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# resolution(Matrix) -- compute the comparison map between resolutions of the source and target of a module map represented by a matrix

- Function: resolution
- Usage:
    `resolution f`
- Inputs:
  - f, a matrix, a module homomorphism N <--- M
- Optional inputs:
  - DegreeLimit => ..., default value null, compute only up to this degree
  - FastNonminimal => ..., default value false, compute a non-minimal graded free resolution
  - HardDegreeLimit => ..., default value {},
  - LengthLimit => ..., default value infinity, stop when the resolution reaches this length
  - PairLimit => ..., default value infinity, stop when this number of pairs has been handled
  - ParallelizeByDegree (missing documentation) => ..., default value false,
  - SortStrategy => ..., default value 0,
  - StopBeforeComputation => ..., default value false, whether to stop the computation immediately
  - Strategy => ..., default value null,
  - SyzygyLimit => ..., default value infinity, stop when this number of syzygies is reached
- Outputs:
  - a chain complex map, a chain map from a projective resolution of the source of f to a resolution of the target of f

## Description

    i1 : R = ZZ[x,y,z]

    o1 = R

    o1 : PolynomialRing

    i2 : N = R^1/(x,y,z)

    o2 = cokernel | x y z |

                                1
    o2 : R-module, quotient of R

    i3 : M = R^1/(x^2,y^2,x*y*z,z^2)

    o3 = cokernel | x2 y2 xyz z2 |

                                1
    o3 : R-module, quotient of R

    i4 : f = map(N,M,1)

    o4 = | 1 |

    o4 : Matrix N <-- M

    i5 : res f

              1             1
    o5 = 0 : R  <--------- R  : 0
                   | 1 |

              3                        4
         1 : R  <-------------------- R  : 1
                   {1} | x 0 yz 0 |
                   {1} | 0 y 0  0 |
                   {1} | 0 0 0  z |

              3                                6
         2 : R  <---------------------------- R  : 2
                   {2} | xy yz 0 0  0  0  |
                   {2} | 0  0  0 yz 0  0  |
                   {2} | 0  0  0 0  yz xz |

              1                      3
         3 : R  <------------------ R  : 3
                   {3} | 0 yz 0 |

         4 : 0 <----- 0 : 4
                  0

    o5 : ChainComplexMap

## See also

- free resolutions of modules

## Ways to use this method:

- resolution(Matrix) -- compute the comparison map between resolutions of the source and target of a module map represented by a matrix

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldChainComplexes/docs/doc10.m2:234:0.