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

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