For a general description of homomorphisms, we refer to chapter MAPPINGS. This section describes some special aspects of homomorphisms whose domain or codomain is a rewrite group.
Groups in the category GrpRWS currently are accepted as codomains only in some special situations. The most important cases in which a rewrite group can be used as a codomain are group homomorphisms whose domain is in one of the categories FINITELY PRESENTED GROUPS, GrpGPC, GrpRWS or GrpAtc.
Returns the homomorphism from the rewrite group R to the group G defined by the expression S which can be the one of the following:It is the user's responsibility to ensure that the provided generator images actually give rise to a well-defined homomorphism. No checking is performed by the constructor.
- (i)
- A list, sequence or indexed set containing the images of the n generators R.1, ..., R.n of R. Here, the i-th element of S is interpreted as the image of R.i, i.e. the order of the elements in S is important.
- (ii)
- A list, sequence, enumerated set or indexed set, containing n tuples <xi, yi> or arrow pairs xi -> yi, where xi is a generator of R and yi∈G (i=1, ..., n) and the set {x1, ..., xn} is the full set of generators of R. In this case, yi is assigned as the image of xi, hence the order of the elements in S is not important.
Note that it is currently not possible to define a homomorphism by assigning images to the elements of an arbitrary generating set of R.