# isTLexSeg -- whether a set of t-spread monomials is a t-lex segment

## Synopsis

• Usage:
isTLexSeg(l,t)
• Inputs:
• l, a list of t-spread monomials of a polynomial ring
• Outputs:
• , whether the list l of monomials is a t-lex segment

## Description

the function isTLexSeg(l,t) is true whether the list of monomials l is a t-lex segment, that is, the set of all the t-spread monomials smaller than the maximum of l and greater than the minimum of l, with respect to $>_\mathrm{slex}.$

Examples:

 i1 : S=QQ[x_1..x_7] o1 = S o1 : PolynomialRing i2 : isTLexSeg({x_1*x_4*x_7,x_1*x_5*x_7,x_2*x_4*x_6,x_2*x_4*x_7,x_2*x_5*x_7},2) o2 = true i3 : isTLexSeg({x_1*x_4*x_7,x_2*x_4*x_6,x_2*x_4*x_7,x_2*x_5*x_7},2) o3 = false