Description
the function
tShadow(u,t) gives the
t-spread shadow of
u, that is, the set of all the
t-spread monomials of the shadow of
u. The overloading function
tShadow(l,t) gives the
t-spread shadow of
l, that is, the set of all the
t-spread monomials of the shadow of each
t-spread monomial belonging to
l.
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
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i2 : u=x_2*x_6*x_10
o2 = x x x
2 6 10
o2 : S
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i3 : tShadow(u,3)
o3 = {x x x x , x x x x }
2 6 10 13 2 6 10 14
o3 : List
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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
|