by n.国防部(m,n)给其余款项在分工米,由n。
See also: div.还看到:师。
e.g. mod(4,3) gives 1.例如国防部(4,3)给1。
* movetomoveto internal内部
moveto(x2,y2) moves from the current x,y to x2,y2. moveto(x2,y2)离开当前的x,y x2,y2。it is graphics function so it only works on graphics mode.它是图形功能,它只适用于图形模式。
See also: arc, line, linerel, putpixel.还看到:弧形、线、linerel,putpixel。
e.g. graph, moveto(100,100), lineto(200,200), readchar, text例如图,moveto(100100),lineto(200200),readchar、文本
* moverelmoverel internal内部
moverel(dx,dy) moves from the current x,y to x+dx,y+dy. moverel(dx,去世)离开当前的x,y + dx x,y +去世。it is graphics function so it only works on graphics mode.它是图形功能,它只适用于图形模式。
See also: arc, line, lineto, putpixel.还看到:弧形、线、lineto,putpixel。
e.g. graph, moverel(10,10), linerel(100,100), readchar, text.例如图,moverel(10、10),linerel(100100),readchar、文本。
* multmult internal+external内部+外部
mult(x)mult(x) internal内部
It gives a list of multipliers of x. It converts product into a list of multipliers.它提供一个列表。它转换为x的乘数效应较小,产品进入名单乘数。
e.g. mult(a*b) gives [a,b].例如mult(* b)给(a,b)。
mult(x, n)mult(x,n)
It gives the n-th multiplier of x if possible. 给出了各种类型x,如果可能的话。乘数multi(x_,n_) := member(multi(x), n).多(x_、n_):=会员(多(x),n)。
e.g. multi(a*b*c, 1) gives a.例如多(* b * c,1)了。
See also: multi, term, type.还看到:多、期限、类型。
* newline换行符 internal内部
newline writes a new line. 写一个新行。换行符The output following the command newline will be written on next line.输出换行符后将写在命令下一行。
* ninteninte
ninte(y, x from xmin to xmax) numerically integrates y.ninte(y,从x xmin到xmax)数值集y。
See also: inte.还看到:强烈的。
e.g. ninte(x^2, x from 0 to 1) gives例如ninte(x ^ 2、x从0到1)所赐的
* nlimnlim
nlim(y, x=x0) numerically limits y when x=x0.nlim(y,x = x0)数值范围当x = x0 y。
See also: lim.还看到:小林。
e.g. nlim(sin(x)/x, x=0) gives 1.例如nlim(罪(x)、x / x = 0)给1。
* not不
not(x) is logic not. (x)是没有逻辑。It gives 1 if x=0, or 0 if x=1.它给1 = 0 x或0 x = 1。
See also: and, not.还看到,不是。
e.g. not(1) gives 0, not(0) gives 1.例如不用给0(1),而不是(0)给1。
* nsolvensolve
nsolve(cos(x)=x,x,x0,n)nsolve(因为(x)= x,x,x0、n) numerically solves the equation with initial x0 and iteration n, using Newston's method. 解决了数值方程迭代初始x0、氮、使用Newston的方法。By default n=5, you can increase the n value if you want more close to exact solution. 默认情况下,5例,你可以增加n值,如果你想更接近于精确解。It only gives one root near x0 if equation has multi roots.它只会给一个人如果方程根x0附近多根。
nsolve(cos(x)=x, x)nsolve(因为(x)= x,x) numerically solves equation with default initial x0=1 and n=5.默认初始方程数值解决x0 = 1和5例。
nsolve(cos(x)=x, x,x0)nsolve(因为(x)= x,x,x0) numerically solves the equation with initial x0 and n=5.解决了数值方程和n初始x0 = 5。
See also: solve, dsolve.还看到:解决,dsolve。
e.g. nsolve(sin(x)=0, x,3) gives 3.14.例如nsolve(罪(x)= 0,x,3)让3.14。
* null空 internal内部
null is a symbol used to indicate the absence of an expression or a result. 空是一个符号用来表示缺乏的)一个表达式或一个结果。When it appears as an output expression, no output is printed.当它看起来象是一个输出的表情,没有输出打印出来。
See also: block, output.还看到:街区,输出。
e.g. block(output:=on, null).例如块(输出:=,空)。
* num胡 internal内部
