William Stein wrote: > happen to us, please speak up. I think something like JSAGE > (http://sagemath.org/jsage/) > -- if it were to take off -- would really help. >
Ok, for a start: In December last year there was an article in one of the oldest math journals in the world: Nieuw Archief voor Wiskunde (translation: New Archive for Mathematics) founded by the oldest mathematical society in the world (Wiskundig Genootschap), founded in 1778. In this prestigious :-) journal you will find my article, which is now publicly available: http://www.math.leidenuniv.nl/%7Enaw/serie5/deel07/dec2006/spies.pdf I used Sage for some crucial results. After discussions with Michael Abshoff at SD6 (and earlier questions by William) I'm ready to ask for refereeing my little program dance.sage for inclusion in JSAGE :-) dancing.sage: ########################################################################## # Copyright (C) 2006 Jaap Spies, [EMAIL PROTECTED] # # Distributed under the terms of the GNU General Public License (GPL): # # http://www.gnu.org/licenses/ ########################################################################## """ Usage from sage sage: attach 'dancing.sage' sage: dance(4) h^4 - 2*h^3 + 9*h^2 - 8*h + 6 """ # use variable 'h' in the polynomial ring over the rationals h = QQ['h'].gen() def dance(m): """ Generates the polynomial solutions of the Dancing School Problem Based on a modification of theorem 7.2.1 from Brualdi and Ryser, Combinatorial Matrix Theory See NAW 5/7 nr. 4 december 2006 p. 285 INPUT: integer m OUTPUT: polynomial in 'h' EXAMPLE: sage: dance(4) h^4 - 2*h^3 + 9*h^2 - 8*h + 6 AUTHOR: Jaap Spies (2006) """ n = 2*m-2 M = MatrixSpace(ZZ, m, n) A = M([0 for i in range(m*n)]) for i in range(m): for j in range(n): if i > j or j > i + n - m: A[i,j] = 1 rv = A.rook_vector() print rv s = sum([(-1)^k*rv[k]*falling_factorial(m+h-k, m-k) for k in range(m+1)]) print s It depends on sage.matrix.matrix2: rook_vector() which in turn depends on the permanent function. and falling_factorial which is in sage.rings.arith All this functions have the same author: me, so refereeing is strongly adviced! And of cause already done :-)! Jaap Thanks to Michael Abshoff dance(11) and dance(12) finished on sage.math! --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
