Macaulay2 » Documentation
Packages » LexIdeals :: isLPP
next | previous | forward | backward | up | index | toc

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

- Usage:
    `B=isLPP I`
- Inputs:
  - I, an ideal, an ideal in a polynomial ring
- Outputs:
  - B, a Boolean value, 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

## 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

## Ways to use isLPP:

- `isLPP(Ideal)`

## For the programmer

The object isLPP is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LexIdeals.m2:947:0.