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
m1 ... mc / c! <= e(R/I),
where mi 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]; |
i2 : multLowerBound ideal(a^4,b^4,c^4) lower bound = 64 degree = 64 o2 = true |
i3 : multLowerBound ideal(a^3,b^5,c^6,a^2*b,a*b*c) lower bound = 16 degree = 46 o3 = true |