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SegreClasses :: isComponentContained

isComponentContained -- This method tests containment of (irreducible) varieties; more generally it tests if a top-dimensional irreducible component of the scheme associated an ideal is contained in the scheme associated to another ideal

Synopsis

Description

For a subschemes X of an irreducible subscheme Y of ℙn1x...xℙnm this command tests whether or not a top-dimensional irreducible (and reduced) component of X is contained in Y

R = makeProductRing({2,2,2})
x=(gens R)_{0..2}
y=(gens R)_{3..5}
z=(gens R)_{6..8}
m1=matrix{{x_0,x_1,5*x_2},y_{0..2},{2*z_0,7*z_1,25*z_2}}
m2=matrix{{9*z_0,4*z_1,3*z_2},y_{0..2},x_{0..2}}
W=minors(3,m1)+minors(3,m2);
f=random({1,1,1},R);
Y=ideal (z_0*W_0-z_1*W_1)+ideal(f);
X=((W)*ideal(y)+ideal(f));
time isComponentContained(X,Y)
print "we could confirm this with the computation:"
B=ideal(x)*ideal(y)*ideal(z)
time isSubset(saturate(Y,B),saturate(X,B))

Ways to use isComponentContained :