Artifact c37c4f3218fed783e50d24d5e1a80cb75b76554d7d96f16bd7c87b795e247da3:
- Executable file
r37/packages/qsum/qsum.tst
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
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— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 3614) [annotate] [blame] [check-ins using] [more...]
- Executable file
r38/packages/qsum/qsum.tst
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 3614) [annotate] [blame] [check-ins using]
% Test file for the REDUCE package QSUM % % Copyright (c) Wolfram Koepf, Harald Boeing, Konrad-Zuse-Zentrum Berlin, 1997 % % Implementation of the q-Gosper and q-Zeilberger algorithms % % Reference: % % Koornwinder, T. H.: % On Zeilberger's algorithm and its q-analogue: a rigorous description. % J. of Comput. and Appl. Math. 48, 1993, 91-111. % % Some examples are from % % Koekoek, R. and Swarttouw, R.F.: % The Askey-scheme of Hypergeometric Orthogonal Polynomials and its q-analogue. % Report 94-05, Technische Universiteit Delft, Faculty of Technical Mathematics % and Informatics, Delft, 1994. % % Gasper, G. and Rahman, M.: % Basic Hypergeometric Series. % Encyclopedia of Mathematics and its Applications 35. % Ed. by G.-C. Rota, Cambridge University Press, London and New York, 1990. % Results of manual qsum.tex % load qsum; qgosper(qpochhammer(a,q,k)*q^k/qpochhammer(q,q,k),q,k); qgosper(qpochhammer(a,q,k)*qpochhammer(a*q^2,q^2,k)* qpochhammer(q^(-n),q,k)*q^(n*k)/(qpochhammer(a,q^2,k)* qpochhammer(a*q^(n+1),q,k)*qpochhammer(q,q,k)),q,k); qgosper(qpochhammer(q^(-n),q,k)*z^k/qpochhammer(q,q,k)*z^n,q,k); off qgosper_down; qgosper(q^k*qbrackets(k,q),q,k); on qgosper_down; qgosper(q^k,q,k,0,n); qsumrecursion(qpochhammer(q^(-n),q,k)*z^k/qpochhammer(q,q,k),q,k,n); on qsumrecursion_certificate; proof:=qsumrecursion(qpochhammer(q^(-n),q,k)*z^k/qpochhammer(q,q,k),q,k,n); off qsumrecursion_certificate; % proof of statement lhside:= qsimpcomb(sub(summ(n)=part(proof,3), summ(n-1)=sub(n=n-1,part(proof,3)),part(proof,1))); rhside:= qsimpcomb((part(proof,2)*part(proof,3)- sub(k=k-1,part(proof,2)*part(proof,3)))); qsimpcomb((rhside-lhside)/part(proof,3)); % proof done operator qlaguerre, qcharlier; % q-Laguerre polynomials, Koekoek, Swarttouw (3.21) qsumrecursion(qpochhammer(q^(alpha+1),q,n)/qpochhammer(q,q,n), {q^(-n)}, {q^(alpha+1)}, q, -x*q^(n+alpha+1), qlaguerre(n)); % q-Charlier polynomials, Koekoek, Swarttouw (3.23) qsumrecursion({q^(-n),q^(-x)},{0},q,-q^(n+1)/a,qcharlier(n)); % continuous q-Jacobi polynomials, Koekoek, Swarttouw (3.10) %% on qsum_nullspace; %% term:= qpochhammer(q^(alpha+1),q,n)/qpochhammer(q,q,n)* %% qphihyperterm({q^(-n),q^(n+alpha+beta+1), %% q^(alpha/2+1/4)*exp(I*theta), q^(alpha/2+1/4)*exp(-I*theta)}, %% {q^(alpha+1), -q^((alpha+beta+1)/2), -q^((alpha+beta+2)/2)}, %% q, q, k)$ %% qsumrecursion(term,q,k,n,2); %% off qsum_nullspace; % Some more qgosper results with proof % % Gasper, Rahman (2.3.4) term:=qpochhammer(a,q,k)*qpochhammer(a*q^2,q^2,k)*qpochhammer(q^(-n),q,k)* q^(n*k)/(qpochhammer(a,q^2,k)*qpochhammer(a*q^(n+1),q,k)*qpochhammer(q,q,k)); result:=qgosper(qpochhammer(a,q,k)*qpochhammer(a*q^2,q^2,k)* qpochhammer(q^(-n),q,k)*q^(n*k)/ (qpochhammer(a,q^2,k)*qpochhammer(a*q^(n+1),q,k)*qpochhammer(q,q,k)),q,k); qsimpcomb(result-sub(k=k-1,result)-term); % Gasper, Rahman (3.8.16) term:=(1-a*c*q^(4*k))*(1-b/c*q^(-2*k))*qpochhammer(a,q,k)*qpochhammer(b,q,k)* qpochhammer(q^(-3*n),q^3,k)*qpochhammer(a*c^2/b*q^(3*n),q^3,k)*q^(3*k)/ ((1-a*c)*(1-b/c)*qpochhammer(c*q^3,q^3,k)*qpochhammer(a*c/b*q^3,q^3,k)* qpochhammer(a*c*q^(3*n+1),q,k)*qpochhammer(b/c*q^(1-3*n),q,k)); result:=qgosper((1-a*c*q^(4*k))*(1-b/c*q^(-2*k))*qpochhammer(a,q,k)* qpochhammer(b,q,k)*qpochhammer(q^(-3*n),q^3,k)*qpochhammer(a*c^2/ b*q^(3*n),q^3,k)*q^(3*k)/((1-a*c)*(1-b/c)*qpochhammer(c*q^3,q^3,k)* qpochhammer(a*c/b*q^3,q^3,k)*qpochhammer(a*c*q^(3*n+1),q,k)* qpochhammer(b/c*q^(1-3*n),q,k)),q,k); qsimpcomb(result-sub(k=k-1,result)-term); end;