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There is GroebnerBasis to compute a Gröbner basis of an ideal in a polynomial ring, but I am looking for a package to perform operations on ideals $I,J\subseteq\Bbb Q[x_1,\ldots,x_n]$, such as computing the following:

  • $I\cap J$
  • $I+J$
  • $(I:J)$
  • $\sqrt{I}$
  • $\dim(I)$

It would also be desirable to have a method for computing the primary decomposition. I can implement all of that myself, but I'd rather use an existing package if one exists.

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