tNextMon -- give the t-lex successor of a given t-spread monomial

Synopsis

Usage:

tNextMon(u,t)
Inputs:
- u, a t-spread monomial of a polynomial ring
- t, a positive integer that idenfies the t-spread contest
Optional inputs:
- FixedMax => ..., default value false, optional boolean argument for tNextMon
Outputs:
- a ring element, the greatest t-spread monomial less than u, with respect to lexcografic order

Description

the function tNextMon(u,t) gives the t-lex successor of t, that is, the greatest t-spread monomial less than u with respect to $>_\mathrm{slex}.$
If FixedMax is true the function tNextMon(u,t,FixedMax=>true) gives the t-lex successor for which the maximum of the support is $\max\textrm{supp}(\texttt{u}).$
Given a $t$-spread monomial $u=x_{i_1}x_{i_2}\cdots x_{i_d}$, we define $\textrm{supp}(u)=\{i_1,i_2,\ldots, i_d\}$.

Examples:

i1 : S=QQ[x_1..x_16]

o1 = S

o1 : PolynomialRing

i2 : tNextMon(x_2*x_6*x_10*x_13,3)

o2 = x x x  x
      2 6 10 14

o2 : S

i3 : tNextMon(x_2*x_6*x_10*x_13,3,FixedMax=>true)

o3 = x x x  x
      2 7 10 13

o3 : S

Ways to use `tNextMon` :

"tNextMon(RingElement,ZZ)"

For the programmer

The object tNextMon is a method function with options.

tNextMon -- give the t-lex successor of a given t-spread monomial

Synopsis

Description

See also

Ways to use tNextMon :

For the programmer

Ways to use `tNextMon` :