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# preImage -- Compute the preimage.

- Usage:
    `preImage(A,v)`
- Inputs:
  - A, a matrix, of full rank.
  - v, a vector, in target A.
- Outputs:
  - a vector, in source A.

## Description

Computes the preimage of v under A. If v is not in image A then returns false.

    i1 : A=matrix {{1, 0}, {0, 1}, {-1, -1}}

    o1 = | 1  0  |
         | 0  1  |
         | -1 -1 |

                  3       2
    o1 : Matrix ZZ  <-- ZZ

    i2 : b=vector {-2,2,0}

    o2 = | -2 |
         |  2 |
         |  0 |

           3
    o2 : ZZ

    i3 : v=preImage(A,b)

    o3 = | -2 |
         |  2 |

           2
    o3 : ZZ

    i4 : A*v

    o4 = | -2 |
         |  2 |
         |  0 |

           3
    o4 : ZZ

## Ways to use preImage:

- `preImage(Matrix,Vector)`

## For the programmer

The object preImage is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SRdeformations.m2:7564:0.