Computeralgebrasystem

A Computer Algebra System (CAS ) is a computer program that is used to process algebraic expressions. It not only solves math problems with numbers ( as a simple calculator ), but also those with symbolic expressions ( such as variables, functions, polynomials and matrices).

Functionalities

The algebraic in the narrow sense of a CAS tasks include:

  • Simplify algebraic expressions and compare
  • Solve algebraic equations
  • Solve linear systems of equations and perform calculations with matrices
  • Factorization of integers and polynomials
  • Features differentiate and integrate ( Algebraic integration)
  • Reckon with decimal numbers with arbitrary precision ( with a good CAS can, for example with less programming effort the circle number π (pi) to tens of thousands of decimal places determine )

In addition, part of the functional of many CAS:

  • Represent functions and data in two or three dimensions graphically
  • Analytic- algebraic solving systems of ( ordinary ) differential equations.
  • Not to solve analytically separable integrals and differential equations by numerical integration ( "quadrature" ).

In contrast to the "general - purpose systems " that cover as large a part of mathematics, there are many specialized systems, for example, to group theory, Gröbner bases, Algebraic Number Theory, etc.

Examples of computer algebra systems

One of the first computer algebra systems was Schoon chip, developed in 1963 by Martinus JG Veltman.

Proprietary systems

  • Derive (now firmware in TI calculators and as a teacher / student version for PC / MAC)
  • (Never ) Macsyma
  • Magma
  • Maple
  • Mathcad
  • Mathematica
  • MuPAD (never as a standalone product, part of MATLAB )
  • WIRIS (also an online version, see Related links)

Open -source systems

  • Axiom
  • Cocoa ( Commutative algebra, Gröbner bases)
  • GAP ( group theory )
  • GeoGebra ( Dynamic geometry with a limited Reduce- porting)
  • Giac / Xcas ( further development of the CAS system that is used in HP calculators )
  • KANT ( Algebraic Number Theory )
  • Macaulay2 ( Commutative algebra, Gröbner bases)
  • Maxima
  • Reduce
  • Saga
  • Singular ( Commutative algebra, Gröbner bases, singularity theory )
  • Yacas

Implementations in graphics-capable calculators

Computer algebra systems are also used as firmware in calculators:

  • CASIO Algebra FX 2.0 Plus, ClassPad 330 (successor of ClassPad 300) ClassPad II (FX - CP400 )
  • Texas Instruments: TI- 89, TI -92, Voyage 200 (based on Derive ), TI -Nspire CAS
  • HP: HP -48, HP Prime
Symbolic computation Symbolic integration Schoonschip Derive (computer algebra system) Axiom (computer algebra system) GAP (computer algebra system) List of interactive geometry software Reduce (Computeralgebrasystem) Maxima (software) Sage (mathematics software) TI-89 series TI-92 series Hewlett-Packard HP-48 series Symbolic mathematics German Mathematical Society
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