Axiom is adding BLAS, the Basic Linear Algebra Subroutines, and

LAPACK, the Linear Algebra Package to Axiom. There are two reasons.

First, most numeric-oriented programmers expect these libraries.It

would make it easier to experiment if they were readily available.

Second, there are interesting research paths which cannot be done

using standard external libraries.

A few interesting future paths present themselves.

The standard BLAS/LAPACK is purely numeric. The current work is moving

them from Fortran to Lisp and then to Spad. These routines have

separate code for real, double, complex, and complex16 arrays and

matrices. Axiom has a much richer notion of type so it raises the

question: Can we extend BLAS/LAPACK to Axiom's other types?

NIST has a standard file format called "Matrix Market" for portable

matrix files. The format is general but only a few types are

defined. Axiom's version will clearly have to define more. Axiom will

shortly be able to read and write these standard file formats. The

standard defines "complex" as a matrix type but does not distinguish

between complex(int), complex(float), etc. so the Axiom version will

have at least that extension. However, based on the next idea it will

also need "symbolic" as a type.

This raises another interesting research question, mixing numeric and

symbolic entries in BLAS/LAPACK. An enormous amount of effort is spent

handling overflow/underflow and scaling. Most of these problems can be

rendered exact if some of the entries are symbolic.

Even more interesting is the latest book called "The End of Error:

Unum Computing". Gustafson allows dynamic expansion of the floating

number format as well as redefining infinity. This representation

gives exact results and interval results. I'm working on an

implementation. There is interesting research both in terms of Axiom

(e.g. Expression(Unum)) and BLAS/LAPACK numerics using Unums.

Tim

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