Browsing by Author "Detinko, Alla"
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- ItemAlgebra, matrices, and computers(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2019) Detinko, Alla; Flannery, Dane; Hulpke, AlexanderWhat part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that rely on the theory of matrix groups and new methods for handling matrix groups in a computer.
- ItemExperimenting with Zariski dense subgroups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Detinko, Alla; Flannery, Dane; Hulpke, AlexanderWe give a method to describe all congruence images of a finitely generated Zariski dense group H< SL(n; Z). The method is applied to obtain efficient algorithms for solving this problem in odd prime degree n; if n = 2 then we compute all congruence images only modulo primes. We propose a separate method that works for all n as long as H contains a known transvection. The algorithms have been implemented in GAP, enabling computer experiments with important classes of linear groups that have recently emerged.
- ItemGAP functionality for Zariski dense groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Detinko, Alla; Flannery, Dane; Hulpke, AlexanderIn this document we describe the functionality of GAP [4] routines for Zariski dense or arithmetic groups that are developed in [1, 2, 3]. The research underlying the software was supported through the programme "Research in Pairs", at the Mathematisches Forschungsinstitut Oberwolfach, and part of the software was written during a stay in June 2017. The hospitality we received has been greatly appreciated. Our research was also supported by a Marie Sklodowska-Curie Individual Fellowship grant under Horizon 2020 (EU Framework Programme for Research and Innovation), and a Simons Foundation Collaboration Grant Nr. 244502. All support is acknowledged with gratitude.