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Macaulay2Doc :: dd

dd -- differential in a chain complex

Description

dd -- a symbol used as a key in a chain complex, under which are stored the differentials.

The differentials are stored as the members in a chain complex map of degree -1. The map C.dd_i is the one whose source is the module C_i, and it is arranged to be zero if no map has been stored in that spot.

i1 : R = ZZ/101[a,b];
i2 : C = resolution cokernel vars R

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

o2 : ChainComplex
i3 : C.dd

          1               2
o3 = 0 : R  <----------- R  : 1
               | a b |

          2                  1
     1 : R  <-------------- R  : 2
               {1} | -b |
               {1} | a  |

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

o3 : ChainComplexMap
i4 : C.dd_2

o4 = {1} | -b |
     {1} | a  |

             2       1
o4 : Matrix R  <--- R

See also

For the programmer

The object dd is a symbol.