SetOrderingRWS(rws, ordering [,list])
ReorderGeneratorsRWS(rws, p)
SetOrderingRWS changes the ordering on the words of the rewriting
system rws to ordering, which must be one of the strings
``shortlex", ``recursive", ``wtlex" and ``wreathprod". The
default is ``shortlex", and this is the ordering of rewriting systems
returned by FpGroupToRWS. The orderings ``wtlex" and
``wreathprod" require the third parameter, list, which must be a
list of non-negative integers in one-one correspondence with the
generators of rws, in the order that they are displayed in the
generatorOrder field. They have the effect of attaching weights or
levels to the generators, in the cases ``wtlex" and ``wreathprod",
respectively.
Each of these orderings depends on the order of the generators, The
current ordering of generators is displayed under the generatorOrder
field when rws is printed. This ordering can be changed by the
function ReorderGeneratorsRWS. The second parameter p to this
function should be a permutation that moves at most ng points, where
ng is the number of generators. This permutation is applied to the
current list of generators.
In the ``shortlex" ordering, shorter words come before longer ones,
and, for words of equal length, the lexicographically smaller word
comes first, using the ordering of generators specified by the
generatorOrder field. The ``wtlex" ordering is similar, but
instead of using the length of the word as the first criterion, the
total weight of the word is used; this is defined as the sum of the
weights of the generators in the word. So ``shortlex" is the
special case of ``wtlex" in which all generators have the same
nonzero weight.
The ``recursive" ordering is the special case of ``wreathprod"
in which the levels of the ng generators are 1, 2, ldots, ng, in
the order defined by the generatorOrder field. We shall not attempt
to give a complete definition of these orderings here, but refer the
reader instead to pages 46--50 of Sims94. The ``recursive"
ordering is the one appropriate for a power-conjugate presentation of
a polycyclic group, but where the generators are ordered in the
reverse order from the usual convention for polycyclic groups. The
confluent presentation will then be the same as the power-conjugate
presentation. For example, for the Heisenberg group < x,y,z
hspace{1mm} | hspace{1mm} [x,z]=[y,z]=1, [y,x]=z > , a
good ordering is ``recursive" with the order of generators
[z^{-1},z,y^{-1},y,x^{-1},x]. This example is included in
Examples below.
GAP 3.4.4