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SegreClasses :: segreDimX

segreDimX

Synopsis

Description

For subschemes X,Y of ℙn1x...xℙnm this command computes the dimension X part of the Segre class s(X,Y) of X in Y as a class in the Chow ring of ℙn1x...xℙnm. This is faster than computing the entire Segre class.

i1 : R = makeProductRing({2,2})

o1 = R

o1 : PolynomialRing
i2 : x = gens(R)

o2 = {a, b, c, d, e, f}

o2 : List
i3 : Y = ideal(random({2,2},R));

o3 : Ideal of R
i4 : X = Y+ideal(x_0*x_3+x_1*x_4);

o4 : Ideal of R
i5 : A = makeChowRing(R)

o5 = A

o5 : QuotientRing
i6 : time s = segreDimX(X,Y,A)
     -- used 0.0498993 seconds

       2             2
o6 = 2H  + 4H H  + 2H
       1     1 2     2

o6 : A
i7 : time segre(X,Y,A)
     -- used 0.0702225 seconds

        2 2     2         2     2             2
o7 = 12H H  - 6H H  - 6H H  + 2H  + 4H H  + 2H
        1 2     1 2     1 2     1     1 2     2

o7 : A

Ways to use segreDimX :