For subschemes X,Y of ℙn1x...xℙnm this command computes a list of the projective degrees of a subscheme X in the subscheme Y as classes in the Chow ring of ℙn1x...xℙnm.
i1 : R = makeProductRing({3,3})
o1 = R
o1 : PolynomialRing
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i2 : x = gens(R)
o2 = {a, b, c, d, e, f, g, h}
o2 : List
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i3 : D = minors(2,matrix{{x_0..x_3},{x_4..x_7}})
o3 = ideal (- b*e + a*f, - c*e + a*g, - c*f + b*g, - d*e + a*h, - d*f + b*h,
------------------------------------------------------------------------
- d*g + c*h)
o3 : Ideal of R
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i4 : X = ideal(x_0*x_1,x_1*x_2,x_0*x_2) o4 = ideal (a*b, b*c, a*c) o4 : Ideal of R |
i5 : projectiveDegrees(X,D)
3 3 2 3 3 2 3 2 2 3
o5 = {10H H , 6H H , 6H H , 3H H , 3H H , 3H H }
1 2 1 2 1 2 1 2 1 2 1 2
o5 : List
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i6 : A = makeChowRing(R) o6 = A o6 : QuotientRing |
i7 : pd = projectiveDegrees(X,D,A)
3 3 2 3 3 2 3 2 2 3
o7 = {10H H , 6H H , 6H H , 3H H , 3H H , 3H H }
1 2 1 2 1 2 1 2 1 2 1 2
o7 : List
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