{VERSION 4 0 "APPLE_PPC_MAC" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 47 "Worksheet for testing the Maple f unction qzeilb" }}{PARA 0 "" 0 "" {TEXT -1 94 "(summation of terminati ng q-hypergeometric series by the q-version of Zeilberger's algorithm) ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 73 "Copy right 1992, 1996, 1998, 2000 by Tom H. Koornwinder (thk@wins.uva.nl). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 168 "The \+ 1992 version was a competely rewritten version of a Maple procedure q_ ident_prover.maple by D. Zeilberger.\nThe 1996 version was adapted to \+ Maple V, Release 3 and 4." }}{PARA 0 "" 0 "" {TEXT -1 57 "The 1998 ver sion was adapted to Maple V, Release 4 and 5." }}{PARA 0 "" 0 "" {TEXT -1 96 "The present version, 11 December 2000, works in Maple 6 \+ as well as in Maple V, Release 4 and 5." }}{PARA 0 "" 0 "" {TEXT -1 167 "Thanks to Peter Paule, Axel Riese and Wolfram Koepf for helpful r emarks.\nThanks to Harald Boeing & Wolfram Koepf for the procedure q_e xponent from their package qsum.\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "read qzeilb:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "t:=4:" }}}{PARA 0 "" 0 "" {TEXT -1 17 "q-Chu-Vandermon de" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "qzeilb([q^(-n),b],[c], q,q,f(n),1,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?qzeilb:~computing~ P,~R1~and~R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=2.816G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%Fqzeilb:~computing~maximal~degree~of~ PG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=3.266G" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%:qzeilb:~solving~equationsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=3.283G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Writ e~the~input~series~asG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\" nG-%$SumG6$-F%6$F'%\"kG/F-;\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# %&Then~G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/-%$SumG6$,&-%\"fG6$%\"nG% \"kG\"\"\"*&*&,&*&%\"bGF-%\"qGF-!\"\"*&)F3F+F-%\"cGF-F-F--F)6$,&F+F-F- F4F,F-F-,&F5F-F3F4F4F4/F,;\"\"!%\"mG,$*&**F6F-,&F4F-*&)F3F?F-F3F-F-F-, &*&F7F-FEF-F-F-F4F--F)6$F+,&F?F-F-F-F-F-*(F;F-FEF-,&F6F-F-F4F-F4F42F>F +" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=4.700G" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%2Hence~f(n)~equalsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*&*&,&*&%\"bG\"\"\"%\"qGF(!\"\"*&)F)%\"nGF(%\"cGF(F(F(-%\"fG6#,&F-F (F(F*F(F(,&F+F(F)F*F*2\"\"!F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Hen ce~f(n)~equalsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*(),$*&%\"bG\"\" \"%\"qGF)!\"\"%\"nGF)-%%qfacG6%*&%\"cGF)F(F+F*F,F)),$F*F+,$F,F+F)F)-F. 6%F1F*F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "qzeilb([b],[ \+ ],q,q,f(n),0,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?qzeilb:~computin g~P,~R1~and~R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,time=.33e-1G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%Fqzeilb:~computing~maximal~degree~of~ PG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,time=.83e-1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:qzeilb:~solving~equationsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,time=.83e-1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&, &%\"qG!\"\"*&%\"bG\"\"\")F&,&%\"nGF*F*F*F*F*F*-%%qfacG6%F)F&F-F*F**(-F /6%F&F&F-F*F&F*,&F'F*F)F*F*F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "qzeilb([q^(-n)],[ ],q,q,f(n),1,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?qzeilb:~computing~P,~R1~and~R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.183G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%Fqzeilb:~comput ing~maximal~degree~of~PG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.23 3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:qzeilb:~solving~equationsG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.250G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Write~the~input~series~asG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"nG-%$SumG6$-F%6$F'%\"kG/F-;\"\"!F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&Then~G" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$/-%$SumG6$,&-%\"fG6$%\"nG%\"kG\"\"\"*&*(,&%\"qG!\"\")F1F+F-F-,&* &F1F-&%\"aG6#\"\"!F-F-F-F2F--F)6$,&F+F-F-F2F,F-F-F3F2F-/F,;F9%\"mG,$*& *(,&F2F-*&)F1F?F-F1F-F-F-,(*&F6F-F3F-F-*(FEF-F1F-F6F-F2FEF-F--F)6$F+,& F?F-F-F-F-F-*&FEF-,&F3F-F-F2F-F2F22F9F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.867G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Hence~f(n)~equ alsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&*(,&%\"qG!