Let
I be a homogeneous ideal of codimension
c in a polynomial ring
R such that
R/I is Cohen-Macaulay. Herzog, Huneke, and Srinivasan conjectured that if
R/I is Cohen-Macaulay, then
m_1 ... m_c / c! <= e(R/I) <= M_1 ... M_c / c!,
where
m_i is the minimum shift in the minimal graded free resolution of
R/I at step
i,
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. If
R/I is not Cohen-Macaulay, the upper bound is still conjectured to hold.
multBounds tests the inequalities for the given ideal, returning
true if both inequalities hold and
false otherwise.
multBounds prints the bounds and the multiplicity (called the degree), and it calls
multUpperBound and
multLowerBound.
S=ZZ/32003[a..c]; |
multBounds ideal(a^4,b^4,c^4) |
multBounds ideal(a^3,b^4,c^5,a*b^3,b*c^2,a^2*c^3) |