next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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).

i1 : n=6

o1 = 6
i2 : R = makeProductRing({n})

o2 = R

o2 : PolynomialRing
i3 : x=gens(R)

o3 = {a, b, c, d, e, f, g}

o3 : List
i4 : 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)}

o4 = | a    b    c    d    |
     | 3d   4e   5f   6g   |
     | c    d    e    f    |
     | a+5b b+6c c+7d d+8e |

             4       4
o4 : Matrix R  <--- R
i5 : C=ideal mingens(minors(3,m));

o5 : Ideal of R
i6 : P=ideal(x_0,x_4,x_3,x_2,x_1)

o6 = ideal (a, e, d, c, b)

o6 : Ideal of R
i7 : containedInSingularLocus(P,C)

o7 = true

Ways to use containedInSingularLocus :