# isGenSegment -- gen-segment ideals

## Synopsis

• Usage:
isGenSegment J
• Inputs:
• J, , or
• J, an ideal, a strongly stable ideal.
• Outputs:
• ,

## Description

The first element of the sequence is a boolean value. It tells if the ideal is a segment, i.e. if there exists a term ordering such that every generator of the ideal is strictly greater than every monomial outside the ideal of the same degree. If true, the second element of the sequence contains the list of weights giving the corresponding ordering on the monomials.

 i1 : QQ[x,y,z]; i2 : isGenSegment(ideal(x^2,x*y,y^4)) o2 = (true, {6, 3, 1}) o2 : Sequence i3 : isGenSegment(ideal(x^2,x*y^3,y^4)) o3 = (true, {4, 3, 1}) o3 : Sequence

## Ways to use isGenSegment :

• "isGenSegment(Ideal)"
• "isGenSegment(MonomialIdeal)"

## For the programmer

The object isGenSegment is .