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)) |