num(x) gives the numeric value of x. It converts all numbers to the real number.胡(x)给出了x的数值。它把所有的数字真实的数字。
See also: numeric.还看到:数字。
e.g. num(pi) gives 3.1416.如:胡(pi)让3.1416。
* number号码 internal内部
number("1") converts string "1" into number 1.数字(“1”)转换成字符串“1”到1号。
See also: string.还看到:字符串。
* numenume internal内部
nume(x) gives numerator of x. It only works for rational number.nume(x)给出x。它只作为理性的号码。
See also: deno.还看到:deno。
e.g. nume(2/3) gives 2.例如nume(2/3)给2。
* numeric数字 internal内部
The switch of numeric calculation.数值计算的开关。
numeric:=on数字:=在 numeric computation.数值计算。
numeric:=off数字:=了 disable numeric computation, this is default.禁用数值计算、这是默认值。
See also: num.还看到:麻木。
* off了 internal内部
When the switch is set to off, it is inactive.当水开关设置为关了,这是消极的。
e.g. numeric:=off, output:=off, expand:=off例如数字:=掉,输出:=掉,扩大:=了
* on在 internal内部
When the switch is set to on, it is active.当水开关设置为上,它是积极的。
See also: off, output.还看到:掉,输出。
e.g. numeric:=on, expand:=on, expandexp:=on, lowercase:=on, output:=on例如数字:=,扩大:=,expandexp:=,小写:=,输出:=
* openfile一个打开文件 internal内部
openfile("filename") opens the disk file "filename" for writing. 一个打开文件(文件名)打开磁盘文件"文件名”的写作。The filename is any MS-DOS file name. 文件名是任何ms - dos文件名。After doing something, the file must be closed by closefile("filename").在做某一件事,文件必须关闭closefile(“文件名”)。
See also: closefile, readfile.还看到:closefile,readfile。
* or或 internal内部
The logic operator. 它的逻辑算符。The result is 1, 0 or unevaluated.结果是1、0或unevaluated。
See also: and.看,。
e.g. 1 or 0 gives 1.例句。1或0给1。
* order秩序
order(y, x) gives the highest order of x in y. y must be polynomial with order < 5.订购(y,x)给出了x的最高层次的y . y必须多项式订单< 5。
See also: coef, coefall.还看到:系数,coefall。
e.g.例句。
IN:在: order(x^2+5*x+6, x)订单(x ^ 2 + 5 * x + 6,x)
OUT: 2出:2
* output输出 internal内部
The switch of the output format.开关的输出格式。
See also: math, basic, fortran, on, off.还看到:数学、基础、fortran,上、下。
e.g. output:=basic, output:=fortran, output:=math, output:=on, output:=off.如输出:=基础,输出:= fortran语言输出:=数学、输出:=,输出:=掉。
* oval椭圆形
oval(x,y, xRadius,yRadius) draws an oval at point(x,y) with x-radius and y-radius. 椭圆形(x,y,xRadius,yRadius)绘制了一个椭圆点(x,y)和y-radius x-radius。It must be in graphics mode.它必须在图形模式。
See also: ellipse.还看到:椭圆。
e.g. graph, oval(200,200,200,100), readchar, text例如图,椭圆形(200200200100),readchar、文本
* paraplotparaplot
plot the parametric functions of x=x(t) and y=y(t) by绘制参数功能= x(t)x和y = y(t)
paraplot(x(t),y(t),t)paraplot(x(t),y(t),t)
paraplot(x(t),y(t),t,tmin,tmax)paraplot(x(t),y(t),t tmin,tmax)
paraplot(x(t),y(t),t,tmin,tmax,ymin,ymax)paraplot(x(t),y(t),t tmin,tmax,ymin,ymax)
See also: plot,polaplot.还看到:阴谋,polaplot。
e.g. graph, paraplot(sin(t),sin(2*t),t)例���图,paraplot(罪(t)、罪(2 * t),t)
* partsumpartsum
partsum(y,x) gives partial sum of y (symbolic sum).partsum(y,x)给部分笔y(象征性金额)。
See also: infsum, sum.还看到:infsum、金额。
e.g. partsum(n^2, n) gives 1/6 n (1 + n) (1 + 2 n)例如partsum(n ^ 2 n)给1/6 n(1 + n)(1 + 2 n)
* pipi
