symbolic algebra - Definition. Was ist symbolic algebra
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Was (wer) ist symbolic algebra - definition

MATHEMATICAL SOFTWARE WITH THE ABILITY TO MANIPULATE MATHEMATICAL EXPRESSIONS IN A WAY SIMILAR TO THE TRADITIONAL MANUAL COMPUTATIONS OF MATHEMATICIANS AND SCIENTISTS
Computerized algebra systems; Computerized algebra system; Computer algebra systems; Computer algebraic system; Computer Algebra System; Computer algebra package; Symbolic solver; Computer algebra environment; Symbolic algebra; Computer-algebra systems; Equation solver; Symbolic algebra system
  • A Texas Instruments [[TI-Nspire]] calculator that contains a computer algebra system

Computer algebra system         
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
Computer algebra         
  •  date=Dec 1985 }} Here: p.15</ref>
SCIENTIFIC AREA AT THE INTERFACE BETWEEN COMPUTER SCIENCE AND MATHEMATICS
Symbolic computation; Symbolic math; Symbolic Reasoning; Symbolic reasoning; Algebraic algorithms; Symbolic calculation; Algebraic computation; Symbolic computing; Symbolic and algebraic computation; Computational algebra; Symbolic mathematics; Symbolic processing; Symbolic differentiation; Symbolic maths; Simplification (symbolic computation); Draft:Computer Algebra in Scientific Computing; Simplification (computer algebra); History of computer algebra; History of symbolic computation; Simplification of expressions in computer algebra systems; Syntactic equality; Symbolic computation expression
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
symbolic mathematics         
  •  date=Dec 1985 }} Here: p.15</ref>
SCIENTIFIC AREA AT THE INTERFACE BETWEEN COMPUTER SCIENCE AND MATHEMATICS
Symbolic computation; Symbolic math; Symbolic Reasoning; Symbolic reasoning; Algebraic algorithms; Symbolic calculation; Algebraic computation; Symbolic computing; Symbolic and algebraic computation; Computational algebra; Symbolic mathematics; Symbolic processing; Symbolic differentiation; Symbolic maths; Simplification (symbolic computation); Draft:Computer Algebra in Scientific Computing; Simplification (computer algebra); History of computer algebra; History of symbolic computation; Simplification of expressions in computer algebra systems; Syntactic equality; Symbolic computation expression
<mathematics, application> (Or "symbolic math") The use of computers to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the numerical quantities represented by those symbols. Such a system might be used for symbolic integration or differentiation, substitution of one expression into another, simplification of an expression, change of subject etc. One of the best known symbolic mathematics software packages is Mathematica. Others include ALAM, ALGY, AMP, Ashmedai, AXIOM*, CAMAL, CAYLEY, CCalc, CLAM, CoCoA(?), ESP, FLAP, FORM, FORMAL, Formula ALGOL, GAP, JACAL, LiE, Macaulay, MACSYMA, Magic Paper, MAO, Maple, Mathcad, MATHLAB, MuMath, Nother, ORTHOCARTAN, Pari, REDUCE, SAC-1, SAC2, SAINT, Schoonschip, Scratchpad I, SHEEP, STENSOR, SYMBAL, SymbMath, Symbolic Mathematical Laboratory, TRIGMAN, UBASIC. Usenet newsgropup: news:sci.math.symbolic. (1995-04-12)

Wikipedia

Computer algebra system

A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.

Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics.

General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as:

  • a user interface allowing a user to enter and display mathematical formulas, typically from a keyboard, menu selections, mouse or stylus.
  • a programming language and an interpreter (the result of a computation commonly has an unpredictable form and an unpredictable size; therefore user intervention is frequently needed),
  • a simplifier, which is a rewrite system for simplifying mathematics formulas,
  • a memory manager, including a garbage collector, needed by the huge size of the intermediate data, which may appear during a computation,
  • an arbitrary-precision arithmetic, needed by the huge size of the integers that may occur,
  • a large library of mathematical algorithms and special functions.

The library must not only provide for the needs of the users, but also the needs of the simplifier. For example, the computation of polynomial greatest common divisors is systematically used for the simplification of expressions involving fractions.

This large amount of required computer capabilities explains the small number of general-purpose computer algebra systems. Significant systems include Axiom, Maxima, Magma, Maple, Mathematica, and SageMath.