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).
i1 : R=ZZ/32003[a..c];
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i2 : multLowerBound ideal(a^4,b^4,c^4)
lower bound = 64 degree = 64
o2 = true
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i3 : multLowerBound ideal(a^3,b^5,c^6,a^2*b,a*b*c)
lower bound = 16 degree = 46
o3 = true
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