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 |