Mathematica
Mathematica is a commercial software package the company Wolfram Research and is one of the most commonly used mathematical and scientific software packages dar. Mathematica 1.0 was launched in 1988 to market.
Program package Mathematica
The software package " Mathematica " includes, among other things,
- A computer algebra system for symbolic processing of equations
- A numerical analysis software for numerically solving or evaluation of equations
- A visualization tool to display graphs and 3D/2D graphics
- A programming language, the elements of procedural, object-oriented, functional, and rule-based programming combines.
The author and company founder Stephen Wolfram began development work in 1986, the first version of Mathematica was released in 1988.
Use and method of work
Mathematica code is entered into a so-called notebook interface that also supports special mathematical symbols ( in contrast to classical programming languages, that only allow pure text). The evaluation or execution of the program code is generally carried out immediately after the input by an interpreter, or programming errors results are thus readily apparent, it can be an interactive program. If program code through several times, such as when non-interactive program call, the program code is automatically compiled. The program code is operating system independent. Mathematica is available for Windows, Linux, Mac OS. Up to and including version 6.0.3 in addition for MS- DOS, NeXT, OS / 2, Unix and VMS.
Version 8 for the so-called free form of input into Mathematica available, which makes it possible to use, instead of the input of the correct syntax for calculations and other commands, a "natural " English. The graph of the sine function with bright red fill and dashed lines - - For example, the same result is achieved if the Show [ Plot [ Sin [x ], { x, -6.6, 6.6 }, { Filling -> Axis, FillingStyle -> Lighter [ Red ]}], Gridlines -> Automatic, Grid Line Style - > dashed ] inputs, as well as the freeform input using plot sin x with light red filling and dashed gridlines takes as a command. Once you have made a made with freeform input command can be translated into the same exact syntax or make detailed changes so that knowledge about the syntax still remains strong advantage.
Mathematica is used in science or in the study of scientific or economic subjects. Also, it is aimed at professional users in industry and business. So banks are using Mathematica to simulate stock price performance, valuation of derivatives, risk assessment and conversion and so on. The requirement for the correctness of the results is therefore high ( analytically and numerically ).
In addition to basic arithmetic, derivative and integral calculus, solving systems of equations, matrix manipulation and numerical calculations in arbitrary precision ( no restriction to the machine precision ) are a variety of specific functions, such as in the areas of combinatorics, implemented. The Mathematica programming language includes implicit type assignment and conversion, automatic memory management and pattern analysis techniques (English pattern matching ). The programmer is not set to a style:
Language
Main article: Functional Programming
Mathematica supports functional programming and is dynamically typed. In Mathematica there are only functions and permanently installed symbols, ∞ - infinity. For unwanted side effects of imperative programming are bypassed. Instead of processor instructions a set of function definitions are set forth to be run through. As a further distinction from other languages is a line can not be evaluated in Mathematica not an error but a return.
Samples
Example 1: primes
Several prime numbers are calculated by the function
Output {2, 3, 5, 7, 11}
Example 2: mean value calculation
Below are three ways to calculate with " Mathematica " the average of a list of values. In interactive mode, Mathematica numbered the inputs and outputs and provides the results directly.
Define list of values :
Using Mathematica built-in function:
List manipulation using:
Procedural approach: