# Operations on ideals of polynomial rings

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.