B=multBounds I
Let I be a homogeneous ideal of codimension c in a polynomial ring R such that R/I is CohenMacaulay. Herzog, Huneke, and Srinivasan conjectured that if R/I is CohenMacaulay, 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 CohenMacaulay, 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.
This conjecture was proven in 2008 work of EisenbudSchreyer and BoijSoderberg.



Note that multBounds makes no attempt to check to see whether R/I is CohenMacaulay.
The object multBounds is a method function.