# tSpreadIdeal -- give the ideal generated by the t-spread monomials which are among the generators of a given ideal

## Synopsis

• Usage:
• Inputs:
• I, a graded ideal of a polynomial ring
• t, a positive integer that idenfies the t-spread contest
• Outputs:
• an ideal, the ideal generated by all the t-spread monomials belonging to the generator set of the ideal I

## 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 monomals.

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