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

Description

the function tLexSeg(v,u,t) gives the t-lex segment defined by v and u, that is, the set of all the t-spread monomials smaller than v and greater than u, with respect to $>_\mathrm{slex}.$
This function iteratively uses the method tNextMon(u,t) until the returned monomial is u.

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

Ways to use tLexSeg:

  • tLexSeg(RingElement,RingElement,ZZ)

For the programmer

The object tLexSeg is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/TSpreadIdeals.m2:786:0.