pi=3.1416...pi = 3.1416…, as the built-in constant, pi is converted to 3.1416... ,内置的常数,pi转化为3.1416…when the switch numeric:=on.当水开关数字:=。
See also: e.还看到:e。
* plot情节
plot(y,x) plots a function y=f(x) in xy plane with the default values x from -5 to 5, and y from -5 to 5.情节(y,x)展示了函数y = f(x)在xy平面与预设值x从5点到5,y = 5到5。
plot(y,x,xmin,xmax)情节(x,y,xmin,xmax)
plot(y,x,xmin,xmax,ymin,ymax)情节(x,y,xmin,xmax,ymin,ymax)
See also: dotplot, polar.还看到:dotplot、极性。
e.g. graph, plot(x^3,x)例如图、情节(x ^ 3、x)
* polaplotpolaplot
polaplot(r,t) plots a function r=f(t) in polar coordinates with the default values t from 0 to 2 pi, and r from 0 to 5.polaplot(r,t)展示了函数r = f(t),在极坐标的默认值t从0到2圆周率,和r从0到5点。
polaplot(r,t,tmin,tmax)polaplot(r,t tmin,tmax)
polaplot(r,t,tmin,tmax,rmin,rmax)polaplot(r,t tmin,tmax,rmin,拒绝)
See also: dotplot, paraplot, polaplot.还看到:dotplot,paraplot,polaplot。
e.g. graph, polaplot(1,t)例如图,polaplot(1,t)
* power权力 internal内部
power(x^n) gives the power n.力量(x ^ n)给电力n。
See also: base, power, type.还看到:基地、电力、��型。
e.g. base(x^n) gives x, type(x^n) gives "^", power(x^n) gives n.例如基地(x ^ n)给x,类型(x ^ n)给“^”、权力(x ^ n)给n。
* prod促进
prod(f,x,xmin,xmax)促进(f,x,xmin,xmax) with the default step dx = 1.使用默认的dx步= 1。
prod(f,x,xmin,xmax,dx)促进(f,x,xmin,xmax,dx) evaluates the product of f when x runs from评估产品f当x跑
xmin to xmax with step dx.xmin层对xmax dx。
See also: sum, list, table.还看到:金额、表,表。
* prologprolog internal内部
prolog is the value of the switch output. 价值是prolog开关输出。It forces the output in the Prolog format, i.e. internal form.它迫使产出的Prolog格式,即内部形式。
See also: output, basic, fortran.还看到:输出、基础、fortran。
e.g.例句。
IN:在: outout:=prologoutout:= prolog
IN:在: a+b+ b
OUT: plus(var("a"),var("b"))出:还有(var(“一个”),var(b)
* psolvepsolve
psolve(f(x), x) solves polynomial f(x)=0 for x. The order of polynomial < 3.psolve(f(x)、x)解决了多项式f(x)= 0 x。秩序的多项式< 3。
See also: solve, nsolve, dsolve.还看到:解决,nsolve,dsolve。
e.g. psolve(x^2+5*x+6, x) gives [-2,-3].例如psolve(x ^ 2 + 5 * x + 6,x)给[2,3]。
* putpixelputpixel internal内部
putpixel(x,y,color) puts pixel on the point (x,y) with color. putpixel(x,y,颜色)把像素在点(x,y)和颜色。It only works on the graphics mode.它只适用于图形模式。
See also: line, lineto, linerel.还看到:行,lineto,linerel。
e.g. graph, putpixel(100,100,1), readchar, text例如图,putpixel(100100:1),readchar、文本
* random随机 internal内部
random随机gives a uniformly distributed pseudo random real in给出了一个均匀的伪随机数
the range 0 to 1.范围0到1。
random(n)随机(n) gives a uniformly distributed pseudo random integer给出了均匀分布的伪随机整数
in the range 0 to n. (n < 36000).在范围0到n。(n < 36000)。
e.g. random gives 0.11111, random(5) gives 2.例如随机让0.11111、随机(5)给2。
* ratio比 internal内部
ratio(x) converts x to a rational number.比x(x)转换到一个合理的数字。
See also: num.还看到:麻木。
e.g. ratio(0.5) gives 1/2.例如比(0.5)给1/2。
* re稀土 internal内部
re(x) gives the real part of the complex number x.稀土(x)就给真实的部分复数x。
See also: im, abs, sign.还看到:我、abs、签字。
e.g. re(1+2*i) gives 1.如你(1 + 2 *我)给1。
* readcharreadchar internal内部
