Let
I be a homogeneous ideal of codimension
c in a polynomial ring
R. Huneke and Srinivasan (and later Herzog and Srinivasan in the non-Cohen-Macaulay case) conjectured that
e(R/I) <= M_1 ... M_c / c!,
where
M_i is the maximum shift in the minimal graded free resolution of
R/I at step
i, and
e(R/I) is the multiplicity of
R/I.
multUpperBound tests this inequality for the given ideal, returning
true if the inequality holds and
false otherwise, and it prints the upper bound and the multiplicity (listed as the degree).
R=ZZ/32003[a..c]; |
multUpperBound ideal(a^4,b^4,c^4) |
multUpperBound ideal(a^3,b^5,c^6,a^2*b,a*b*c) |