Computer algebra system
A computer algebra system ( CAS ) is a computer program used to process algebraic expressions. It not only solves math problems with numbers (like a simple calculator ), but also those with symbolic expressions (like variables , functions , polynomials, and matrices ).
The algebraic tasks of a CAS in the narrower sense include:
- Simplify and compare algebraic expressions
- solve algebraic equations
- Solve systems of linear equations and perform calculations with matrices
- Factoring integers and polynomials
- Differentiate and integrate functions ( algebraic integration )
- expect fractions
- calculate with decimal numbers with any precision (with a good CAS, for example, you can determine the circle number π (pi) to tens of thousands of decimal places with little programming effort )
In addition, many CAS functions include:
- Functions and data in two or three dimensions to represent graphically
- analytical-algebraic solving of systems of (ordinary) differential equations.
- solve analytically insoluble integrals and differential equations by numerical integration ("quadrature").
In contrast to the "general purpose systems", which cover as large a part of mathematics as possible, there are many special systems, for example for group theory , Gröbner bases , algebraic number theory, etc.
Examples of computer algebra systems
One of the first computer algebra systems was Schoonschip , which was developed in 1963 by Martinus JG Veltman .
- Derive (later firmware in TI calculators and as a teacher / student version for PC / Mac, now discontinued)
- Macsyma (discontinued)
- MuPAD (discontinued as an independent product, part of Matlab )
- WIRIS (also as an online version; see under web links)
Open source systems
- CoCOA ( commutative algebra , Gröbner bases )
- CPMP tools
- GAP ( group theory )
- GeoGebra ( dynamic geometry initially with a restricted Reduce port , now with Giac)
- Giac / Xcas (is used in HP pocket calculators and by GeoGebra )
- KANT ( Algebraic Number Theory )
- Macaulay2 ( commutative algebra , Gröbner bases )
- Singular ( commutative algebra , Gröbner bases , singularity theory)
- Expressions in bar
Implementations on portable computing systems
Computer algebra systems are also used as firmware in portable computing systems:
- Casio : Algebra FX 2.0 Plus , ClassPad 330 (successor to ClassPad 300 ), ClassPad II (FX-CP400)
- Texas Instruments : TI-89 , TI-92 , Voyage 200 (based on Derive ), TI-Nspire CAS
- HP : HP-28C , HP 48 , HP Prime
- Computer algebra specialist group - joint specialist group of GI , DMV and GAMM
- H.-G. Graves: Script for the course Introduction to Symbolic Computing. (PDF) winter semester 2010/11. Retrieved March 23, 2012 .
- Online version of CAS WIRIS
- ^ Magma Computational Algebra System. News. Computational Algebra Group, accessed March 21, 2020 .
- ↑ CPMP tools software. Retrieved February 8, 2020 .
- ^ Expression in Bar. Retrieved March 4, 2020 .