The HapLargeGroupResolutionRep Representation

The large group representation has one additional component called groupring. Elements of the modules in a resolution are represented by lists of group ring elements. The length of the list corresponds to the dimension of the free module.

All methods for the generic representation do also work for the large group representation. Some of them are wrappers for special methods which do only work for this representation. The following list only contains the methods which are not already present in the generic representation.

Note that the input or the output of these functions does not comply with the standard representation.

group ring
This returns the group ring of resolution. Note that by the way that group rings are handled in &GAP;, this is not equal to GroupRing(R,GroupOfResolution(resolution)) where R is the ring of the resolution.
group element
Returns the product of x and y. The NC version does not check whether x and y are actually elements of the group of resolution.
boolean
Returns true if letter has the form of a letter (a module element with exactly one non-zero entry which has exactly one non-zero coefficient) a module of resolution in the HapLargeGroupResolution representation. Note that it is not tested if letter actually is a letter in any term of resolution
boolean
Returns true if word has the form of a word of a module of resolution in the HapLargeGroupResolution representation. Note that it is not tested if word actually is a word in any term of resolution.
boolean
Returns true if and only if letter is a letter (a word of length 1) of the termth module of resolution in the hapLargeGroupResolution representation. I.e. it tests if letter is a module element with exactly one non-zero entry which has exactly one non-zero coefficient.
boolean
Tests if word is an element of the termth module of resoultion.
free ZG letter in large group representation
Multiplies the letter letter with the group element g and returns the result. The NC version does not check whether g is an element of the group of resolution and letter can be a letter.
free ZG word in large group representation
Multiplies the word word with the group element g and returns the result. The NC version does not check whether g is an element of the group of resolution and word can be a word.
list of letters/words in large group representation
Returns a set of generators for the termth module of resolution. The returned value is a list of vectors of group ring elements.
free ZG word in the large group representation
Returns the boundary of the nth generator of the termth module of resolution as a word in the n-1st module (in large group representation). The NC version does not check whether there is a termth module and if it has at least n generators.
free ZG word in large group representation
Calculates the boundary of the letter letter of the termth module of resolution in large group representation. The NC version does not check whether letter actually is a letter in the termth module.
free ZG word in large group representation
Calculates the boundary of the element word of the termth module of resolution in large group representation. The NC version does not check whether word actually is a word in the termth module.