$OpenXM: OpenXM/src/todo.txt,v 1.9 2003/03/25 06:53:55 takayama Exp $

/*&english

SHORT TERM

* A unified environment to solve systems of algebraic equations.

* Decompose the install target to
  install-bin
  install-lib
  install-doc
  install-man  

OpenXM PROTOCOL ITSELF

* Notify the error "ox server ox_hogehoge does not exists."

* Restarting server
  (ox_sm1 does not restore the stack after the error.)

* Make the control process as an ox stackmachine.

* Security level (cf. sm1 [(SecureMode) 1] system_variable)

* SPEED UP!

OX SERVERS:

* ox_polymake  (Polytopes) 

* ox_sound
     OX server for mathematically synthesized music.
     For example, I want to hear the sound of (x-1)(x-2)(x-3)*sin(x).

* ox_open_gl   and ox_java_view
     It outputs a high quality graphics.
     Can you draw a high-quality graph of z=x^2-y^2?
     Can you draw a high-quality graph of z=1/(x^2+y^2)?
     Can you draw a zero set of x^3-y^2 z^2?
     Scientific visualization.
     Data format for mathematical graphical data.
     Generation of video like "turning the sphare inside out"

* ox_turtle
     turtle graphics server.
     Graphics of Cell Automaton.  See the book by Miyachi.

* ox_gap
     GAP, opal, etc, etc, ...
     www.matx.org (A free soft like MatLab)
     New CMO should be defined. 


INTERFACE

* What is the best language for our project
  in view of mathematics and distributed computation?
 
* A nice help system.  Learning mathematics via the help system.

* KLIC interface for OpenXM.

* (Nara) Standard Lisp interface for OpenXM.

* 
  Web frontend for OpenXM servers.  w3c.
  Exposition of math programs on web ( asir-contrib/packages/src/dsolv)
  See also  "Algebra, Interactive" (a book by A.Cohen).

* Web cite that keeps math data.  How to organize data?
   see, e.g.,  http://www.goto.info.waseda.ac.jp/~otsuka/polytope/index.html
   http://mathnet.kusm.kyoto-u.ac.jp/index.html
   http://mathmuse.sci.ibaraki.ac.jp

* OX_DATA_MP     (See http://snake.mcs.kent.edu/areas/protocols/mp.html)


MATHEMATICS:

*  Algorithmic study of D-modules and enveloping algebras
   (Beilinson-Bernstein correspondence).

*  Construction of solutions around irregular singular point

*  High precision computation of hypergeometric integrals
   including Selberg type integrals.

*  Rational solutions of hypergeometric systems.

*  Algorithmic treatment of Orlik-Solomon algebra.

*  Distributed computation of GB.
   Distributed computations in computer algebra in general.
   MPI version of OpenXM.  Multiplying huge polynomials, etc.


TEXTS :
* Japanese version of the web cite.

See also
   ox_math/todo.txt
   kan96xx/todo.txt

*/