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
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i2 : isTLexIdeal(ideal {x_1*x_3,x_1*x_5},2)
o2 = false
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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
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