鲁达 Mathematica软件介绍
Introduction to Mathematica Software
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Dear you ,
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Today, the editor brings you introduction to Mathematica Software,
welcome your visit!
This tweet usually takes about 5 minutes to read.
Please be patient and read.
一
Mathematica基本介绍
Basic introduction to Mathematica
Mathematica是一款科学计算软件，很好地结合了数值和符号计算引擎、图形系统、编程语言、文本系统、和与其他应用程序的高级连接。
Mathematica is a scientific computing software that nicely combines numerical and symbolic computing engines, graphics systems, programming languages, text systems, and advanced connectivity to other applications.
二
Mathematica的一些功能
some functions of Mathematica
- 使用一行代码可显示的图形
- 矩阵和数据操纵工具，包括对稀疏矩阵的处理
- 2维和3维数据以及函数的可视化和动画工具
- 求解方程组、常微分方程、偏微分方程、微分代数方程、时滞微分方程、递推关系式等等
- 离散和连续微积分的数值和符号工具
- 多变量统计程序库，包括支持100多种数据分布的数据拟合、假设检验、概率和期望的运算
- 程序语言支持：过程式编程语言、函数式编程语言和面向对象的编程语言
- 图像处理工具 ，包括图像识别
- 提供用于图论中图的分析和可视化的工具
- Graphics that can be displayed with one line of code
- Matrix and data manipulation tools, including handling of sparse matrices
- Visualization and animation tools for 2D and 3D data and functions
- Solve equations, ordinary differential equations, partial differential equations, differential algebraic equations, delay differential equations, recurrence relations, etc.
- Numerical and symbolic tools for discrete and continuous calculus
- Multivariate statistical library, including data fitting, hypothesis testing, probability and expectation operations supporting more than 100 data distributions
- Program language support: procedural programming languages, functional programming languages, and object-oriented programming languages
- Image processing tools, including image recognition
- Provide tools for analysis and visualization of graphs in graph theory
三
Mathematica基本知识
Basic knowledge of Mathematica
1
四个处理指令
Four processing instructions
- Expand[expr]：将expr展开
- Factor[expr]：将expr因式分解
- Simplify[expr]：将expr化简成精简的式子
- FullSimplify[expr]：Mathematica 会尝试更多的化简公式，将 expr化成更精简的式子
- Expand[expr]：expands expr
- Factor[expr]：factorize expr
- Simplify[expr]：simplify expr into a simplified expression
- FullSimplify[expr]：Mathematica will try more simplification formulas, reducing expr into a more simplified formula
2
多项式转换
polynomial transformation
- ExpandAll[expr]：把算式全部展开
- Together[expr]：将expr各项通分在并成一项
- Apart[expr]：把分式拆开成数项分式的和
- Apart[expr,var]：视var以外的变数为常数，将 expr拆成数项的和
- Cancel[expr]：把分子和分母共同的因子消去
- ExpandAll[expr]：expands all expressions
- Together[expr]：combine all items of expr into one item
- Apart[expr]：splits a fraction into a sum of fractions
- Apart[expr,var]：treats variables other than var as constants, and splits expr into the sum of its terms
- Cancel[expr]：removes the factors common to the numerator and denominator
3
转换函数
Conversion function
- Collect[expr,x]：将expr表示成x的多项式，
- 如Collect[expr,{x,y,…}]：将expr分别表示成 x,y,…的多项式
- FactorTerms[expr]：将expr的数值因子提出，
- 如 FactorTerms[expr,x]：将expr中把所有不包含x项的因子提出
- FactorTerms[expr,{x,y,…}]：将expr中把所有不包含{x,y,...}项的因子提出
- Collect[expr,x]：represents expr as a polynomial of x,
- For example, Collect[expr,{x,y,…}] expresses expr as polynomials of x, y,…
- FactorTerms[expr]：extracts the numerical factors of expr,
- For example, FactorTerms[expr,x] will extract all factors in expr that do not contain x terms
- FactorTerms[expr,{x,y,…}]：extract all factors in expr that do not contain {x,y,…} terms
4
四种括号
Four kinds of brackets
- (term) 圆括号，括号内的term先计算
- f[x] 方括号，内放函数的引数
- {x,y,z} 大括号或串列括号，内放串列的元素
- p[[i ]] 或 Part[p,i] 双方括号，p的第i项元素
- p[[i,j]] 或 Part[p,i,j] p的第i项第j个元素
- (term) parentheses, the term in the parentheses is calculated first
- f[x] square brackets, the arguments of the function are placed inside
- {x,y,z} curly brackets or list brackets, enclosing the elements of the list
- p[[i ]] or Part[p,i] square brackets, i-th element of p
- p[[i,j]] or Part[p,i,j] i-th item j-th element of p
5
缩短输出指令
Shorten output instructions
- expr//Short：显示一行的计算结果
- Short[expr,n]：显示n行的计算结果
- Command;：执行command，但不列出结果
- expr//Short：display the calculation result of a line
- Short[expr,n]：displays the calculation result of n lines
- Command;：execute command without listing results
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参考资料：谷歌翻译、百度、CSDN
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