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tLexMon -- give the smallest initial t-lex segment containing a given monomial

Description

the function tLexMon(u,t) gives the initial t-lex segment defined by u, that is, the set of all the t-spread monomials greater than u, with respect to $>_\mathrm{slex}.$
This function calls the method tLexSeg(v,u,t), where v is the greatest t-spread monomial of the polynomial ring. Let $S=K[x_1,\ldots,x_n]$ and $u\in M_{n,d,t}$, then $v=x_1x_{1+t}\cdots x_{1+(d-1)t}$.

Examples:

i1 : S=QQ[x_1..x_9]

o1 = S

o1 : PolynomialRing
 
i2 : tLexMon(x_2*x_5*x_8,2)

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 3 9   1 4 6   1 4 7   1 4 8   1 4 9 
     ------------------------------------------------------------------------
     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 7   1 5 8   1 5 9   1 6 8   1 6 9   1 7 9   2 4 6   2 4 7   2 4 8 
     ------------------------------------------------------------------------
     x x x , x x x , x x x }
      2 4 9   2 5 7   2 5 8

o2 : List
 
i3 : tLexMon(x_2*x_5*x_8,3)

o3 = {x x x , x x x , x x x , x x x , x x x , x x x , x x x }
       1 4 7   1 4 8   1 4 9   1 5 8   1 5 9   1 6 9   2 5 8

o3 : List

See also

Ways to use tLexMon:

  • tLexMon(RingElement,ZZ)

For the programmer

The object tLexMon is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/TSpreadIdeals.m2:822:0.