Hi all, I will be attending Sage Days 10 in Nancy, but am very new to Sage and need some pointers on where to find stuff. Also, I have heard about some recent developments in C++ linear algebra libraries and wonder how this relates to Sage.
The most recent development is Matrix Template Library (MTL) 4. http://www.osl.iu.edu/research/mtl/mtl4/ This enables the use to write linear algebra expressions in C++ in a more "natural" notation. There is also Glas. http://glas.sourceforge.net/doc/index.html http://sourceforge.net/projects/glas This is intended to provide a generic C++ interface to linear algebra complete with concepts. http://glas.sourceforge.net/doc/index.html Also, over a period of time I have developed a Clifford algebra library, GluCat http://glucat.sourceforge.net http://sourceforge.net/projects/glucat GluCat implements Clifford algebras over the real field. OK, so questions. 0. Does Sage define concepts in the same way as MTL and Glas? 1. How does Sage do linear algebra over the real and complex fields? Does Sage provide matrix functions such as matrix square root and logarithm, in the same way as, eg. Matlab? Is this done via Scipy or Octave, or at a lower level? 2. How do I go about combining exact and inexact linear algebra? Does Sage provide a common interface to both? In C++? In Python? At the core of the matrix_multi<> class in GluCat is the generation and manipulation of basis matrices. These are -1,0,1 matrices which generate finite groups. Right now these are implemented as compressed uBLAS matrices over the type Scalar_T (typically float or double), but I see no reason why they can be re-implemented as matrices over the integers, or even over the field Z/3Z, as long as multiplication of a basis matrix by a Scalar_T is suitably defined in the context of the Clifford algebra. 3. How would I go about extending GluCat to cover Clifford algebras over finite fields, fields of non-zero characteristic, especially characteristic 2? Some of the answer to this depends on the existing design of GluCat, some on the nature of Clifford algebras, but maybe the exact linear algebra used in Sage may help here. 4. How would I go about incorporating GluCat into Sage? Would it be better to leave GluCat as standalone library and provide some sort of interfacing? Would this be along the lines of SWIG? Would it be better to interface GluCat to GAP or does GAP only deal with discrete algebras? --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
