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TSpreadIdeals > isTSpread

isTSpread -- whether a monomial, a list of monomials or a monomial ideal is t-spread

Synopsis

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 monomals.

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

Ways to use isTSpread :

For the programmer

The object isTSpread is a method function.