Fillmore--Springer--Cnops Construction Implemented in GiNaC
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Abstract
This paper presents an implementation of the Fillmore--Springer--Cnops construction (FSCc) along with illustrations of its usage. FSCc linearises the linear-fraction action of the Moebius group in R^n. This has clear advantages in several theoretical and applied fields including engineering. Our implementation is based on the Clifford algebra capacities of the GiNaC computer algebra system (http://www.ginac.de/), which were described in cs.MS/0410044 The core of this realisation of FSCc is done for an arbitrary dimension of R^n with a metric given by an arbitrary bilinear form. We also present a subclass for two dimensional cycles (i.e. circles, parabolas and hyperbolas), which add some 2D specific routines including a visualisation to PostScript files through the MetaPost (http://www.tug.org/metapost.html) or Asymptote (http://asymptote.sourceforge.net/) packages. This software is the backbone of many results published in math.CV/0512416 and we use its applications their for demonstration. It can be ported (with various level of required changes) to other CAS with Clifford algebras capabilities similar to GiNaC.Keywords
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This publication has 3 references indexed in Scilit:
- An example of Clifford algebras calculations with GiNaCAdvances in Applied Clifford Algebras, 2005
- An Introduction to Dirac Operators on Manifolds2002
- Clifford Algebras and the Classical Groups1995