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# possibleDenominators -- Possible denominators of deformations.

- Usage:
    `possibleDenominators(I)`
    `possibleDenominators(I,v)`
- Inputs:
  - I, an ideal, monomial, reduced.
  - v, a list, of variables of ring I.
- Outputs:
  - L, a list,

## Description

Computes a list L of possible denominators of Laurent monomials representing FirstOrderDeformations of I. The list L is stratified into lists with ascending degree of the denominators. Each denominator is represented as a list of variables.

If the second argument v is given, one obtains only denominators contained (as a list) in v.

    i1 : R=QQ[x_0..x_4];

    i2 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0);

    o2 : Ideal of R

    i3 : possibleDenominators(I)

    o3 = {{{x }, {x }, {x }, {x }, {x }}, {{x , x }, {x , x }, {x , x }, {x ,
             0     1     2     3     4       0   1     1   2     2   3     0
         ------------------------------------------------------------------------
         x }, {x , x }}}
          4     3   4

    o3 : List

    i4 : possibleDenominators(I,{x_0,x_1,x_2});

## See also

- deformationsFace -- Compute the deformations associated to a face.
- deform -- Compute the deformations associated to a Stanley-Reisner complex.

## Ways to use possibleDenominators:

- `possibleDenominators(Ideal)`
- `possibleDenominators(Ideal,List)`
- `possibleDenominators(List,List)`

## For the programmer

The object possibleDenominators is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SRdeformations.m2:7536:0.