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TSpreadIdeals > tSpreadIdeal

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

Synopsis

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

See also

Ways to use tSpreadIdeal :

For the programmer

The object tSpreadIdeal is a method function.