You are here
Homesymbolic computation
Primary tabs
symbolic computation
1 Symbolic Computation
Also called formula manipulation or algebraic computation.
Symbolic computation refers to the automatic transformation of mathematical expressions in symbolic form, hence in an exact way, as opposed to numerical and hence limitedprecision floatingpoint computation. Typical operations include differentiation and integration, linear algebra and matrix calculus, operations with polynomials, or the simplification of algebraic expressions.
Programs or systems in this area which provide a language interface are called Computer Algebra Systems (or CASes). There are also symbolic computation libraries for existing programming languages.
Primarily designed for applications in theoretical physics or mathematics, these systems (which are often interactive in the case of CASes) can be used in any area where straightforward but tedious or lengthy calculations with formulae are required.
2 Systems
Some well known, general symbolic computation CASes are:
These systems have different scope and facilities, and some are easier to use or to access than others. There is a trend away from generalized CAS systems to more specialized, applicationspecific systems, such as:

SINGULAR (algebraic geometry, esp. singular varieties)
Some nonCAS symbolic computation libraries, with their supported languages, are:

GiNaC (C++)
References
 1 Based on content from the Data Analysis Briefbook
Mathematics Subject Classification
33F99 no label found1708 no label found16Z05 no label found13P99 no label found12Y05 no label found11Y40 no label found14Q99 no label found68W30 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
 Corrections
Comments
note which CASes are free software?
Since PlanetMath itself uses the FDL, and strives to keep its content free (in the FSF's sense of the term, i.e. <i>libre</i>) I think it would be good to clearly note which of the CASes listed above are free (again <i>libre</i>, or GPLcompatible).
Feel free to ignore me if you don't see free/nonfree as an useful distinction. I'm not entirely convinced it is one, but it seems like the one naturally suggested by PlanetMath's use of the FDL.
Offhand, I'm sure that Mathematica and Maple are commercial, while GNU Maxima and GiNaC are free.
numeric computation software?
Is there an entry for purely numeric computation software? I mean something like Matlab or Octave. If so, this entry should probably link to it somehow.
Re: note which CASes are free software?
missing several:
yacas, aribas, magnus, etc
f
G > H G
p \ /_  ~ f(G)
\ / f ker f
G/ker f
Re: numeric computation software?
I don't think one exists. Feel free to start it =)
apk
Re: note which CASes are free software?
Can you file an addendum with more info?
apk
Re: note which CASes are free software?
http://www.cs.kun.nl/~freek/digimath/index.html
SymbolicComputation.com
SymbolicComputation.com is online. Try Sym a free open source algebra program.