On 10/11/16 16:46, Kurt Pagani wrote:
On 10 November 2016 at 10:37, Martin Baker <ax87...@martinb.com
<mailto:ax87...@martinb.com>> wrote:
Hi Kurt,
> Your "GroupPresentation" actually isn't a group, so I wonder whether it
wouldn't
> be favourable to implement a domain, e.g. "FinitelyPresentedGroup" which
could
> be reused elsewhere. If you take on the burden to augment some group
theory to
> Fricas anyway, you might consider doing it along the lines of GAP:
> http://www.gap-system.org/Manuals/doc/ref/chap47.html
<http://www.gap-system.org/Manuals/doc/ref/chap47.html>
>
> (1) -> GroupPresentation has Group
>
> (1) false
Well in Fricas terms PermutationGroup isnt a group either:
(1) -> PermutationGroup(Integer) has Group
(1) false
Type: Boolean
I'm surprised, indeed :(
I had a look in permgrps.spad where we find the explanation:
<https://github.com/hemmecke/fricas/blob/master-hemmecke/src/algebra//permgrps.spad#L1>
--
PermutationGroup implements permutation groups acting on a set S, i.e.
all subgroups of the symmetric group of S, represented as a list of
permutations (generators). Note that therefore the objects are not
members of the Language category /Group/
<http://fricas.github.io/api/Group.html#l-group>. Using the idea of base
and strong generators by Sims, basic routines and algorithms are
implemented so that the word problem for permutation groups can be solved.
Hi Kurt,
In simpler terms: PermutationGroup and GroupPresentation are never going
to implement the category 'Group' because in PermutationGroup and
GroupPresentation % represents the whole group whereas in Group %
represents an element of the group.
However, we could implement category 'Group' by having a domain called
'Word' (over Symbols or Permutations) where the multiplication operation
is the concatenation of words with simplification given by the relations.
It seems to me that such a proposed domain would help simplify existing
and proposed code as follows:
1) Tidy up some of the local functions in PermutationGroup which work
with words in an ad hoc and messy way.
2) Would simplify my conversion from PermutationGroup to
GroupPresentation which uses words.
3) Be a basis for examples such as LyndonWord
Martin B
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