Description
the function
tStronglyStableIdeal(I,t) gives the smallest
t-strongly stable ideal containing
I, that is, $B_t(G(I))$ where $G(I)$ is the minimal set of generators of $I$
We recall that if $u\in M_{n,d,t}\subset S=K[x_1,\ldots,x_n]$ then $B_t(u)$ is the smallest
t-strongly stable ideal of $S$ containing $u.$
Moreover, a subset $N\subset M_{n,d,t}$ is called a
t-strongly stable set if taking a
t-spread monomial $u\in N$, for all $j\in \mathrm{supp}(u)$ and all $i,\ 1\leq i\leq j$, such that $x_i(u/x_j)$ is a
t-spread monomial, then it follows that $x_i(u/x_j)\in N$.
A
t-spread monomial ideal
I is
t-strongly stable if $[I_j]_t$ is a
t-strongly stable set for all $j$, where $[I_j]_t$ is the
t-spread part of the $j$-th graded component of
I.
Examples:
i1 : S=QQ[x_1..x_9]
o1 = S
o1 : PolynomialRing
|
i2 : tStronglyStableIdeal(ideal {x_2*x_5*x_8},2)
o2 = ideal (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 4 6 1 3 8 1 4 7 2 4 6 1 4 8
------------------------------------------------------------------------
x x x , x x x , x x x , x x x , x x x , x x x )
1 5 7 2 4 7 1 5 8 2 4 8 2 5 7 2 5 8
o2 : Ideal of S
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i3 : tStronglyStableIdeal(ideal {x_2*x_5*x_8},3)
o3 = ideal (x x x , x x x , x x x , x x x )
1 4 7 1 4 8 1 5 8 2 5 8
o3 : Ideal of S
|