File: [local] / OpenXM / src / ox_math / todo.txt (download)
Revision 1.3, Thu Dec 16 01:22:41 1999 UTC (24 years, 6 months ago) by takayama
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Added more to todo.txt's. Work hard!
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$OpenXM: OpenXM/src/ox_math/todo.txt,v 1.3 1999/12/16 01:22:41 takayama Exp $
* 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.
asir --> ox_math(EigenValues) and ox_gnuplot
Example 3:
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.
Mathematica --> ox_asir.
Example 5:
Taylor expansion.
asir --> ox_math.
* Find rational solutions of Garnier systems by exhaustive search.
It is a nice problem of solving algebraic equations.
* Add sample programs of asir for the Noro's lecture note:
unkei:~noro/papers/niigata.ps.gz
on computer algebra systems.
* Sample programs of asir for the book
Mori Masatake, Fortran 77 Suuchi-Keisan Programming, Iwanami.
* Sample programs for asir
[This item should be moved to src/asir-contrib soon.]
Example 1:
Write sample programs that implements algorithms
in the following books:
R.Sedgewick, Algorithms in C.
Knuth : The Art of Programming, Semi-numerical algorithms.
Cox-O'Shea-Little : Ideals, Varieties, and Algorithms.
Hikita Teruo, C de kaku Algorithm, Science-sha
Chapter 11, geometry algorithm,
Chapter 12, Parallel programming and algorithms.
Example 2:
Rewrite sample programs in
Kida, Makino : Ubasic ni yoru Computer Seisuu-ron, Nihon Hyoron-sha
by asir and OpenXM.