Re: [sage-support] Morphisms between free groups.
Now it seems "subs" does work. I must have done something wrong. Sorry for
the noise.
On Friday, February 4, 2022 at 3:55:19 PM UTC+1 dim...@gmail.com wrote:
>
>
> On Fri, 4 Feb 2022, 11:02 David Joyner, wrote:
>
>> On Fri, Feb 4, 2022 at 4:40 AM 'Michel VAN DEN BERGH' via sage-support
>> wrote:
>> >
>> > Dear all,
>> >
>> > I need to do something which I thought would be quite simple. I have
>> free groups
>> > F, G with generators x1,x2,x3,x4 and x,y respectively and I need to
>> compute the image of an element under the homomorphism F-->G:x1->x, x2->y,
>> x3->x, x4->y.
>> >
>> > I could not find anything in the manual about morphisms between free
>> groups. I tried subs, but that does not work since the parents of the
>> elements of F and G are (of course) different.
>> >
>> > The workaround I used is to work in the free group H with generators
>> x1,x2,x3,x4,x,y and to use subs. However this is also inconvenient since I
>> need the action of the braid group with 4 strands on F. It does not act on
>> H because of the limitation "#strands=#generators".
>> >
>> > So this means I have to use only part of the braid group with 6 strands.
>> >
>> > In the end it all works but it is terribly hacky for some which seems
>> to be a very clean thing to do.
>> >
>> > I would be grateful for any suggestions.
>>
>> Michel:
>>
>> One idea is to check out
>> https://doc.sagemath.org/html/en/reference/groups/sage/groups/braid.html
>>
>> Another idea is to download braid-1.1.tar.gz, untar in the pkg
>> subdirectory and type LoadPackage("braid");
>>
>
>
> most, if not all, functionality of braid is nowadays in
> https://gap-packages.github.io/MapClass/
>
> (which is in our gap_packages)
>
>
> FYI, the pkg subdir is inside sage-9*/local/share/gap
>> You can find a pdf manual for the braid package at
>> https://arxiv.org/abs/math/0304376
>> Currently, the link to braid-1.1.tar.gz at
>> https://www.gap-system.org/Packages/undep.html
>> is bad but I have a copy. Just email me privately.
>>
>> - David
>>
>> > Michel
>> >
>> >
>> > --
>> > You received this message because you are subscribed to the Google
>> Groups "sage-support" group.
>> > To unsubscribe from this group and stop receiving emails from it, send
>> an email to sage-support...@googlegroups.com.
>> > To view this discussion on the web visit
>> https://groups.google.com/d/msgid/sage-support/f7d460d0-390b-455d-ae90-72b105e8e926n%40googlegroups.com
>> .
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "sage-support" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to sage-support...@googlegroups.com.
>>
> To view this discussion on the web visit
>> https://groups.google.com/d/msgid/sage-support/CAEQuuAVmSsLxS%2Bi50JNUqrK%3DUm%3DquJaZ2ueNuedAVzr6xKSMzQ%40mail.gmail.com
>> .
>>
>
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Re: [sage-support] Morphisms between free groups.
On Fri, 4 Feb 2022, 11:02 David Joyner, wrote:
> On Fri, Feb 4, 2022 at 4:40 AM 'Michel VAN DEN BERGH' via sage-support
> wrote:
> >
> > Dear all,
> >
> > I need to do something which I thought would be quite simple. I have
> free groups
> > F, G with generators x1,x2,x3,x4 and x,y respectively and I need to
> compute the image of an element under the homomorphism F-->G:x1->x, x2->y,
> x3->x, x4->y.
> >
> > I could not find anything in the manual about morphisms between free
> groups. I tried subs, but that does not work since the parents of the
> elements of F and G are (of course) different.
> >
> > The workaround I used is to work in the free group H with generators
> x1,x2,x3,x4,x,y and to use subs. However this is also inconvenient since I
> need the action of the braid group with 4 strands on F. It does not act on
> H because of the limitation "#strands=#generators".
> >
> > So this means I have to use only part of the braid group with 6 strands.