readchar reads a character from the keyboard. 读取一个字符readchar键盘。It is useful to freeze the graphics by readchar. 它是非常有用的图形由readchar冻结。This is similar to pause, but it returns the character from the keyboard as its value.与此相似的停顿,但它返回的字符,键盘为它的价值。
See also: readchar, readfile, readln, writes.还看到:readchar,readfile,readln,写。
e.g. graph, line(100,100,300,300), readchar, text例如图、线(100100300300),readchar、文本
* readfilereadfile internal内部
readfile("file") reads (or runs) the file named "file". (“文件”)readfile读(或跑)的文件命名为"文件"。The filename is any MS-DOS file name.文件名是任何ms - dos文件名。
See also: readchar, readfile, readline, writes.还看到:readchar,readfile,readline,写。
* readlinereadline internal内部
readline reads a line of strings from the keyboard into the readline.readline读一行字符串到readline从键盘。
See also: readchar, readfile, readline, writes.还看到:readchar,readfile,readline,写。
* repeat重复 internal内部
repeat(expr until test) repeats expr until test gives 1.重复直到expr测试)重复直到测试出1 . expr
See also: do, list.还看到:,列表。
e.g.例句。
IN:在: x:=1, repeat(x:=x+1, x>5)谢:= 1,重复(x:= x + 1,x > 5)
OUT: x := 6出:谢:= 6
* reverse逆向
reverse(x) reverses a list x in reverse order.反向(x)翻转一个列表x在相反的顺序。
See also: member.还看到:成员。
e.g. reverse([1,2,3]) gives [3,2,1].例如逆序([1、2、3)给予[3、2、1]。
* right权利 internal内部
right(x=a) gives the right hand side of an equation.正确的(x =)给右手边的一个等式。
See also: left, solve.还看到:左、解决。
e.g. right(x+y = 3) gives 3.如右(x + y = 3)给3。
* root根
root(x,n) gives all branch of n-th root. 根(x,n)给所有分支,可开方。The first member of list is the P.V.第一届会员的P.V.列表
e.g. root(4,2) gives [2,-2].如根(4)、2)[1,2]了。
* round圆 internal内部
round(x) converts x to the rounded integer closest to x.圆(x)转换成x形圆整数接近x。
See also: trunc.还看到:trunc。
e.g. round(2.4) gives 2, round(2.5) gives 3.如圆(2.4)给2、圆(2.5)给3。
* sec秒
sec(x) is the secant function of x. The angle x is measured in radians (multiply by degree to convert from degrees). (x)是美国证券交易委员会(sec)的功能进行了x。角度弧度测量x(乘程度的转换度)。sec(x)=1/cos(x).秒(x)= 1 /因为(x)。
See also: asec, cos.还看到:了一类正则,因为。
* sechsech
sech(x) is the hyperbolic secant function of x. sech(x)=1/cosh(x).sech(x)是双曲函数sech进行x(x)= 1 /事业(x)。
See also: asech, cosh.还看到:asech,事业。
* series系列
series(y, x)系列(y,x) gives series expansion of y at x=0 to order of 5.给出的级数展开y在x = 0点5。
series(y, x, order)系列(x,y,顺序) gives series expansion of y at x=0 to order.给出的级数展开y在x = 0秩序。
See also: sum.还看到:总和。
e.g. series(sin(x),x) gives x - 1/6*x^3 + 1/120*x^5.例如系列(罪(x)、x)给x - 1/6 * x ^ * x ^ 3 + 1/120 5。
* sequence序列 internal内部
sequence(x) gives a sequence. 序列(x)给一个序列。It only work on a list.它只工作在单子上。
See also: type, argue.还看到:打字,吵架。
e.g. sequence( [a,b] ) gives a,b例如序列(a,b)给a、b
* setbkcolorsetbkcolor internal内部
setbkcolor(x) sets the background color, where the argument value is 0 to 15, or the color word. setbkcolor(x)设置背景颜色,那里的参数值是0到15,或颜色词。The default background color is 0 (black). 默认的背景颜色是0(黑色)。It only works on graphics mode.它只适用于图形模式。
e.g. graph, setbkcolor(1), line(100,100,200,200), readchar, text.例如图,setbkcolor(1)、线(100100200200),readchar、文本。
