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, a Boolean value, whether the input ideal is multi-homogeneous with respect to the grading of its ring

Description

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