Let
I be a homogeneous ideal of codimension
c in a polynomial ring
R such that
R/I is Cohen-Macaulay. Huneke and Srinivasan conjectured that
m_1 ... m_c / c! <= e(R/I),
where
m_i is the minimum shift in the minimal graded free resolution of
R/I at step
i, and
e(R/I) is the multiplicity of
R/I.
multLowerBound tests this inequality for the given ideal, returning
true if the inequality holds and
false otherwise, and it prints the lower bound and the multiplicity (listed as the degree).
R=ZZ/32003[a..c]; |
multLowerBound ideal(a^4,b^4,c^4) |
multLowerBound ideal(a^3,b^5,c^6,a^2*b,a*b*c) |