# tLexSeg -- give the t-lex segment with given extremes

## Synopsis

• Usage:
tLexSeg(v,u,t)
• Inputs:
• v, a t-spread monomial of a polynomial ring
• u, a t-spread monomial of a polynomial ring
• t, a positive integer that idenfies the t-spread contest
• Outputs:
• a list, the set of all the t-spread monomials smaller than v and greater than u, with respect to lexcografic order

## Description

the function tLexSeg(v,u,t) gives the t-lex segment defined by v and u, that is, the set of all the t-spread monomials smaller than v and greater than u, with respect to $>_\mathrm{slex}.$
This function iteratively uses the method tNextMon(u,t) until the returned monomial is u.

Examples:

 i1 : S=QQ[x_1..x_14] o1 = S o1 : PolynomialRing i2 : tLexSeg(x_2*x_5*x_10*x_13,x_2*x_6*x_9*x_12,2) o2 = {x x x x , x x x x , x x x x , x x x x , x x x x , x x x x , 2 5 10 13 2 5 10 14 2 5 11 13 2 5 11 14 2 5 12 14 2 6 8 10 ------------------------------------------------------------------------ x x x x , x x x x , x x x x , x x x x , x x x x , x x x x } 2 6 8 11 2 6 8 12 2 6 8 13 2 6 8 14 2 6 9 11 2 6 9 12 o2 : List i3 : tLexSeg(x_2*x_5*x_10*x_13,x_2*x_6*x_9*x_12,3) o3 = {x x x x , x x x x , x x x x , x x x x } 2 5 10 13 2 5 10 14 2 5 11 14 2 6 9 12 o3 : List