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TSpreadIdeals > tStronglyStableMon

tStronglyStableMon -- give the t-strongly stable set generated by a given monomial

Synopsis

Description

the function tStronglyStableMon(u,t) gives the list of all the monomials belonging to the t-strongly stable set generated by u, that is, $B_t\{u\}.$
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_9]

o1 = S

o1 : PolynomialRing
 
i2 : tStronglyStableMon(x_2*x_5*x_8,2)

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 , x x x ,
       1 3 5   1 3 6   1 3 7   1 3 8   1 4 6   1 4 7   1 4 8   1 5 7   1 5 8 
     ------------------------------------------------------------------------
     x x x , x x x , x x x , x x x , x x x }
      2 4 6   2 4 7   2 4 8   2 5 7   2 5 8

o2 : List
 
i3 : tStronglyStableMon(x_2*x_5*x_8,3)

o3 = {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 : List

See also

Ways to use tStronglyStableMon :

For the programmer

The object tStronglyStableMon is a method function.