i1 : S = QQ[a,b,c,d]; |
i2 : I = ideal (b^2-a*d, a*d-b*c, c^2-b*d); o2 : Ideal of S |
i3 : M = monomialIdeal (b^2, b*c, c^2); o3 : MonomialIdeal of S |
i4 : L = lcmLattice (I); |
i5 : L.GroundSet 2 2 2 2 2 2 2 2 o5 = {1, c , b*c, b*c , b , b c, b c , a*c*d, a*c d, a*b*d, a*b*c*d, a*b*c d, ------------------------------------------------------------------------ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 a*b d, a*b c*d, a*b c d, a d , a c*d , a c d , a b*d , a b*c*d , ------------------------------------------------------------------------ 2 2 2 2 2 2 2 2 2 2 2 2 2 a b*c d , a b d , a b c*d , a b c d } o5 : List |
i6 : L.RelationMatrix o6 = | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 | | 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 | | 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 | | 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 | | 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 | | 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 | | 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 | | 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 | | 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | 24 24 o6 : Matrix ZZ <--- ZZ |
i7 : LM = lcmLattice (M); |
i8 : LM.GroundSet 2 2 2 2 2 2 o8 = {1, c , b*c, b*c , b , b c, b c } o8 : List |
i9 : LM.RelationMatrix o9 = | 1 1 1 1 1 1 1 | | 0 1 0 1 0 0 1 | | 0 0 1 1 0 1 1 | | 0 0 0 1 0 0 1 | | 0 0 0 0 1 1 1 | | 0 0 0 0 0 1 1 | | 0 0 0 0 0 0 1 | 7 7 o9 : Matrix ZZ <--- ZZ |