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ChainComplexExtras :: chainComplexMap

chainComplexMap -- Defines a ChainComplexMap via a list of matrices.

Synopsis

Description

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 : mapList = apply((min kRes..max kRes), i -> multBya_i)

o4 = (| a |, {1} | a b c |, 0, 0, 0)
             {1} | 0 0 0 |
             {1} | 0 0 0 |

o4 : Sequence
i5 : multBya2 = chainComplexMap(kRes,kRes,toList mapList)

          1             1
o5 = 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

o5 : ChainComplexMap
i6 : multBya2 == multBya

o6 = true

Ways to use chainComplexMap :

For the programmer

The object chainComplexMap is a method function with options.