tLexSeg -- give the t-lex segment with given extremes

Synopsis

• Usage:

  tLexSeg(v,u,t)

• Inputs:
  • v, a t-spread monomial of a polynomial ring
  • u, a t-spread monomial of a polynomial ring
  • t, a positive integer that idenfies the t-spread contest
• Outputs:
  • a list, the set of all the t-spread monomials smaller than v and greater than u, with respect to lexcografic order

Description

Examples:

i1 : S=QQ[x_1..x_14]

o1 = S

o1 : PolynomialRing

i2 : tLexSeg(x_2*x_5*x_10*x_13,x_2*x_6*x_9*x_12,2)

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  ,
       2 5 10 13   2 5 10 14   2 5 11 13   2 5 11 14   2 5 12 14   2 6 8 10 
     ------------------------------------------------------------------------
     x x x x  , x x x x  , x x x x  , x x x x  , x x x x  , x x x x  }
      2 6 8 11   2 6 8 12   2 6 8 13   2 6 8 14   2 6 9 11   2 6 9 12

o2 : List

i3 : tLexSeg(x_2*x_5*x_10*x_13,x_2*x_6*x_9*x_12,3)

o3 = {x x x  x  , x x x  x  , x x x  x  , x x x x  }
       2 5 10 13   2 5 10 14   2 5 11 14   2 6 9 12

o3 : List

See also

• tNextMon -- give the t-lex successor of a given t-spread monomial
• tLexIdeal -- returns the t-spread lex ideal with a given ft-vector or with the same ft-vector of a given t-strongly stable ideal