[GiNaC-list] GiNaC library for FSC construction

Vladimir Kisil kisilv at maths.leeds.ac.uk
Wed Dec 28 11:16:33 CET 2005

 	Dear All,
   I wrote a GiNaC library (http://arxiv.org/abs/cs.MS/0512073) which
implements the Fillmore-Springer-Cnops construction (see abstract bellow).

Best wishes to all for the coming New Year 2006!
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
--                      www: http://maths.leeds.ac.uk/~kisilv/

Computer Science, abstract

From: Vladimir V Kisil [view email]
Date: Sat, 17 Dec 2005 15:09:11 GMT   (149kb)

Fillmore--Springer--Cnops Construction Implemented in GiNaC
Authors: Vladimir V. Kisil
Comments: LaTeX, 53 p; 9 PS graphics in one figure, the full source files
are included, see last section of the paper
Report-no: LEEDS-MATH-PURE-2005-29
Subj-class: Mathematical Software; Computational Geometry; Symbolic

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 there for demonstration.

It can be ported (with various level of required changes) to other CAS
with Clifford algebras capabilities similar to GiNaC.

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