# tVeroneseIdeal -- give the Veronese ideal of t-spread monomials of a given degree

## Synopsis

• Usage:
tVeroneseIdeal(S,d,t)
• Inputs:
• S, a polynomial ring
• d, a nonnegative integer that identifies the degree of the monomials
• t, a positive integer that idenfies the t-spread contest
• Outputs:
• an ideal, the ideal generated by all the t-spread monomials of S of degree d

## Description

the function tVeroneseIdeal(S,d,t) returns the Veronese ideal of t-spread monomials of degree d, that is, the ideal generated by all the t-spread monomials of S of degree dThis function calls the method tVeroneseSet(S,d,t).

Examples:

 i1 : S=QQ[x_1..x_8] o1 = S o1 : PolynomialRing i2 : tVeroneseIdeal(S,3,2) o2 = ideal (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 ------------------------------------------------------------------------ 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 5 8 1 6 8 2 4 6 2 4 7 2 4 8 2 5 7 2 5 8 2 6 8 3 5 7 ------------------------------------------------------------------------ x x x , x x x , x x x ) 3 5 8 3 6 8 4 6 8 o2 : Ideal of S i3 : tVeroneseIdeal(S,3,4) o3 = ideal 0 o3 : Ideal of S

## See also

• tNextMon -- give the t-lex successor of a given t-spread monomial
• tLexSeg -- give the t-lex segment with given extremes
• isTLexSeg -- whether a set of t-spread monomials is a t-lex segment
• tLexMon -- give the smallest initial t-lex segment containing a given monomial
• tVeroneseSet -- give the Veronese set of t-spread monomials of a given degree

## Ways to use tVeroneseIdeal :

• tVeroneseIdeal(Ring,ZZ,ZZ)

## For the programmer

The object tVeroneseIdeal is .