# isTSpread -- whether a monomial, a list of monomials or a monomial ideal is t-spread

## Synopsis

• Usage:
isTSpread(u,t), isTSpread(l,t) or isTSpread(I,t)
• Inputs:
• u, a monomial of a polynomial ring
• l, a list of monomials of a polynomial ring
• I, a monomial ideal of a polynomial ring
• t, a positive integer that idenfies the t-spread contest
• Outputs:
• , whether a given monomial u, a list of monomials l or a monomial ideal I is t-spread

## Description

the function isTSpread(-,t) has three overloading changing for the first parameter. It checks whether a given monomial u, a list of monomials l or a monomial ideal I is t-spread.
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 $j\in [d-1].$
A list of monomials is t-spread if all the monomials of the list are t-spread. A monomial ideal is called t-spread if it is generated by t-spread monomals.

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 : isTSpread(l#0,3) o3 = true i4 : isTSpread(l,3) o4 = true i5 : isTSpread(ideal l,3) o5 = true i6 : isTSpread(ideal l,4) o6 = false