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Commutative algebra -- Software.

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View Resource Macaulay 2 Home Page

Two mathematics professors at the University of Illinois at Urbana-Champaign are the authors of Macaulay 2, a powerful software tool that supports "research in algebraic geometry and commutative algebra." The Macaulay 2 home page offers the program's source code free for download, which can be compiled under the UNIX, Windows, or Macintosh operating systems. There is also extensive online...

https://faculty.math.illinois.edu/Macaulay2/
View Resource Singular: A Computer Algebra System for Polynomial Computations

Developed by mathematicians at the University of Kaiserslautern in Germany, Singular is a "Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory." The software is available for free online in Windows, Macintosh, and UNIX versions. The authors of Singular offer extensive documentation, examples, and...

http://www.singular.uni-kl.de/