dd -- differential in a chain complex

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:

ChainComplex -- the class of all chain complexes