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⇤ ← Revision 5 as of 2009-03-07 21:25:40 →
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Editor: BurcinErocal
Comment: added links for to_poly solver
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Editor: chapoton
Comment: link
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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 [[http://groups.google.com/group/sage-devel|sage-devel googlegroup]] or the people already working on your item of interest. 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 [[http://groups.google.com/group/sage-devel|sage-devel googlegroup]] or the people already working on your item of interest. 
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=== Pynac and Maxima based symbolics === ||<#FFFF66>For more up-to-date information, see the [[http://trac.sagemath.org/wiki/symbolics|trac wiki page on symbolics]].||
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Most symbolics functionality in Sage relies on [[http://maxima.sf.net|Maxima]]. While Maxima is a very mature and capable software package, there are some problems with using it in Sage. Namely,
  * the pexpect interface to Maxima is slow, and
  * Sage developers cannot fix problems in Maxima or enhance its functionality.

To provide a better framework for symbolics in Sage, and to make implementation of new symbolics functionality that relies on components of Sage easier; we created a fork of the C++ library [[http://www.ginac.de|GiNaC]], called Pynac, which works with Python types. There are still some low level changes required in Pynac before it can be used as a basis for symbolics in Sage, we keep track of these at the [[symbolics/pynac_todo|Pynac todo list]].

With the switch to Pynac based symbolics, it will be possible to implement native functionality in Sage. Here is a brief list of areas that need work.
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   * Minh Van Nguyen is working on this.
  * [[http://books.google.at/books?id=9fOUwkkRxT4C&pg=PR2&hl=en#PPA473,M1|A summary of heuristics used in Maple]] from Algorithms in Computer Algebra by Geddes, Czapor and Labahn
  * A survey by Keith Geddes: [[http://www.cs.uwaterloo.ca/~kogeddes/papers/Integration/IntSurvey.html|Algorithms for Indefinite and Definite Integration in Maple]]
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 * Transforms
  * laplace, inverse_laplace, hilbert, mellin, etc.
  * Some discussion on the sage-support list in [[http://groups.google.com/group/sage-support/browse_thread/thread/7b48e5dbd06f9f46|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
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   $$ \sum_{s \ge m} \binom{s}{m} \frac{(n)_s}{(\frac{n}{2} + 1)_s 2^{s}} = \frac{(n)_m}{2^{
m}(\frac{n}{2}+1)_m} \,_2 F_1 \left( \begin{array}{cc} m+1, m+n \\ m+ \frac{n}{2} +1 \end{array} ; \frac{1}{2} \right) = \frac{2^{n-1} \Gamma(\frac{n}{2} +1) \Gamma(\frac{m}{2} + \frac{n}{2})}{\Gamma(\frac{m}{2} + 1)\Gamma(n)}$$		 $$\sum_{s \ge m} {s \choose m} \frac{(n)_s}{(\frac{n}{2} + 1)_s 2^{s}} = \frac{(n)_m}{2^{m}(\frac{n}{2}+1)_m} \,_2 F_1 \left( \begin{array}{cc} m+1, m+n \\ m+ \frac{n}{2} +1 \end{array} ; \frac{1}{2} \right) = \frac{2^{n-1} \Gamma(\frac{n}{2} +1) \Gamma(\frac{m}{2} + \frac{n}{2})}{\Gamma(\frac{m}{2} + 1)\Gamma(n)}$$
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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

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)