GiNaC-cycle

This is an implementation of the Schwerdtfeger--Fillmore--Springer--Cnops construction (SFSCc) based on the Clifford algebra capacities of the GiNaC computer algebra system. SFSCc linearises the linear-fraction action of the Möbius group. This turns to be very useful in several theoretical and applied fields including engineering. The core of this realisation of SFSCc is done for an arbitrary dimension, while a subclass for two dimensional cycles add some 2D-specific routines including a visualisation to PostScript files through the MetaPost or Asymptote software. The package is realised as a C++ library and there are several Python wrapper of it, which can be used in interactive mode. This library is a backbone of many results published in several works of the author, which serve as illustrations of its usage. It can be ported (with various level of required changes) to other CAS with Clifford algebras capabilities. There is an ISO image of a Live Debian DVD which can be used to boot a computer with i386 architecture or run inside an emulator, e.g. Virtual box. This library is now a part of a wider MoebInv project: https://swmath.org/software/27527.


References in zbMATH (referenced in 15 articles , 2 standard articles )

Showing results 1 to 15 of 15.
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  1. Biswas, Debapriya; Dutta, Sandipan: Möbius action of (\mathrmSL(2; \mathbbR)) on different homogeneous spaces (2022)
  2. Biswas, Debapriya; Dutta, Sandipan: Geometric invariants under the Möbius action of the group (SL(2;\mathbbR)) (2021)
  3. Kisil, Vladimir V.; Reid, James: Conformal parametrisation of loxodromes by triples of circles (2019)
  4. Kisil, Vladimir V.: An extension of Möbius-Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library (2018)
  5. Mustafa, Khawlah A.: The groups of two by two matrices in double and dual numbers, and associated Möbius transformations (2018)
  6. Özdemir, Mustafa: Introduction to hybrid numbers (2018)
  7. Brewer, Sky: Projective cross-ratio on hypercomplex numbers (2013)
  8. Kisil, Vladimir V.: Induced representations and hypercomplex numbers (2013)
  9. Kisil, Vladimir V.: Hypercomplex representations of the Heisenberg group and mechanics (2012)
  10. Kisil, Vladimir V.: Erlangen program at large-1: geometry of invariants (2010)
  11. Kisil, Vladimir V.: Two-dimensional conformal models of space-time and their compactification (2007)
  12. Kisil, Vladimir V.: Fillmore-Springer-Cnops construction implemented in GiNaC (2007)
  13. Kisil, Vladimir V.: An example of Clifford algebras calculations with GiNaC (2005)
  14. Kisil, Vladimir V.: An example of Clifford algebras calculations with ginac (2004) ioport
  15. Kisil, Vladimir V.; Biswas, Debapriya: Elliptic, parabolic and hyperbolic analytic function theory-0: geometry of domains (2004)