$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.