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tVeroneseSet -- give the Veronese set of t-spread monomials of a given degree

Synopsis

Description

the function tVeroneseSet(S,d,t) gives the Veronese set of t-spread monomials of degree d, that is, the set of all the t-spread monomials of S of degree dThis function calls the method tLexSeg(v,u,t), where v is the greatest t-spread monomial of the polynomial ring and u the smallest one. If $S=K[x_1,\ldots,x_n]$ then $v=x_1x_{1+t}\cdots x_{1+(d-1)t}$ and $u=x_{n-(d-1)t}\cdots x_{n-t} x_{n}$. This set is also denoted by $M_{n,d,t}$.

Examples:

i1 : S=QQ[x_1..x_8]

o1 = S

o1 : PolynomialRing
 
i2 : tVeroneseSet(S,3,2)

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

o2 : List
 
i3 : tVeroneseSet(S,3,3)

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 tVeroneseSet :

For the programmer

The object tVeroneseSet is a method function.