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# source(FirstOrderDeformation) -- The source of a deformation.

- Function: source
- Usage:
    `source(f)`
- Inputs:
  - f, a first order deformation,
- Outputs:
  - a module,

## Description

Returns the source of the homomorphisms represented by f.

    i1 : R=QQ[x_0..x_4]

    o1 = R

    o1 : PolynomialRing

    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,-1,0,2,0})

           2
          x
           3
    o5 = ----
         x x
          0 1

    o5 : first order deformation space of dimension 1

    i6 : source f

    o6 = image | x_3x_4 x_0x_4 x_2x_3 x_1x_2 x_0x_1 |

                                 1
    o6 : R-module, submodule of R

## See also

- FirstOrderDeformation -- The class of all first order deformations of monomial ideals.
- firstOrderDeformation -- Makes a first order deformation.
- addCokerGrading -- Stores a cokernel grading in a polynomial ring.

## Ways to use this method:

- source(FirstOrderDeformation) -- The source of a deformation.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SRdeformations.m2:4426:0.