# firstOrderDeformation -- Makes a first order deformation.

## Synopsis

• Usage:
firstOrderDeformation(mg,v)
firstOrderDeformation(I,v)
• Inputs:
• I, an ideal, monomial, reduced, in a PolynomialRing, or
• I, , reduced
• mg, , row, with generators of a reduced monomial ideal.
• Outputs:

## Description

Generates a first order deformation ideal mg. If it is given an ideal I then generators of I are stored to have a reference for parameters. You can also give non-minimal generators.

 i1 : R=QQ[x_0..x_4]; i2 : addCokerGrading(R) o2 = | -1 -1 -1 -1 | | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | 5 4 o2 : Matrix ZZ <--- ZZ i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0) o3 = ideal (x x , x x , x x , x x , x x ) 0 1 1 2 2 3 3 4 0 4 o3 : Ideal of R i4 : mg=mingens I; 1 5 o4 : Matrix R <--- R i5 : f=firstOrderDeformation(mg, vector {-1,1,0,0,0}) x 1 o5 = -- x 0 o5 : first order deformation space of dimension 1

## Ways to use firstOrderDeformation :

• "firstOrderDeformation(Ideal,Vector)"
• "firstOrderDeformation(Matrix,Vector)"
• "firstOrderDeformation(MonomialIdeal,Vector)"

## For the programmer

The object firstOrderDeformation is .