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Questions involving the software MAGMA. (For the algebraic structure called magma, please, use the tag magmas.) This tag should hardly ever be the only tag of a question; typically there should be additional tags to indicate the mathematical content of the question. Please note that questions that are purely support-questions on MAGMA are not a good fit for this site.
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Primary invariants on MAGMA for a graded ring
Here is a simple example I tried in Magma:
P<x1,x2,y1,y2> := PolynomialRing(RationalField(), [1, 2, 1, 2]);
I := ideal<P |x1*y2 , x2*y1>;
R:=P/I;
p := PrimaryInvariants(R);
However, when I run this, Magma … My understanding is that Magma doesn't extend this functionality to general polynomial quotient rings like the example above. …