- Usage:
`containedInSingularLocus(IX,IY)`

- Inputs:
`IX`, an ideal, a multi-homogeneous prime ideal defining a closed subscheme of ℙ^{n1}x...xℙ^{nm}; makeProductRing builds the graded coordinate ring of ℙ^{n1}x...xℙ^{nm}.`IY`, an ideal, a multi-homogeneous primary ideal defining a closed subscheme of ℙ^{n1}x...xℙ^{nm}; makeProductRing builds the graded coordinate ring of ℙ^{n1}x...xℙ^{nm}.

- Optional inputs:
`Verbose =>`a Boolean value

- Outputs:
`contSingLoc`, a Boolean value, whether or not the variety X associated to IX is contained in the singular locus of the vareity asssociated to the radical of IY

For a subvariety X of ℙ^{n1}x...xℙ^{nm} and an irreducible subscheme Y of ℙ^{n1}x...xℙ^{nm} 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 |

- containedInSingularLocus(Ideal,Ideal)