> >
> > In the end it all works but it is terribly hacky for some which seems to
> be a very clean thing to do.
> >
> > I would be grateful for any suggestions.
>
> Michel:
>
> One idea is to check out
> https://doc.sagemath.org/html/en/reference/groups/sage/groups/braid.html
>
> Another idea is to download braid-1.1.tar.gz, untar in the pkg
> subdirectory and type LoadPackage("braid");
>
most, if not all, functionality of braid is nowadays in
https://gap-packages.github.io/MapClass/
(which is in our gap_packages)
FYI, the pkg subdir is inside sage-9*/local/share/gap
> You can find a pdf manual for the braid package at
> https://arxiv.org/abs/math/0304376
> Currently, the link to braid-1.1.tar.gz at
> https://www.gap-system.org/Packages/undep.html
> is bad but I have a copy. Just email me privately.
>
> - David
>
> > Michel
> >
> >
> > --
> > You received this message because you are subscribed to the Google
> Groups "sage-support" group.
> > To unsubscribe from this group and stop receiving emails from it, send
> an email to sage-support+unsubscr...@googlegroups.com.
> > To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/f7d460d0-390b-455d-ae90-72b105e8e926n%40googlegroups.com
> .
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-support+unsubscr...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/CAEQuuAVmSsLxS%2Bi50JNUqrK%3DUm%3DquJaZ2ueNuedAVzr6xKSMzQ%40mail.gmail.com
> .
>
--
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Re: [sage-support] Morphisms between free groups.
On Fri, Feb 4, 2022 at 4:40 AM 'Michel VAN DEN BERGH' via sage-support
wrote:
>
> Dear all,
>
> I need to do something which I thought would be quite simple. I have free
> groups
> F, G with generators x1,x2,x3,x4 and x,y respectively and I need to compute
> the image of an element under the homomorphism F-->G:x1->x, x2->y, x3->x,
> x4->y.
>
> I could not find anything in the manual about morphisms between free groups.
> I tried subs, but that does not work since the parents of the elements of F
> and G are (of course) different.
>
> The workaround I used is to work in the free group H with generators
> x1,x2,x3,x4,x,y and to use subs. However this is also inconvenient since I
> need the action of the braid group with 4 strands on F. It does not act on H
> because of the limitation "#strands=#generators".
>
> So this means I have to use only part of the braid group with 6 strands.
>
> In the end it all works but it is terribly hacky for some which seems to be a
> very clean thing to do.
>
> I would be grateful for any suggestions.
Michel:
One idea is to check out
https://doc.sagemath.org/html/en/reference/groups/sage/groups/braid.html
Another idea is to download braid-1.1.tar.gz, untar in the pkg
subdirectory and type LoadPackage("braid");
FYI, the pkg subdir is inside sage-9*/local/share/gap
You can find a pdf manual for the braid package at
https://arxiv.org/abs/math/0304376
Currently, the link to braid-1.1.tar.gz at
https://www.gap-system.org/Packages/undep.html
is bad but I have a copy. Just email me privately.
- David
> Michel
>
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-support+unsubscr...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/f7d460d0-390b-455d-ae90-72b105e8e926n%40googlegroups.com.
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[sage-support] Morphisms between free groups.
Dear all, I need to do something which I thought would be quite simple. I have free groups F, G with generators x1,x2,x3,x4 and x,y respectively and I need to compute the image of an element under the homomorphism F-->G:x1->x, x2->y, x3->x, x4->y. I could not find anything in the manual about morphisms between free groups. I tried subs, but that does not work since the parents of the elements of F and G are (of course) different. The workaround I used is to work in the free group H with generators x1,x2,x3,x4,x,y and to use subs. However this is also inconvenient since I need the action of the braid group with 4 strands on F. It does not act on H because of the limitation "#strands=#generators". So this means I have to use only part of the braid group with 6 strands. In the end it all works but it is terribly hacky for some which seems to be a very clean thing to do. I would be grateful for any suggestions. Michel -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/f7d460d0-390b-455d-ae90-72b105e8e926n%40googlegroups.com.
