# tLexMon -- give the smallest initial t-lex segment containing a given monomial

## Synopsis

• Usage:
tLexMon(u,t)
• Inputs:
• 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 greater than u, with respect to lexcografic order

## Description

the function tLexMon(u,t) gives the initial t-lex segment defined by u, that is, the set of all the t-spread monomials greater than u, with respect to $>_\mathrm{slex}.$
This function calls the method tLexSeg(v,u,t), where v is the greatest t-spread monomial of the polynomial ring. Let $S=K[x_1,\ldots,x_n]$ and $u\in M_{n,d,t}$, then $v=x_1x_{1+t}\cdots x_{1+(d-1)t}$.

Examples:

 i1 : S=QQ[x_1..x_9] o1 = S o1 : PolynomialRing i2 : tLexMon(x_2*x_5*x_8,2) 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 , x x x , 1 3 5 1 3 6 1 3 7 1 3 8 1 3 9 1 4 6 1 4 7 1 4 8 1 4 9 ------------------------------------------------------------------------ x x x , x x x , x x x , x x x , x x x , x x x , x x x , x x x , x x x , 1 5 7 1 5 8 1 5 9 1 6 8 1 6 9 1 7 9 2 4 6 2 4 7 2 4 8 ------------------------------------------------------------------------ x x x , x x x , x x x } 2 4 9 2 5 7 2 5 8 o2 : List i3 : tLexMon(x_2*x_5*x_8,3) o3 = {x x x , x x x , x x x , x x x , x x x , x x x , x x x } 1 4 7 1 4 8 1 4 9 1 5 8 1 5 9 1 6 9 2 5 8 o3 : List