## Synopsis

• Usage:
tShadow(u,t)
• Inputs:
• u, a t-spread monomial of a polynomial ring
• l, a list of t-spread monomials of a polynomial ring
• t, a positive integer that idenfies the t-spread contest
• Outputs:
• a list, the list of all the t-spread monomial of the shadow of the t-spread monomial u or of the list l

## Description

Let $S=K[x_1,\ldots,x_n]$ and $u\in M_{n,d,t}$, that is, u is a $t$-spread monomial of degree $d$. The t-spread shadow of u, is defined as $\mathrm{Shad}_t(u)=\{ux_i\ :\ i\in [n]\}\cap M_{n,d+1,t}$. The algorithm is optimized for the $t$-spread environment.

Examples:

 i1 : S=QQ[x_1..x_14] o1 = S o1 : PolynomialRing i2 : u=x_2*x_6*x_10 o2 = x x x 2 6 10 o2 : S i3 : tShadow(u,3) o3 = {x x x x , x x x x } 2 6 10 13 2 6 10 14 o3 : List i4 : tShadow(u,4) o4 = {x x x x } 2 6 10 14 o4 : List i5 : l={x_3*x_6*x_10, x_1*x_5*x_9} o5 = {x x x , x x x } 3 6 10 1 5 9 o5 : List i6 : tShadow(l,3) o6 = {x x x x , x x x x , x x x x , x x x x , x x x x } 1 5 9 12 1 5 9 13 1 5 9 14 3 6 10 13 3 6 10 14 o6 : List i7 : tShadow(l,4) o7 = {x x x x , x x x x } 1 5 9 13 1 5 9 14 o7 : List

• isTSpread -- whether a monomial, a list of monomials or a monomial ideal is t-spread