Computer Algebra System - Symbolic Manipulations

Symbolic Manipulations

The symbolic manipulations supported typically include:

  • simplification to a smaller expression or some standard form, including automatic simplification with assumptions and simplification with constraints
  • substitution of symbols or numeric values for certain expressions
  • change of form of expressions: expanding products and powers, partial and full factorization, rewriting as partial fractions, constraint satisfaction, rewriting trigonometric functions as exponentials, transforming logic expressions, etc.
  • partial and total differentiation
  • some indefinite and definite integration (see symbolic integration), including multidimensional integrals
  • symbolic constrained and unconstrained global optimization
  • solution of linear and some non-linear equations over various domains
  • solution of some differential and difference equations
  • taking some limits
  • integral transforms
  • series operations such as expansion, summation and products
  • matrix operations including products, inverses, etc.
  • statistical computation
  • theorem proving and verification which is very useful in the area of experimental mathematics
  • optimized code generation

In the above, the word some indicates that the operation cannot always be performed.

Read more about this topic:  Computer Algebra System

Famous quotes containing the word symbolic:

    I find it profoundly symbolic that I am appearing before a committee of fifteen men who will report to a legislative body of one hundred men because of a decision handed down by a court comprised of nine men—on an issue that affects millions of women.... I have the feeling that if men could get pregnant, we wouldn’t be struggling for this legislation. If men could get pregnant, maternity benefits would be as sacrosanct as the G.I. Bill.
    Letty Cottin Pogrebin (20th century)