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
|