Description
the function
tStronglyStableSeg(v,u,t) gives the set of
t-spread monomials belonging to the strongly stable set generated by
u and smaller than
v, that is, $B_t[v,u]=\{w\in B_t\{u\}\ :\ v\geq_\mathrm{slex} w\}.$
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 set of monomials of $M_{n,d,t}$ 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 $x_i(u/x_j)\in N$.
Examples:
i1 : S=QQ[x_1..x_14]
o1 = S
o1 : PolynomialRing
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i2 : tStronglyStableSeg(x_2*x_5*x_9*x_12,x_2*x_6*x_10*x_13,2)
o2 = {x x x x , x x x x , x x x x , x x x x , x x x x , x x x x ,
2 5 9 12 2 5 9 13 2 5 10 12 2 5 10 13 2 6 8 10 2 6 8 11
------------------------------------------------------------------------
x x x x , x x x x , x x x x , x x x x , x x x x , x x x x ,
2 6 8 12 2 6 8 13 2 6 9 11 2 6 9 12 2 6 9 13 2 6 10 12
------------------------------------------------------------------------
x x x x }
2 6 10 13
o2 : List
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i3 : tStronglyStableSeg(x_2*x_5*x_9*x_12,x_2*x_6*x_10*x_13,3)
o3 = {x x x x , x x x x , x x x x , x x x x , x x x x , x x x x }
2 5 9 12 2 5 9 13 2 5 10 13 2 6 9 12 2 6 9 13 2 6 10 13
o3 : List
|