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 suggested applications to give users a proper introduction. Registration is not required to download the software, but it is necessary to receive support and updates.
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