OpenXM/src/ox_math/todo.txt - diff

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version 1.1, 1999/12/15 10:34:32

version 1.5, 2000/03/17 04:51:59

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$OpenXM: OpenXM/src/ox_math/todo.txt,v 1.4 1999/12/16 02:04:35 takayama Exp $

* The package Selberg.

* Online usage

* Mathematica-contrib that matches to asir-contrib

See OpenXM/src/asir-contrib/packages/doc/cman.texi

* We need examples of client programs which can be used

in class rooms or in study of mathematics.

Example 1:

\beta nbc basis.

Mathematica --> ox_asir (\beta nbc package)

Reference : Orlik and Terao, Arrangements of Hyperplanes, Springer.

Example 2:

Generate randomly symmetric matrices and

display the distribution of the maximal eigenvalues.

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Translate the Selberg differential equation to

a Pfaffian form.

Mathematica --> ox_sm1.

asir --> ox_sm1.

Reference : Aomoto and Kita, Hypergeometric Functions, Appendix.

Example 4:

Mathematica Note book that explains what is primary ideal

decomposition.

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Example 5:

Taylor expansion.

asir --> ox_math.

Example 6:

Find examples from the books of Sejivic, Knuth, Cox-O'Shea-Little.

* Find rational solutions of Garnier systems by exhaustive search.

It is a nice problem of solving algebraic equations.