See also: setcolor.还看到:setcolor。
* setcolorsetcolor internal内部
setcolor(x) sets the foreground color, where the argument value is 0 to 15, or the color word. setcolor(x)设置前景色,那里的参数值是0到15,或颜色词。The default foreground color is 7 (white). 默认的景色是7(白色)。It only works on graphics mode.它只适用于图形模式。
e.g. graph, setcolor(1), line(100,100,200,200), readchar, text.例如图,setcolor(1)、线(100100200200),readchar、文本。
See also: setbkcolor.还看到:setbkcolor。
* setlinestylesetlinestyle internal内部
setlinestyle(style, direction, thickness) sets the line style, where style is the style name, direction is the line direction, thickness is the thickness of the line.setlinestyle(风格、方向、厚度)套线的风格,在款式风格的名字,方向是线方向,厚度厚度的线。
it only works on the graphics mode.它只适用于图形模式。
See also: setlinestyle, settextstyle.还看到:setlinestyle,settextstyle。
e.g. graph, setlinestyle(2,1,2), line(100,100,300,300), readchar, text例如图,setlinestyle(2、1、2)、线(100100300300),readchar、文本
* settextjustifysettextjustify internal内部
settextjusttify(hor,vert) sets text justification values used by writes(). settextjusttify(何珥山、点)套理由使用文本值写()。Text written by writes() after the settextjustify() will be justified around the current pointer in the manner specified.所写的文字写()后settextjustify()必因耶和华得称为义、在当前指针所指定的方式。
See also: settextstyle, writes.还看到:settextstyle,写。
* settextstylesettextstyle internal内部
settextstyle(font, direction, size) sets the text style, font, and character magnification factor, where font is the font name, direction is the text direction, size is the character size. settextstyle(字体、方向、大小)设置文本风格、字体、字符放大因子,当字体的字体名称、方向文本方向、大小是性格的尺寸。it only works on the graphics mode.它只适用于图形模式。
e.g. graph, textstyle(2,1,2), writes("abc"), readchar, text.例如图,textstyle(2、1、2),写(“abc”),readchar、文本。
See also: setlinestyle.还看到:setlinestyle。
* setviewportsetviewport internal内部
setviewport(x1,y1,x2,y2,clip) sets the view port from (x1,y1) to (x2,y2) on the graphics screen. setviewport(x1,x2,y2,日元,夹子)设置观点港由(x1,日元)到(x2,y2)在图形屏幕。Everything is invisible if it out of the (x1,y1) to (x2,y2). 如果一切都看不见的x1,日元)到(x2,y2)。It only works on the graphics mode.它只适用于图形模式。
e.g. graph, line(100,100,300,300), setviewport(200,200,300,300,1), line(100,200,100,200), readchar, text例如图、线(100100300300),setviewport(200200300300:1)、线(100200100200),readchar、文本
See also: graph, text.还看到:图形、文本。
* sisi
si(x) is the sin integral, si(x) = inte(sin(x)/x, x).si(x)就是罪积分、si(x)=交互(罪(x)/ x,x)。
See also: ci, ei, gamma, erf.还看到:ci,ei,伽马、广泛。
* sign标志 internal内部
sign(x) is the sign function of x. Its value is 1, 0 or -1.签署(x)的符号是x。它的功能值为1时,0或1。
/ 11 if re(x) > 0; or both re(x) = 0 and im(x) > 0.如果你(x)> 0;或两个稀土(x)= 0的时候,我(x)> 0。
sign(x) =签署(x)= 00 if x=0.如果x = 0。
\ -1\ 1 otherwise.不然。
the same as the definition by arg(x):相同的高温的定义(x):
/ 1/ 1 if -pi/2 < arg(x) <= pi/2.如果-pi / 2 <高温(x)< = pi / 2。
sign(x) =签署(x)= 00 if x=0.如果x = 0。
\ -1\ 1 otherwise.不然。
You can assume x is positive or negative by sign(x) := 1 or sign(x) := -1.你可以假定x是积极的还是消极的签名(x):= 1或签署(x):= 1。
