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multLowerBound -- determine whether the multiplicity of an ideal satisfies the lower bound of the Herzog-Huneke-Srinivasan conjecture

Synopsis

Description

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)

See also

Ways to use multLowerBound :