The question above.
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$\begingroup$ I know that the spell checker in your browser will not be able to see the typo in your title, but presumably you can? $\endgroup$– Mariano Suárez-ÁlvarezSep 28, 2010 at 12:31
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$\begingroup$ I fixed the typo. $\endgroup$– Timothy ChowSep 28, 2010 at 14:19
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2 Answers
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Sort of yes, because there is a better algorithm for rings, known under umbrella name of Grobner Basis. It works the nicest for commutative algebras, but there are various versions for algebras over Euclidian domains, associative algebras, Lie algebras etc. What is the ring you are after?
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Yes, this is implemented as the Vector Enumeration in magma:
http://magma.maths.usyd.edu.au/magma/htmlhelp/text942.htm#9432
This is also included in GAP.