# isLPP -- determine whether an ideal is an LPP ideal

## Synopsis

• Usage:
B=isLPP I
• Inputs:
• I, an ideal, an ideal in a polynomial ring
• Outputs:
• B, , true if I is an LPP ideal in ring I and false otherwise

## Description

Given an ideal I in a polynomial ring R, isLPP checks that I is Artinian and that the power sequence is weakly increasing. Then isLPP computes bases of R/I in each degree up through the maximum degree of a minimal generator of I to determine whether I is an LPP ideal in R.

 i1 : R=ZZ/32003[a..c]; i2 : isLPP LPP(R,{1,3,4,3,2},{2,2,4}) o2 = true i3 : isLPP ideal(a^3,b^3,c^3,a^2*b,a^2*c,a*b^2*c^2) o3 = true i4 : isLPP ideal(a^3,b^4) --not Artinian since no power of c o4 = false i5 : isLPP ideal(a^3,b^4,c^3) --powers not weakly increasing o5 = false i6 : isLPP ideal(a^3,b^3,c^3,a^2*b,a*b^2) o6 = false