# tSpreadList -- give the set of all t-spread monomials of a given list

## Synopsis

• Usage:
• Inputs:
• l, a list of t-spread monomials 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 belonging to l

## Description

the function tSpreadList(l,t) gives the list of all the t-spread monomials l.
This function calls the method isTSpread(u,t) to check whether the monomial u is t-spread, for all the monomials that belong to the list l.
Let $u=x_{i_1}x_{i_2}\cdots x_{i_d}$ a monomial of $S=K[x_1,\ldots,x_n]$, with $1\le i_1\le i_2\le\dots\le i_d\le n$. The monomial u is called $t$-spread if $i_{j+1}-i_j\ge t$ for all $j\in [d-1]$.

Examples:

 i1 : S=QQ[x_1..x_14] o1 = S o1 : PolynomialRing i2 : l={x_3*x_7*x_10*x_14, x_1*x_5*x_9*x_13} o2 = {x x x x , x x x x } 3 7 10 14 1 5 9 13 o2 : List i3 : tSpreadList(l,4) o3 = {x x x x } 1 5 9 13 o3 : List i4 : tSpreadList(l,5) o4 = {} o4 : List