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TateOnProducts :: isQuism

isQuism -- Test to see if the ChainComplexMap is a quasiisomorphism.

Synopsis

Description

A quasiisomorphism is a chain map that is an isomorphism in homology.Mapping cones currently do not work properly for complexes concentratedin one degree, so isQuism could return bad information in that case.
i1 : R = ZZ/101[a,b,c]

o1 = R

o1 : PolynomialRing
i2 : kRes = res coker vars R

      1      3      3      1
o2 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o2 : ChainComplex
i3 : multBya = extend(kRes,kRes,matrix{{a}})

          1             1
o3 = 0 : R  <--------- R  : 0
               | a |

          3                     3
     1 : R  <----------------- R  : 1
               {1} | a b c |
               {1} | 0 0 0 |
               {1} | 0 0 0 |

          3         3
     2 : R  <----- R  : 2
               0

          1         1
     3 : R  <----- R  : 3
               0

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

o3 : ChainComplexMap
i4 : isQuism(multBya)

o4 = false
i5 : F = extend(kRes,kRes,matrix{{1_R}})

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

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

          3                     3
     2 : R  <----------------- R  : 2
               {2} | 1 0 0 |
               {2} | 0 1 0 |
               {2} | 0 0 1 |

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

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

o5 : ChainComplexMap
i6 : isQuism(F)

o6 = true

Ways to use isQuism :

For the programmer

The object isQuism is a method function.