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 -- Vladimir V. Kisil email: kisilv@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Computer Science, abstract cs.MS/0512073 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 Computation 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.