## Symbolics in Sage

These pages are aimed at developers of symbolics functionality in Sage. If you're interested in helping out with any of the items below please contact the sage-devel googlegroup or the people already working on your item of interest.

For more up-to-date information, see the trac wiki page on symbolics. |

### TODO

- Integration
- Minh Van Nguyen is working on this.

A summary of heuristics used in Maple from Algorithms in Computer Algebra by Geddes, Czapor and Labahn

A survey by Keith Geddes: Algorithms for Indefinite and Definite Integration in Maple

Heuristics from maxima (relevant parts of the maxima manual have some documentation)

Transcendental Risch (from Bronstein's book)

- Solve
Talk by Barton Willis on Maxima's to_poly solve function

test suite for Maxima's to_poly solver

- Limits
- Differential equation solver
documentation of Sum^it library might be useful

- Basic simplification routines
- trig
- radical
- rational
- binomial/factorial?

- Transforms
- laplace, inverse_laplace, hilbert, mellin, etc.
Some discussion on the sage-support list in this thread.

- Orthogonal polynomials
The orthogonal polynomials defined by sage in the module

`sage.functions.orthogonal_polys`are wrappers to maxima, we should provide native implementations of these, preferably with an argument to specify the parent of the resulting polynomialStefan Reiterer ([email protected]) is working on this

Some of the functionality listed above is provided by Maxima wrappers at the moment.

- Summation
Burcin Erocal ([email protected]) is working on this

- Hypergeometric functions

- Meijer G-Functions
- Generating functions
- This is a building block for many things. A prerequisite for this is linear algebra over polynomial rings, Burcin Erocal is working on this.
gfun by Bruno Salvy and Paul Zimmermann included in Maple

GeneratingFunctions by Christian Mallinger for MMA