e.g. sign(2) gives 1, sign(1+i) gives 1.例如签署(2)给1、标志(1 + 1)给1。
See also: abs, arg, re, im, >, <.还看到:abs、高温、稀土,im,>,<。
* sin罪 internal + external内部+外部
sin(x) is the sine function of x. The angle x is measured in radians. 罪(x)是正弦函数x。测量角度弧度x。(multiply by degree to convert from degrees).(乘程度的转换度)。
See also: asin, csc.还看到:asin,csc。
* sinhsinh
sinh(x) is the hyperbolic sine function of x. sinh(x) = (exp(x)-exp(-x))/2.sinh(x)是双曲正弦函数sinh x(x)=(经验(x)-exp(-x)/ 2。
See also: asinh, acsch.还看到:作用,acsch。
* solve解决 internal内部
solve(x^2=0, x) solves a polynomial ordered up to 4.解决(x ^ 2 = 0,x)解决一个多项式命令来到4。
solve([expr1=expr2,expr3=expr4], [x,y]) solves systems of linear equations. 解决([expr1 = = expr4 expr2,expr3]、[x,y)解决系统的线性方程组。It gives all symbolic solutions.它给所有象徵的解决方案。
See also: nsolve.还看到:nsolve。
e.g. solve(x^2+5*x+6=0, x), solve([x+y=3, x-y=1], [x,y]).例如解决(x ^ 2 + 5 * x + 6 = 0,x),解决([x + y = 3,x - y = 1]、[x,y])。
* sqrtsqrt internal内部
sqrt(x) is the square root function of x. It is the same as x^0.5. sqrt(x)是x的平方根函数。它是一样的x ^ 0.5。It only gives the principal value (P.V.) (sign(sqrt(x)) >= 0). root(x,2) gives all branch of square root.它只给的主体价值(P.V.)(签署(sqrt(x))> = 0)。根(x,2)让所有分支的平方根的计算。
See also: root, ^.还看到:根,^。
e.g. sqrt(4) gives 2, num(sqrt(2*i)) gives 1+i.例如sqrt(4)给2、胡(sqrt(2 *我)给1 +我。
* subs替补 internal内部
subs(y, x=x0) substitutes x in y with x0.替补(y,x = x0)替代x与y x0。
e.g. subs(x^6, x=x0) gives x0^6.例如替补(x ^ 6、x = x0)给x0 ^ 6。
* sum金额 external + internal外部+内部
sum(f,x,xmin,xmax)金额(f,x,xmin,xmax)
It evaluates the sum of f when x runs from xmin to xmax with the default step dx=1.它对f的总和,当x是由xmin默认一步xmax dx = 1。
sum(f,x,xmin,xmax,dx)金额(f,x,xmin,xmax,dx) internal内部
It evaluates the sum of f when x runs from xmin to xmax with step dx.它对f的总和,当x是由xmin xmax dx层。
See also: prod, list, table, infsum, partsum.还看到:促进、列表、表、infsum,partsum。
e.g. sum(2^n,n,1,5,1.1), sum(x^n,n,1,5).例如金额(2 ^ n、n、1、5 - 1.1),和(x ^ n、n、1、5)。
* step一步
step is the comma, the same as the comma , . 一步是逗号,逗号的一样。The 6 keywords: from, to, step, then, else, until are the same as comma ,.6关键词:从,,一步,然后,否则,直到同逗点,。
See also: from, to, then, else, until, ,.还看到:从,,然后,否则,直到,。
* string字符串 internal内部
string(x) converts a number x to a string "x".字符串(x)转换成一个数字x为字符串" x "。
See also: number.还看到:号码。
e.g. string(123) gives "123".例如字符串(123)给“123”。
* system系统 internal内部
system("DOS") executes the operating system (DOS) command "DOS".系统(DOS)执行的操作系统(DOS)命令”DOS”。
e.g. system("dir").如系统(“目录”)。
* table表 external + internal外部+内部
table(f,x)表(f,x)
It produces a table of the function values from x=-5 to x=5 with step 1.它产生一个表的函数值从x = 5到x = 5与第一步。
table(f,x,xmin,xmax)表(f,x,xmin,xmax)
It produces a table of the function values from x=-5 to x=5 with the default step dx = 1.它产生一个表的函数值从x = 5到x = 5默认一步dx = 1。
table(f,x,xmin,xmax,dx)表(f,x,xmin,xmax,dx) internal内部
It produces a table of the function values when x runs from xmin to xmax with step dx.它产生一个表的函数值,当x是由xmin xmax dx层。
