The matrix F must have a single row. Inputing an ideal instead has the same effect as inputing gens F. checkComparisonTheorem tests if the hypotheses for the comparison theorem of Piene and Schlessinger hold for the ideal generated by F, see [PS85]. In the following example, the comparison theorem does not hold for the ideal I, but does for the partial truncation J.
i1 : S = QQ[a..d]; |
i2 : I = ideal(a,b^3*c,b^4); o2 : Ideal of S |
i3 : J=ideal b^4+ideal (ambient basis(3,I)) 4 3 2 2 2 2 2 2 o3 = ideal (b , a , a b, a c, a d, a*b , a*b*c, a*b*d, a*c , a*c*d, a*d ) o3 : Ideal of S |
i4 : checkComparisonTheorem I o4 = false |
i5 : checkComparisonTheorem J o5 = true |