## Synopsis

• Usage:
isTLexIdeal(I,t)
• Inputs:
• I, a t-spread ideal of a polynomial ring
• t, a positive integer that idenfies the t-spread contest
• Outputs:
• , whether the ideal I is t-spread lex

## Description

Let $\texttt{S}=K[x_1,\ldots,x_n]$, $\texttt{t}\geq 1$ and a t-spread ideal I. Then I is called a t-lex ideal, if $[I_j]_t$ is a t-spread lex set for all $j$.
We recall that $[I_j]_t$ is the t-spread part of the $j$-th graded component of I. Moreover, a subset $L\subset M_{n,d,t}$ is called a t-lex set if for all $u\in L$ and for all $v\in M_{n,d,t}$ with $v>_\mathrm{slex} u$, it follows that $u\in L$.

Examples:

 i1 : S=QQ[x_1..x_6] o1 = S o1 : PolynomialRing i2 : isTLexIdeal(ideal {x_1*x_3,x_1*x_5},2) o2 = false i3 : isTLexIdeal(ideal {x_1*x_3,x_1*x_4,x_1*x_5,x_1*x_6,x_2*x_4,x_2*x_5},2) o3 = true