The kernel part of PySymbolic (`Kernel.py`

) is almost
complete. It uses very fast GMP arbitrary precision
integers/rational numbers and multi-precision floats for Number
instances. (Initial tests show that PySymbolic will be faster than any
other symbolic package, e.g. see the test-site of
MPFR). TODO for the kernel: implement Function class, more
elementary functions, evaluation of functions, finish complex numbers,
finish parser.

After the PySymbolic kernel is finished, we can start to implement extensions. They should cover the following topics:

- Differentiation
- This is simple, done many times and will do again when kernel provides the Function class
- Simplification
- This is not simple. Need a criterion for the notion of "simplicity". And such that it can be effectively implemented. Suggestions/links are welcome!
- Polynomials
- Factorization of polynomials is desired. For that we need Gröbner basis implementation. I have many references for that, both theory and implementations, but it seems that it we need to implement it directly in Python. NTL should be used for factoring uni-variate polynomials over integers (need volunteers for wrapping NTL to Python!). See also GROEBNER that is free C library.
- Linear Algebra
- Implement Matrix,Vector,Tensor classes. Symbolically calculate determinants, inverse matrices, various decompositions (QR, SVD, etc), solve eigenvalue problems,etc. Theory is simple, just need lots of code. Contributions are welcome!
- Integration
- Theory is complex but I have references to algorithms. So, it just needs implementation.
- Limits
- It is involved topic but I have references to algorithms.
- Sums.
- Both finite and infinite (series). Implement hyper-geometric functions.
- Asymptotic tools
- Taylor,Laurent,etc series. O symbol.
- Solve equations. Roots.
- Linear equations are "simple". Also polynomial equations --- use Gröbner basis stuff.
- Sets
- Implement Set class in kernel (or in C for efficiency). It might be useful also for other extensions.
- Input/Output
- Write Symbolic expressions in Latex,XML,MathML. And vice versa.
- Special functions
- Symbolic manipulation with them, evaluation, simplification.
- ...

- Python 2.0
- GMPY --- the GNU MP-3 interface to Python. Thanks to Alex Martelli!
- (MPFR --- we are working on it)

`pysymbolic`

program and it is open
for discussion, questions, and answers. You can subscribe the list here.
- Snapshots of the pre-release (obsolete, get it directly from CVS):
- rel-0.x/pysymbolic-0.latest.tgz

`pysymbolic`

is being developed under CVS and those who are interested in
the really latest version of `pysymbolic`

(possibly unstable) can
get it from the repository as follows:
- First you need to login (the password is
`guest`

):> cvs -d :pserver:anonymous@cens.ioc.ee:/home/cvs login

- and then do the checkout:
> cvs -z6 -d :pserver:anonymous@cens.ioc.ee:/home/cvs checkout pysymbolic

- In the directory
`pysymbolic`

you can get the updates by hitting> cvs -z6 update -P -d

`pysymbolic`

CVS repository here.
Pearu Peterson <pearu@ioc.ee>

Viimati muudetud: Aug 14 12:31:15 EEST 2001 Submit this page for validation