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
i1 : R = makeProductRing({2,2,2}) o1 = R o1 : PolynomialRing |
i2 : x=(gens R)_{0..2} o2 = {a, b, c} o2 : List |
i3 : y=(gens R)_{3..5} o3 = {d, e, f} o3 : List |
i4 : z=(gens R)_{6..8} o4 = {g, h, i} o4 : List |
i5 : m1=matrix{{x_0,x_1,5*x_2},y_{0..2},{2*z_0,7*z_1,25*z_2}} o5 = | a b 5c | | d e f | | 2g 7h 25i | 3 3 o5 : Matrix R <--- R |
i6 : m2=matrix{{9*z_0,4*z_1,3*z_2},y_{0..2},x_{0..2}} o6 = | 9g 4h 3i | | d e f | | a b c | 3 3 o6 : Matrix R <--- R |
i7 : W=minors(3,m1)+minors(3,m2); o7 : Ideal of R |
i8 : f=random({1,1,1},R); |
i9 : Y=ideal (z_0*W_0-z_1*W_1)+ideal(f); o9 : Ideal of R |
i10 : X=((W)*ideal(y)+ideal(f)); o10 : Ideal of R |
i11 : time isComponentContained(X,Y) -- used 2.29438 seconds o11 = true |
i12 : print "we could confirm this with the computation:" we could confirm this with the computation: |
i13 : B=ideal(x)*ideal(y)*ideal(z) o13 = ideal (a*d*g, a*d*h, a*d*i, a*e*g, a*e*h, a*e*i, a*f*g, a*f*h, a*f*i, ----------------------------------------------------------------------- b*d*g, b*d*h, b*d*i, b*e*g, b*e*h, b*e*i, b*f*g, b*f*h, b*f*i, c*d*g, ----------------------------------------------------------------------- c*d*h, c*d*i, c*e*g, c*e*h, c*e*i, c*f*g, c*f*h, c*f*i) o13 : Ideal of R |
i14 : time isSubset(saturate(Y,B),saturate(X,B)) -- used 13.2894 seconds o14 = true |