table(y[x],x,xmin,xmax,dx)表(y(x),x,xmin,xmax,dx) internal内部
It transforms a list y into a table.它改变了一个列表刺探一张桌子。
See also: list, plot.还看到:列表,情节。
e.g. table(x^2,x,1,4,1).如表(x ^ 2、x、1、4 - 1)。
* tan谭 internal + external内部+外部
tan(x) is the tangent function of x. The angle x is measured in radians (multiply by degree to convert from degrees).褐色(x)是x。正切函数角度弧度测量x(乘程度的转换度)。
See also: atan, cot.还看到:atan、胶辊。
* tanhtanh
tanh(x) is the hyperbolic tangent function of x.tanh(x)是x的双曲正切函数。
See also: atanh, coth.还看到:函数,coth。
* term术语 internal+external内部+外部
term(x)术语(x) internal内部
It gives a list of terms of x. It converts sum into a list of terms.它提供一个列表。它把x条款和单的内容。
e.g. term(a+b) gives [a,b].例如术语a + b)给(a,b)。
term(x, n)词(x,n)
It gives the n-th term of x if possible. 给出了术语的形式x,如果可能的话。term(x_,n_) := member(term(x),n).术语、n_ x_):=会员(术语(x),n)。
See also: multi, term, type.还看到:多、期限、类型。
e.g. term(a+b, 1) gives a, term(a+b, 2) gives b, type(a+b) gives "+".例如术语a + b,1)给、期限a + b,2)给b,类型a + b)给“+”。
* text文本 internal内部
text is the text mode.文本文本模式。
See also: graph.还看到:图形。
e.g.例句。
IN:在: graph, line(100,100,200,200), readchar, text图、线(100100200200),readchar、文本
* then然后
comma. 一个逗号。The same as comma ,.逗号一样。
The 6 keywords: from, to, step, then, else, until are the same as comma ,.6关键词:从,,一步,然后,否则,直到同逗点,。
See also: from, to, step, else, until, ,.还看到:从,一步,否则,直到,。
* to对
it is the comma, the same as the comma (,). 它是一个逗号,逗号的一样()。The 6 keywords: from, to, step, then, else, until are the same as comma ,.6关键词:从,,一步,然后,否则,直到同逗点,。
See also: from, step, then, else, until, ,.还看到:从、步骤、然后,否则,直到,。
* trunctrunc internal内部
trunc(x) converts x to the truncated integer.trunc x(x)转换到截断整数。
See also: round.还看到:圆的。
e.g. trunc(2.9) gives 2.例如trunc(2.9)给2。
* type类型 internal内部
type(x) gives the type of x. Its value is a string. 式(x)给出了x型。它的值是一个字符串。Note that the output of strings in SymbMath is without two quotation marks.需要注意的是,在SymbMath输出串无两个引号。
e.g.例句。
------------------------------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
xx type(x)类型(x)
11 integer整数
1.11.1 real真正
2/32/3 ratio比
1+I1 +我 complex复杂
f(x)f(x) f()f()
[1,2][1,2] []
a一个 symbol象征
"a"“a” string字符串
a+b+ b ++
a*b一个* b *
a^b一个^ b ^
a=b一个= b ==
a==b一个= = b === =
a>b一个> b >
a>=b一个> = b >=> =
a<b一个< b <
a<=b一个< = b <=< =
a<>b一个< > b <>
a,ba、b ,
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You also can test x, e.g. if x is type of real number, by type(x)=="real".你也可以测试x,如果x是类型的实数、通过类型(x)= =“真实”。
* undefined未定义 internal内部
The built-in constant. 内置的常数。It indicates that the value of the expression is undefined, and may be the indeterminate form: 0/0, inf/inf, 0*inf, 0^0. 这表明,表达的是未定义值,可以由不确定性形式:0/0,步/无穷大,0 *步,0 ^ 0。You should try again by lim(y, x=x0).你应该再试一次由小林(y,x = x0)。
See also: lim.还看到:小林。
e.g.例句。
IN:在: f(x_) := sin(x)/xf(x_):=罪/ x(x)
IN:在: f(0)f(0)
OUT: undefined出:未定义
IN:在: lim(f(x), x=0)小林(f(x)、x = 0)
OUT: 1出:1 .
