isLPP -- determine whether an ideal is an LPP ideal
Synopsis
Usage:
isLPP I
Inputs:
I, an ideal, a homogeneous ideal in a polynomial ring
Outputs:
a Boolean value, returns true if I is an LPP ideal in ring I and false otherwise.
Description
Given an ideal I in a polynomial ring R, isLPP first checks to see that I is a monomial ideal. If not, it returns false. If so, 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.
R=ZZ/32003[a..c];
isLPP LPP(R,{1,3,4,3,2},{2,2,4})
isLPP ideal(a^3,b^3,c^3,a^2*b,a^2*c,a*b^2*c^2)
isLPP ideal(a^3,b^4) --not Artinian since no power of c
isLPP ideal(a^3,b^4,c^3) --powers not weakly increasing
isLPP ideal(a^3,b^3,c^3,a^2*b,a*b^2)
See also
isLexIdeal -- determine whether an ideal is a lexicographic ideal
LPP -- return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence
generateLPPs -- return all LPP ideals corresponding to a given Hilbert function