## 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
• Solve
• Limits
• Differential equation solver
• Basic simplification routines
• trig
• 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 polynomial

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

• Summation
• 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

symbolics (last edited 2017-05-15 19:43:59 by chapoton)