next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

preImage -- Compute the preimage.

Synopsis

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)