1 | initial version |

Event though you haven't told us enough data to actually see what the problem is, there is certainly no canned one-liner in Sage that does everything that you want. I'll assume that every equation is invariant under the group, otherwise you'll have to do more representation theory. Your equations also need to be of fixed total degree, otherwise you might get the wrong answer if you truncate your Groebner basis computation at some maximum degree. There is some discussion in http://trac.sagemath.org/sage_trac/ticket/11667 on that very subject.

Roughly, you probably want to do the following. First, compute the Hironaka decomposition of your invariant ring. Express the equations in terms of the primary and secondary invariants. Run the Groebner basis computation in the invariant ring.

2 | No.2 Revision |

~~Event ~~Even though you haven't told us enough data to actually see what the problem is, there is certainly no canned one-liner in Sage that does everything that you want. I'll assume that every equation is invariant under the group, otherwise you'll have to do more representation theory. Your equations also need to be of fixed total degree, otherwise you might get the wrong answer if you truncate your Groebner basis computation at some maximum degree. There is some discussion in http://trac.sagemath.org/sage_trac/ticket/11667 on that very subject.

Roughly, you probably want to do the following. First, compute the Hironaka decomposition of your invariant ring. Express the equations in terms of the primary and secondary invariants. Run the Groebner basis computation in the invariant ring.

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