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multUpperBound -- determine whether the multiplicity of an ideal satisfies the upper bound conjectured by Herzog-Huneke-Srinivasan

Synopsis

Description

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)

See also

Ways to use multUpperBound :