Let M be a module over a polynomial ring P = kk[x_{0,0}..x_{0,a_0}..x_{n-1,0}..x_{n-1,a_{n-1}}] graded with degree x_{i,j} = e_i, the i-th unit vector, and let b = {b_0..b_{n-1}} be a list of integers. The code computes the multigraded Hilbert polynomial mH(h_0,..,h_{n-1}) and returns H(h) = mH(b_0*h_0, .., b_{n-1}*h_{n-1}).
i1 : P = productOfProjectiveSpaces {1,1}
o1 = P
o1 : PolynomialRing
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i2 : Delta = smallDiagonal P
o2 = ideal(- x x + x x )
0,1 1,0 0,0 1,1
o2 : Ideal of P
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i3 : M = P^1/(Delta^2)
o3 = cokernel | x_(0,1)^2x_(1,0)^2-2x_(0,0)x_(0,1)x_(1,0)x_(1,1)+x_(0,0)^2x_(1,1)^2 |
1
o3 : P-module, quotient of P
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i4 : correspondencePolynomial (M,{1,1})
o4 = 4s
o4 : QQ[s]
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i5 : correspondencePolynomial (M,{2,2})
o5 = 8s
o5 : QQ[s]
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The object correspondencePolynomial is a method function with options.