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version 1.1, 1999/12/15 10:34:32 version 1.3, 1999/12/16 01:22:41
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 $OpenXM$  $OpenXM: OpenXM/src/ox_math/todo.txt,v 1.2 1999/12/15 13:32:14 takayama Exp $
   
 * We need examples of client programs which can be used  * We need examples of client programs which can be used
   in class rooms or in study of mathematics.    in class rooms or in study of mathematics.
   Example 1:    Example 1:
     \beta nbc basis.      \beta nbc basis.
     Mathematica --> ox_asir (\beta nbc package)      Mathematica --> ox_asir (\beta nbc package)
       Reference : Orlik and Terao, Arrangements of Hyperplanes, Springer.
   Example 2:    Example 2:
     Generate randomly symmetric matrices and      Generate randomly symmetric matrices and
     display the distribution of the maximal eigenvalues.      display the distribution of the maximal eigenvalues.
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     Translate the Selberg differential equation to      Translate the Selberg differential equation to
     a Pfaffian form.      a Pfaffian form.
     Mathematica --> ox_sm1.      Mathematica --> ox_sm1.
       asir --> ox_sm1.
       Reference : Aomoto and Kita, Hypergeometric Functions, Appendix.
   Example 4:    Example 4:
     Mathematica Note book that explains what is primary ideal      Mathematica Note book that explains what is primary ideal
     decomposition.      decomposition.
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   Example 5:    Example 5:
     Taylor expansion.      Taylor expansion.
     asir --> ox_math.      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.
   
   * 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.
   
   
   
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