Description
the function
isTSpread(-,t) has three overloading changing for the first parameter. It checks whether a given monomial
u, a list of monomials
l or a monomial ideal
I is
t-spread.
Let $u=x_{i_1}x_{i_2}\cdots x_{i_d}$ a monomial of $S=K[x_1,\ldots,x_n]$, with $1\le i_1\le i_2\le\dots\le i_d\le n$. The monomial
u is called $t$-spread if $i_{j+1}-i_j\ge t$ for all $j\in [d-1].$
A list of monomials is
t-spread if all the monomials of the list are
t-spread. A monomial ideal is called
t-spread if it is generated by
t-spread monomials.
Examples:
i1 : S=QQ[x_1..x_14]
o1 = S
o1 : PolynomialRing
|
i2 : l={x_3*x_7*x_10*x_14, x_1*x_5*x_9*x_13}
o2 = {x x x x , x x x x }
3 7 10 14 1 5 9 13
o2 : List
|
i3 : isTSpread(l#0,3)
o3 = true
|
i4 : isTSpread(l,3)
o4 = true
|
i5 : isTSpread(ideal l,3)
o5 = true
|
i6 : isTSpread(ideal l,4)
o6 = false
|