symbolics - Sagemath Wiki

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
- Poor man's integrator
  - 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?
  - maxima documentation
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 polynomial
  - Stefan 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
- HYP from Christian Krattenthaler for MMA
- HYPERG from Bruno Gauthier for Maple
  - This should let us do the following:

\sum_{s \ge m} {s \choose m} \frac{(n)_s}{(\frac{n}{2} + 1)_s 2^{s}} = \frac{(n)_m}{2^{m}(\frac{n}{2}+1)_m} \,_2 F_1 \left( \begin{array}{cc} m+1, m+n \\ m+ \frac{n}{2} +1 \end{array} ; \frac{1}{2} \right) = \frac{2^{n-1} \Gamma(\frac{n}{2} +1) \Gamma(\frac{m}{2} + \frac{n}{2})}{\Gamma(\frac{m}{2} + 1)\Gamma(n)}

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