bttree-discrete-free
A Magma package for identifying discrete free subgroups of the Bruhat-Tits tree, and solving the constructive membership problem
Science Score: 44.0%
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Repository
A Magma package for identifying discrete free subgroups of the Bruhat-Tits tree, and solving the constructive membership problem
Basic Info
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files
README.md
BTTree-Discrete-Free
This package provides tools for deciding whether a subgroup of automorphisms of the Bruhat-Tits tree over a p-adic field is discrete and free, and other algorithms relating to these groups.
This package uses the BTTree package. To attach both packages, run the following command in Magma:
AttachSpec("BTTree-Discrete-Free/spec");
Main intrinsics
IsDiscreteFree(T::BTTree, X::[AlgMatElt]: RequireBasis := false) -> BoolElt, .
Return false, g if g is an elliptic element of <X>. Otherwise return true, Y where Y is a strongly N-reduced basis for <X>.
If RequireBasis is set, then this function will return false, g if g is an element of <X> corresponding to a nontrivial word in X that acts trivially on T.
FundamentalDomain(X::[AlgMatElt], v::BTTVert) -> BTTVert, AlgMatElt
Return the representative of v in the fundamental domain, with the corresponding group action. X must be a strongly N-reduced basis for <X>.
InFreeIsometryGroup(T::BTTree, g::AlgMatElt, X::[AlgMatElt]) -> BoolElt
Return true if g is in <X>. Assumes X is a strongly N-reduced basis.
IsSameGroup(T::BTTree, X::[AlgMatElt], Y::[AlgMatElt]) -> BoolElt
Return true if X and Y generate the same group. Assumes that X and Y are both discrete and free.
Owner
- Name: Ari Markowitz
- Login: ariymarkowitz
- Kind: user
- Repositories: 3
- Profile: https://github.com/ariymarkowitz
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!
cff-version: 1.2.0
title: BTTree-Reduce
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
authors:
- given-names: Ari
family-names: Markowitz
email: ari.markowitz@auckland.ac.nz
affiliation: University of Auckland
orcid: 'https://orcid.org/0009-0009-4752-1480'
repository-code: 'https://github.com/ariymarkowitz/BTTree-Reduce'
abstract: >-
A Magma package for identifying discrete free subgroups of
the Bruhat-Tits tree, and solving the constructive
membership problem
keywords:
- Group theory
- Geometry
license: GPL-3.0