tLastMon -- give the last t-spread monomial of the Borel shadow a given t-spread monomial

Synopsis

Usage:

tLastMon(u,gap,t)
Inputs:
- u, a t-spread monomial of a polynomial ring
- gap, a positive integer representing the difference between the degrees
- t, a positive integer that idenfies the t-spread contest
Optional inputs:
- MaxInd => ..., default value -1, optional integer argument for tLastMon
Outputs:
- a ring element, the smallest t-spread monomial of the Borel shadow of u, with respect to lexcografic order

Description

the function tLastMon(u,gap,t) gives the smallest t-spread monomials of the Borel shadow iterated gaptimes of u, that is, the smallest monomial of $B_\texttt{t}\{\texttt{u}\}$, with respect to $>_\mathrm{slex}.$
If MaxInd is greater than -1 the function tLastMon(u,gap,t,MaxInd=>m) gives the smallest t-spread monomial for which the maximum of the support is m
The Borel shadow of a t-spread monomial u, is defined as the shadow of the strongly stable set generated by u. To work in a t-spread contest, the Borel shadow of u is the t-shadow of $B_\texttt{t}\{u\}$.

Examples:

i1 : S=QQ[x_1..x_16]

o1 = S

o1 : PolynomialRing

i2 : tLastMon(x_2*x_6*x_10*x_13,1,3)

o2 = x x x  x  x
      2 6 10 13 16

o2 : S

i3 : tLastMon(x_2*x_6*x_10*x_13,1,3,MaxInd=>14)

o3 = x x x x  x
      2 5 8 11 14

o3 : S

Ways to use tLastMon :

tLastMon(RingElement,ZZ,ZZ)

For the programmer

The object tLastMon is a method function with options.

tLastMon -- give the last t-spread monomial of the Borel shadow a given t-spread monomial

Synopsis

Description

See also

Ways to use tLastMon :

For the programmer