Description
the function
tSpreadIdeal(I,t) gives the ideal generated by all the
t-spread monomials which are among the generators of the ideal
I.
This function calls the method
tSpreadList(l,t) to sieve the
t-spread monomials from the list
l, of the generators of the ideal
I.
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 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 : I=ideal {x_3*x_7*x_10*x_14, x_1*x_5*x_9*x_13}
o2 = ideal (x x x x , x x x x )
3 7 10 14 1 5 9 13
o2 : Ideal of S
|
i3 : tSpreadIdeal(I,3)
o3 = ideal (x x x x , x x x x )
3 7 10 14 1 5 9 13
o3 : Ideal of S
|
i4 : tSpreadIdeal(I,4)
o4 = ideal(x x x x )
1 5 9 13
o4 : Ideal of S
|