Symbolic computation or algebraic computation, relates to the use of machines, such as computers, to manipulate mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 equation

Equation

An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

s and expressions in symbolic

Symbol

A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...

 form, as opposed to manipulating the approximations of specific numerical

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

 quantities represented by those symbols. Such a system might be used for symbolic integration

Symbolic integration

In calculus symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f, i.e...

 or differentiation

Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

, substitution of one expression into another, simplification of an expression, etc.

Symbolic computation is also sometimes referred to as symbolic manipulation, symbolic processing, symbolic mathematics, or symbolic algebra, but these terms also refer to non-computational manipulation.

Software applications that perform symbolic calculations are called computer algebra system

Computer algebra system

A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...

s.

See also

• Automated theorem prover
• Computer-assisted proof
  Computer-assisted proof
  A computer-assisted proof is a mathematical proof that has been at least partially generated by computer.Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and...
  
  
• Proof checker
• Model checker
• Symbolic-numeric computation
  Symbolic-numeric computation
  In mathematics and computer science, symbolic-numeric computation is the use of software that combines symbolic and numeric methods to solve problems.-References:*, Dongming Wang, Lihong Zhi, Springer, 2007, ISBN 3764379839...
  
  
• Symbolic simulation
  Symbolic simulation
  In computer science, a simulation is a computation of the execution of some appropriately modelled state-transition system. Typically this process models the complete state of the system at individual points in a discrete linear time frame, computing each state sequentially from its predecessor...
  
  
• Symbolic execution
  Symbolic execution
  In computer science, symbolic execution refers to the analysis of programs by tracking symbolic rather than actual values, a case of abstract interpretation. The field of symbolic simulation applies the same concept to hardware...
  
  

External links

• A Gentle Introduction to Static Analysis and Logic Programming showing an example of application of symbolic computation to perform static program analysis.
• Information on Symbolic Computing A good site for beginners
• jHepWork
  JHepWork
  jHepWork is an interactive framework for scientific computation, data analysis and data visualization designed for scientists, engineers and students...
  
   A free program for symbolic calculations
• Wolfram Integrator — Free online symbolic integration with Mathematica
  Mathematica
  Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
  
  
• Mathematical Assistant on Web — symbolic computations online. Allows to integrate in small steps (with hints for next step (integration by parts, substitution, partial fractions, application of formulas and others), powered by Maxima
• Function Calculator from WIMS
  WWW Interactive Multipurpose Server
  The WWW Interactive Multipurpose Server project is designed for supporting intensive mathematics exercises via the Internet or in a computer-equipped classroom with server-side interactivity, accessible at the address http://wims.unice.fr.The system has the following main features:*A modular...
  
  
• Online integral calculator