Resolutions
2009-01-19
1
Experimental
group1
list1
This CD defines resolutions for groups
zggnrt
This symbol represents an element (g_i,z_j) of a free Z[G]-module. It is a function with two
arguments; the first one is an integer i representing the i-th element of the group G; the
second component is an integer j representing the jth-generator of the free Z[G]-module.
Element (g_1,z_3)
1
3
zgterm
This symbol represents a pair coefficient*zggnrt in a free Z[G]-module. It is a function with two
arguments: an integer representing the coefficient and a zggnrt.
Term -4 * (g_1,z_3)
-4
1
3
zgcombination
This symbol represents a combination in a free Z[G]-module, that is to say, a sum of zgterms
c_1 * (g_i_1,z_i_1) + ... + c_n * (g_i_n,z_i_n). The arguments of these functions are a
list of zgterms.
Combination 3 * (g_2,z_6) - 8 * (g_4,z_1)
3
2
6
-8
4
1
resolution
A resolution will be given by 5 elements: group, highest degree, list of ranks of each
Z[G]-module, boundary map and contracting homotopy. The group is represented using symbols
already defined in OpenMath. The highest degree is an integer, and the next element of the
resolution is the list of ranks of each Z[G]-module, that is, a list of integers, one for each
degree from 0 to the highest one. The description of the ZG-boundary and the contracting homotopy
are represented as lists containing the images of the generators of each Z[G]-module, which are
ZGcombinations.
Resolution of length 10 of the cyclic group C_2