* until直到
comma. 一个逗号。The same as comma ,.逗号一样。
The 6 keywords: from, to, step, then, else, until are the same as comma ,.6关键词:从,,一步,然后,否则,直到同逗点,。
See also: from, to, step, then, else, until, ,.还看到:从,一步,然后,否则,直到,。
* writes写 internal内部
writes(x) writes x on the graphics screen.写x(x)写在图形屏幕。
It only works on the graphics mode.它只适用于图形模式。
See also: graph, readchar.还看到:图,readchar。
* zero零 internal内部
zero is the positive-directed 0, as the built-in constant. 零是positive-directed 0,内置的常数。f(x0+zero) is the right-hand sided function value when x approaches to x0 from the positive direction, i.e. x = x0+. f(x0 + 0)是右边站函数值的方法从当x x0正方向,即x = x0 +。f(x0-zero) is the left-sided function value when x approaches to x0 from the negative direction, i.e. x = x0-.f(x0-zero)是左功能价值当x方法从反方向x0,即x = x0 -。
e.g. f(1+zero) is the right-hand sided function value when x approaches to 1 from the positive (+infinity) direction, f(1-zero) is the left-hand sided function value when x approaches to 1 from the negative (-infinity) direction.如f(1 + 0)是右边站函数值x的方法时,从积极的1(+无限)方向,f(1-zero)是左手面函数值x的方法时一号从负(-infinity)方向。
See also: lim.还看到:小林。
e.g.例句。
IN:在: exp(1/(0+zero)), exp(1/(0-zero))实验(1 /(0 + 0)、exp(1 /(0-zero)
OUT: inf, 0出:无穷大,0
++ add or positive sign. 添加或积极的信号。e.g. a+b.例如+ b。
-- subtract or negative sign. 减或负面的标志。e.g. a-b, -1.故如(1)。
* multiply. 繁殖。e.g. a*b.例如一个* b。
/ divide. 除。e.g. a/b.如a / b。
^ power in BASIC, the same as ** in FORTRAN, e.g. 2^3 gives 8.在基本力量,与* * FORTRAN语言,例如2 ^ 3给8。
** power in FORTRAN, the same as ^ in BASIC, e.g. 2**3 gives 8.FORTRAN语言的力量,与^在基础医学、例句。2 * * 3给8。
! factorial, the same as fac(x), e.g. 3! 阶乘,与前沿空中管制官(x)例句。3 !or fac(3) gives 6.(3)或前沿空中管制官给6。
< less than.以内。
<=< = less than or equal to.小于或等于一。
> greater than.比。
>=> = greater than or equal to.大于或等于。
<> unequal不平等
a <> b gives 1 if a is not equal to b, 0 if a is equal to b, or left unevaluated otherwise. 一个< > b给1如果不等于b,0如果等于b,或左unevaluated不然。It only test two real numbers.它只测试两个实数。
e.g. 2 <> 3 gives 1, 2 <> 2 gives 0.例如< >。2 . 3给1、2 < > 2给0。
=== = equal平等
a==b gives 1 if a is equal to b, 0 if a is not equal to b, or left unevaluated otherwise. 一个= = b给1如果等于b,0如果不等于b,或左unevaluated不然。It can test two complex numbers or expressions. 它可以测试两个复杂的数字或表达式。It gives 1 if a and b are the same expression or left unevaluated otherwise.它给如果a和b是相同的表达式或左unevaluated不然。
e.g. 2==2 gives 1, a==a gives 1.例句。2 = = 2给1、一个= =一个给1。
== equation sign方程标志
e.g. x^6+1 = 0如x ^ 6 + 1 = 0
:=:= assignment.任务。
, comma逗号
The words from, to, step, then, else and until are the same as ,.的话,,一步,然后,否则,直到是一样的。
" string sign. 字符串标志。e.g. 例句。"filename.sm".“filename.sm”。
|x|| | x the same as abs(x).一样的abs(x)。
' f'(x) is the same as d(f(x),x).f '(x)是一样的d(f(x)、x)。
# comment statement评论声明
e.g. # this is demo.例句。#这是演示。
[] list. 列表。e.g. [a,b,c]例句。(a、b、c)
()
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