sage-train-track
================
Free group automorphisms and train-track representatives in python/sage.
This is a Sage optional package. It contains code to handle free group
automorphisms (inversion, composition, etc.) and to compute
train-track representatives (absolute and relative, stable and
unstable) as defined by Bestvina and Handel. This includes the
computation of Nielsen paths and indices of iwip automorphisms and
much more. Convex cores of pairs of tree as defined by Guirardel also
appear.
Installation::
sage -pip install train_track
Warning: it seems that Mac OS X 10.13 and later has a security
conflict between SIP and SSL and does not succeed in downloading the
package from https://pypi.python.org. To overcome this difficulty,
just download the tarball train_track-0.1.4.tar.gz from
https://pypi.python.org/simple/train_track
and run::
sage -pip install /path/to/train_track-0.1.4.tar.gz
Warning: if you lack intstallation privilege, you can install only for
yourself::
sage -pip install --user train_track
On Cocalc.com installation can be done either from a terminal as above
or from a cell::
!sage -pip install train_track
Warning, Cocalc free accounts do not have access to internet, first
download the tarball then install.
Usage::
sage: from train_track import *
After this command, you can play with free groups and their automorphisms::
sage: FreeGroup('a,b,c')
Free Group on generators {a, b, c}
sage: FreeGroupAutomorphism('a->bCb,b->Bc,c->BcBa')
Automorphism of the Free Group on generators {a, b, c}: a->a*b,b->a*c,c->a
sage: free_group_automorphisms.Cohen_Lustig_1_6()
Automorphism of the Free Group on generators {a, b, c}: a->c^3*a*c^-3,b->c^-1*a*c^2*a^-1*b*c^-1,c->a*c^2*a^-1*b*c^2*a*c^-2*b^-1*a*c^-2*a^-1*c^4*a^-1*c^-3
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"description": "sage-train-track\n================\n\nFree group automorphisms and train-track representatives in python/sage. \n\nThis is a Sage optional package. It contains code to handle free group\nautomorphisms (inversion, composition, etc.) and to compute\ntrain-track representatives (absolute and relative, stable and\nunstable) as defined by Bestvina and Handel. This includes the\ncomputation of Nielsen paths and indices of iwip automorphisms and\nmuch more. Convex cores of pairs of tree as defined by Guirardel also\nappear.\n\nInstallation::\n\n sage -pip install train_track\n\nWarning: it seems that Mac OS X 10.13 and later has a security\nconflict between SIP and SSL and does not succeed in downloading the\npackage from https://pypi.python.org. To overcome this difficulty,\njust download the tarball train_track-0.1.4.tar.gz from\n\n https://pypi.python.org/simple/train_track\n\nand run::\n\n sage -pip install /path/to/train_track-0.1.4.tar.gz\n\nWarning: if you lack intstallation privilege, you can install only for\nyourself::\n\n sage -pip install --user train_track\n \nOn Cocalc.com installation can be done either from a terminal as above\nor from a cell::\n\n !sage -pip install train_track\n\nWarning, Cocalc free accounts do not have access to internet, first\ndownload the tarball then install.\n \nUsage::\n\n sage: from train_track import *\n\n\nAfter this command, you can play with free groups and their automorphisms::\n\n sage: FreeGroup('a,b,c')\n Free Group on generators {a, b, c}\n sage: FreeGroupAutomorphism('a->bCb,b->Bc,c->BcBa')\n Automorphism of the Free Group on generators {a, b, c}: a->a*b,b->a*c,c->a\n sage: free_group_automorphisms.Cohen_Lustig_1_6()\n Automorphism of the Free Group on generators {a, b, c}: a->c^3*a*c^-3,b->c^-1*a*c^2*a^-1*b*c^-1,c->a*c^2*a^-1*b*c^2*a*c^-2*b^-1*a*c^-2*a^-1*c^4*a^-1*c^-3\n \n\n\n",
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