Singular

Singular is an open source computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.

Free
Open Source
Windows
Linux

singular is an open source computer algebra system for polynomial computations, with special emphasis on commutative and noncommutative algebra, algebraic geometry, and singularity theory.

singular provides:

highly efficient core algorithms,a multitude of advanced algorithms in the above fields,an intuitive, clike programming language,easy ways to make it userextendible through libraries, anda comprehensive online manual and help function.

its main computational objects are ideals, modules and matrices over a large number of baserings. these include:

polynomial rings over various ground fields and some rings (including the integers),localizations of the above,a general class of noncommutative algebras (including the exterior algebra and the weyl algebra),quotient rings of the above,tensor products of the above.singular's core algorithms handlegröbner resp. standard bases and free resolutions,polynomial factorization,resultants, characteristic sets, and numerical root finding.

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Mathematica

Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing.

Commercial Mac OS X Windows Linux Web

Calculus solving Symbolic Computation

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Singular

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