firstOrderDeformation -- Makes a first order deformation.

Usage:

firstOrderDeformation(mg,v)

firstOrderDeformation(I,v)
Inputs:
- I, an ideal, monomial, reduced, in a PolynomialRing, or
- I, a monomial ideal, reduced
- mg, a matrix, row, with generators of a reduced monomial ideal.
Outputs:
- a first order deformation,

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 a method function.

The source of this document is in SRdeformations.m2:5029:0.

firstOrderDeformation -- Makes a first order deformation.

Description

See also

Ways to use firstOrderDeformation:

For the programmer