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I'm working on a Maple package for computing in multivariate polynomial quotient rings, ie: rings of the form k[x1,...,xn]/I where k is a field and I is an ideal of k[x1,...,xn]. I currently have commands for the following:
  • computing inverses
  • exact polynomial division
  • simplifying fractions to a minimal canonical form
  • testing whether something is a zero divisor
  • testing whether the domain is a field or an integral domain
  • testing whether something is a unit, or whether two elements are associate
  • compute a basis of monomials for the quotient ring as a vector space
I'm looking for more commands. Factoring may be out of the question, since the domain may not be a UFD. I don't know how to test for a UFD, and I don't have a general factoring algorithm. Similarly I can compute GCDs in Euclidean domains but I don't know how to test for a Euclidean domain. I would be grateful for any references people could provide. I want an isomorphism command (under the embedding of k), and I can also do chinese remaindering. But what I really want to know is what do people want ?
testing package integral

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