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TSpreadIdeals > tShadow

tShadow -- give the t-spread shadow of a given t-spread monomial or a given list of t-spread monomials

Synopsis

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
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

See also

Ways to use tShadow :

For the programmer

The object tShadow is a method function.