Dear Franz and Martin, just to let you now about the progress of the plethysm and outer product, skew for Schur functions. This will raise some questions about where to implement this functionality.
After a prototyping of Axel Kohnerts fast plethysm algorithm in maple (sorry for that) I found that Kohnert's algorithm suffered very much from the bad performance of my skew (in SchurFkt, and currently in FriCAS), which is done by dualisation s_\mu/s_nu = sum_\rho <s_mu, outer(s_\mu,s_rho)> s_rho many terms lots of zeros from the scalar product. So I investigated in the last days the Lascoux-Schuetzenberger algorithm using Schubert polynomials to multiply many Schur functions and to skew them directly. This algorithm uses: * Schubert polynomials indexed by * permutations * Lehmer codes of permutatiuons * and a simplified version of Monk's rule for Schubert polynomails called transition It constructs a tree where one can read off the result from the leaves. I would like to implement this functionality just in the domain TAB2 (in symfunc.spad.nw) and I would like to avoid a new category/domain permutations or even Schubert polynomials. Do you agree with that? Anyhow this functionality is (will be) currently only used in symfunc.spad.nw I have now implemented a prototype function for skew in maple (which I will add to my SchurFkt package also) which indicates a speed differenced between * skew by dualization (with internally cached combinatorics !!) * skew by Lascoux-Schuetzenberger LS (Kohnert) (plain implementation, no trickery) of about 100 in favour of LS, so LS seems to be mandatory. Furthermore the LS algorithm alows to compute the product of say n Schur functions in a single stroke. This is importand for Kohnert's fast plethysm algorith. This raises the question: How do I implement in FriCAS a function with a variable number of arguments? outer List SchurSymmetricFunction -> SchurSymmetricFunction could be used ? While its good we implemented in Hannover the Littlewood Richardson rule, it will become obsolete for actual computations of products and skews. However, we can compare results for testing against two different algorithms, so I would leave that code in the file. Regarding the plethysm I am stuck, before I have a working implementation of LS I cannot time the two different approches against each other on the same platform. Kohnert has implemented these algorithms in SYMMETRICA and Magma, since that is generic c code timing is not comparable. But I have some Hopf advantages and hope to improve still further. I hope I have some working code by end of next week, however some advice where to place the functionality and how to deal with a variable number of arguments it much welcome. Kind regards BF. -- % PD Dr Bertfried Fauser % Research Fellow, School of Computer Science, Univ. of Birmingham % Honorary Associate, University of Tasmania % Privat Docent: University of Konstanz, Physics Dept <http://www.uni-konstanz.de> % contact |-> URL : http://clifford.physik.uni-konstanz.de/~fauser/ % Phone : +49 1520 9874517 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
