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:
“The act of bellringing is symbolic of all proselytizing religions. It implies the pointless interference with the quiet of other people.”
—Ezra Pound (1885–1972)