Mathematical software
The program Bianchi.gp
has been validated in the PLUME index of the CNRS.
Bianchi.gp computes a fundamental domain for the Bianchi groups in hyperbolic 3-space,
the associated quotient space and essential information about the group homology
and equivariant K-homology of the Bianchi groups.
Bianchi.gp is part of the GP Scripts Library of PARI/GP Development Center.
The intensive computations award C3I has been attributed to A. Rahm's PhD thesis, which was the framework of Bianchi.gp.
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The Torsion Subcomplexes Subpackage (joint work with Tuan Anh Bui) in HAP is a GAP sub-package for Torsion Subcomplex Reduction to be applied to cell complexes with an action of a discrete group.
The paper
The Farrell--Tate and Bredon homology for PSL_4(Z) and other arithmetic groups (joint work with Tuan Anh Bui and Matthias Wendt) explains the Rigid Facets Subdivision algorithm, which is the main new feature in the current version (2.1) of the subpackage.
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The Davis Complex package in HAP, by Alexander D. Rahm and Ruben J. Sanchez-Garcia, is a GAP sub-package which
creates a combinatorial model of the Davis complex of an arbitrary Coxeter group.
The Davis complex has been defined in [M.W. Davis, Groups generated by reflections, Ann. Math. 117 (1983)]; and the present sub-package is a release of the implementation described in [R.J. Sanchez-Garcia, Equivariant K-homology for some Coxeter groups, J. London Math. Soc. (2) 75 (2007)].
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The C++ software HomologyLive: an implementation of the Vietoris-Rips complex adapted to a statistical physics setting. Truncated at dimension 3, to stay within the physical dimensions of the ambient space, and with boundaries recorded as sparse matrices, in order to allow for huge numbers of particles in the simulations while keeping the linear algebra feasible on the machine.
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The C++ software star-to-mesh-transformator (released on GitHub, December 3rd, 2018): This Star-to-Mesh transformator allows to reduce an electrical network which exclusively consists of finitely many Ohmian resistors (it may be a subnetwork in a larger electrical network which also contains components of other types) down to one single Ohmian resistor between two nodes which can be chosen beforehand (let us call them "the electrodes"). This reduction is achieved by eliminating each node which is not an "electrode" by a star-to-mesh transformation, one after another.