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I have tried to understand and program CGT algorithms though I am a beginner still. But I never get to hear Computational Ring Theory. Even GAP largely supports Groups Theory. Is there some initiative in this direction and if no than what is the probable reason for delay ?

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There are plenty of software packages for computational commutative algebra and/or algebraic geometry. Google "Groebner bases", and have a look at the book "Ideals, Varieties and Algorithms" by Cox, Little and O'Shea. For non-commutative rings there is less, though Magma can handle e.g. quaternion algebras. And I suppose representation theory is all about computations over group rings. –  Martin Bright May 22 '13 at 12:28
The package "Singular" is also analogous to GAP, but for rings. –  Ryan Budney May 22 '13 at 13:13
Or have a look at Sage on –  Tom De Medts May 22 '13 at 13:30
Macaulay2 is also good software for commutative rings. –  Stephen Sturgeon May 22 '13 at 14:56

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