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# isMultiHom -- Tests if an ideal is multi-homogeneous with respect to the grading of its ring

## Synopsis

• Usage:
isMultiHom(X)
• Inputs:
• X, an ideal, an ideal in the multi-graded coordinate ring of \PP^{n_1}x...x\PP^{n_m}; makeProductRing builds the graded coordinate ring of \PP^{n_1}x...x\PP^{n_m}.
• Outputs:
• isMultHom, , whether the input ideal is multi-homogeneous with respect to the grading of its ring

## Description

Given an ideal in the coordinate R ring of \PP^{n_1}x...x\PP^{n_m} this method tests if whether the input ideal is multi-homogeneous with respect to the grading on R.

 i1 : R = makeProductRing({1,2}) o1 = R o1 : PolynomialRing i2 : x=gens R o2 = {a, b, c, d, e} o2 : List i3 : degrees R o3 = {{1, 0}, {1, 0}, {0, 1}, {0, 1}, {0, 1}} o3 : List i4 : isMultiHom ideal(x_0^2*x_2+x_1*x_2^2) Input term below is not homogeneous with respect to the grading 2 2 a c + b*c o4 = false i5 : isMultiHom ideal(x_0^2*x_2+x_1^2*x_3) o5 = true

## Ways to use isMultiHom :

• isMultiHom(Ideal)
• isMultiHom(RingElement) (missing documentation)

## For the programmer

The object isMultiHom is .