Function:
ResolutionOfFiniteGroup(Gens,n)
ResolutionOfFiniteGroup(Gens,n,true) |
Description:
This function constructs the first n terms of a smallish free ZG-resolution R of Z for a generic (but not too large) finite group G. A contracting homotopy for the resolution is also given. The input is a list Gens of generators for the group G and a positive integer n. The third argument "true" is optional and invokes Tietze reductions in the construction of the resolution. The output is a list [Dimension,Boundary,Homotopy,Elts] of three functions and a list.
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Mathematical
background:
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Comments:
This function is the basis of many computations in HAP and more work
needs to be done on trying to improve its performance. In particular: 1) The algorithm is very sensitive to the order in which consequences are found. This is determined by the sequence of integers ExtendedElts. It might be possible to find a better order for this sequence. 2) The Tietze simplification could certainly be improved. Documentation: For notes on the code see here. |