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Macaulay2Doc :: resolution(Matrix)

resolution(Matrix) -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target

Synopsis

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
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