Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

Am 13.11.2016 um 19:24 schrieb Martin Baker: > > For homotopy and homology the current GroupPresentation domain gives me a > relatively simple way to do the things I need. I'm not sure if the extra > complexity of the FreeGroup domain would be justified? It seems to me that > these > subjects

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

Kurt and Bill, Thanks for your ideas so far. I had an idea to try to combine what you said with what I am trying to do. It seems to me that there is a very approximate design pattern here since each of these algebraic structures seem to be defined by two domains by pseudo code like this:

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

To avoid confusion let's make an example: L:=[u,v,w] FG2:=FreeGroup OVAR L fg2:=[coerce(s)$FG2 for s in enumerate()$OVAR(L)] LL:=[retract(s)$FG2 for s in fg2] FG2 has Group --> true So FG2 is a free group and we can build terms (1) -> fg2.1 * fg2.2 * inv(fg2.1) - 1 (1) u v u

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

On 12 November 2016 at 13:06, Martin Baker wrote: > On 12/11/16 17:37, Bill Page wrote: >> >> I think I know what you mean however in FriCAS % always represents a >> domain - not an element of a domain. In the category 'Group' % >> represents a domain whose operations satisfy

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

On 12/11/16 17:37, Bill Page wrote: I think I know what you mean however in FriCAS % always represents a domain - not an element of a domain. In the category 'Group' % represents a domain whose operations satisfy group axioms. Perhaps it is unexpected that so few domains in FriCAS satisfy Group

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

On 12 November 2016 at 06:23, Martin Baker wrote: > ... > 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 % >

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

Hello Martin > 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. Indeed. Since

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

On 10/11/16 16:46, Kurt Pagani wrote: On 10 November 2016 at 10:37, Martin Baker > 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.

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

On 10/11/16 16:46, Kurt Pagani wrote: I'm definitely encouraging you to implement T-C. Thats my plan. > Then we will rely on (permgrps.spad): Well it will have to be like this: toPermutationIfCan(GroupPresentation):Union(PermutationGroup S, "failed") because it needs to fail for infinite

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

On 10 November 2016 at 10:37, Martin Baker 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

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

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

Re: [fricas-devel] [PATCH] More simplifications in GroupPresentation

Hello Martin 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

[fricas-devel] [PATCH] More simplifications in GroupPresentation

This patch contains the following changes to GroupPresentation: 1) Improve simplify function to remove duplicate relations. 2) Rename subgroup to quotient. In simplify, relations are now considered duplicates if they are identical or if they are the same after being cycled or if they are the