next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
VersalDeformations :: checkComparisonTheorem

checkComparisonTheorem -- checks if the Piene-Schlessinger comparison theorem holds

Synopsis

Description

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

Ways to use checkComparisonTheorem :