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SegreClasses :: containedInSingularLocus

containedInSingularLocus -- This method tests is an irreducible variety is contained in the singular locus of the reduced scheme of an irreducible scheme

Synopsis

Description

For a subvariety X of ℙn1x...xℙnm and an irreducible subscheme Y of ℙn1x...xℙnm this command tests whether X is contained in the singular locus of the reduced scheme of Y (i.e. the singular locus of the variety defined by the radical of the ideal defining Y).

n=6
R = makeProductRing({n})
x=gens(R)
m=matrix{for i from 0 to n-3 list x_i,for i from 0 to n-3 list (i+3)*x_(i+3),for i from 0 to n-3 list x_(i+2),for i from 0 to n-3 list x_(i)+(5+i)*x_(i+1)}
C=ideal mingens(minors(3,m));
P=ideal(x_0,x_4,x_3,x_2,x_1)
containedInSingularLocus(P,C)

Ways to use containedInSingularLocus :