\"\")F'%\"nG\"\" \"F+,&*&F'F+&%\"aG6#\"\"!F+F+F+F(F+-%\"fG6#,&F*F+F+F(F+F+F)F(F(2F1F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "qzeilb([q^(-n),b,q*c],[q* b,c],q,q,f(n),1,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?qzeilb:~compu ting~P,~R1~and~R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.450G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%Fqzeilb:~computing~maximal~degree~of~ PG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.850G" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%:qzeilb:~solving~equationsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.900G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Write ~the~input~series~asG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"n G-%$SumG6$-F%6$F'%\"kG/F-;\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% &Then~G" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$/-%$SumG6$,&-%\"fG6$%\"nG% \"kG\"\"\"*&*(,&)%\"qGF+F-F-!\"\"F-%\"bGF--F)6$,&F+F-F-F3F,F-F-,&F3F-* &F4F-F1F-F-F3F3/F,;\"\"!%\"mG,$*&*,F1F-,&F3F-*&)F2F=F-F2F-F-F-,&*(F4F- FCF-F2F-F-F-F3F-,.*&F1F-%\"cGF-F-F1F3*(FHF-F1F-F2F-F3F2F-**FHF-FCF-F2F -F1F-F-*(FHF-FCF-F2F-F3F--F)6$F+,&F=F-F-F-F-F-*.F2F-F8F-,&F2F3F1F-F-FC F-,&F3F-FKF-F-F0F-F3F32F-F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time= 1.850G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Hence~f(n)~equalsG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$*&*(,&)%\"qG%\"nG\"\"\"F)!\"\"F)%\"bGF )-%\"fG6#,&F(F)F)F*F)F),&F*F)*&F+F)F&F)F)F*2F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "qzeilb([q^(-n),b],[c],q,z,f(n),2,t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%?qzeilb:~computing~P,~R1~and~R2G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%*time=.250G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%Fqzeilb:~computing~maximal~degree~of~PG" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%*time=.383G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# %:qzeilb:~solving~equationsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*time =.400G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Write~the~input~series~asG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"nG-%$SumG6$-F%6$F'%\"k G/F-;\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&Then~G" }}{PARA 12 " " 1 "" {XPPMATH 20 "6$/-%$SumG6$,(-%\"fG6$%\"nG%\"kG\"\"\"*&*&,.*())% \"qGF+\"\"#F-%\"cGF-F4F-F-*&F2F-F6F-F-*&)F4F5F-F3F-!\"\"*(F6F-F3F-F4F- F:**F3F-%\"zGF-%\"bGF-F4F-F:*&F=F-F9F-F-F--F)6$,&F+F-F-F:F,F-F-*(F3F-F 4F-,&*&F3F-F6F-F-F4F:F-F:F:*&*(,&*(F=F-F>F-F4F-F:FEF-F-,&F4F:F3F-F--F) 6$,&F+F-F5F:F,F-F-*(F4F-F3F-FDF-F:F-/F,;\"\"!%\"mG,$*&**,&F:F-*&)F4FRF -F4F-F-F-,&*&F6F-FXF-F-F-F:F-F4F--F)6$F+,&FRF-F-F-F-F-*&,&F3F-F-F:F-FD F-F:F:2F-F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=1.066G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Hence~f(n)~equalsG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$,&*&*&,.*())%\"qG%\"nG\"\"#\"\"\"%\"cGF-F*F-F-*&F(F-F.F -F-*&)F*F,F-F)F-!\"\"*(F.F-F)F-F*F-F2**F)F-%\"zGF-%\"bGF-F*F-F2*&F5F-F 1F-F-F--%\"fG6#,&F+F-F-F2F-F-*(F)F-F*F-,&*&F)F-F.F-F-F*F2F-F2F-*&*(,&* (F5F-F6F-F*F-F2F>F-F-,&F*F2F)F-F--F96#,&F+F-F,F2F-F-*(F*F-F)F-F=F-F2F2 2F-F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "qzeilb([a^2,q*a,-q *a,b,c,d,a^4*q^(n+1)/b/c/d,q^(-n)]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "[a,-a,a^2*q/b,a^2*q/c,a^2*q/d,b*c*d*a^(-2)*q^(-n),a^2*q^(n+1)],q,q ,f(n),1,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?qzeilb:~computing~P,~ R1~and~R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=1.500G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%Fqzeilb:~computing~maximal~degree~of~PG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=4.200G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:qzeilb:~solving~equationsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+time=4.217G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Writ e~the~input~series~asG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\" nG-%$SumG6$-F%6$F'%\"kG/F-;\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# %&Then~G" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$/-%$SumG6$,&-%\"fG6$%\"nG% \"kG\"\"\"*&*&,B*&)%\"aG\"\")F-))%\"qGF+\"\"%F-F-**)F3\"\"'F-)F6\"\"$F -%\"dGF-%\"bGF-!\"\"**F:F-FF-%\"cGF-F@*&F:F-FF-)F6FHF-F-**FFF-FIF-F>F-F?F-F-**FFF-FIF -FBF-F?F-F-*,FFF-F?F-)FBFHF-F>F-FIF-F-*,FFF-F?F-FBF-)F>FHF-FIF-F-**FFF -FIF-F>F-FBF-F-*,)F3FHF-FGF-FBF-F>F-F6F-F@*,FRF-FGF-FMF-FOF-F6F-F@*,FR F-F?F-FMF-F>F-F6F-F@*,FRF-F?F-FBF-FOF-F6F-F@*(FGF-FMF-FOF-F-F--F)6$,&F +F-F-F@F,F-F-*&,2FCF-*(FFF-FIF-FBF-F@*(FFF-FIF-F?F-F@*(FFF-FIF-F>F-F@* *FRF-F6F-F>F-F?F-F-**FRF-F6F-F>F-FBF-F-**FRF-F6F-FBF-F?F-F-*(F?F-FBF-F >F-F@F-,&*&FRF-F6F-F-F\\oF@F-F@F@/F,;\"\"!%\"mG,$*&*2,&F@F-*&)F7FboF-F 7F-F-F-,&*(FhoF-F7F-FRF-F-F?F@F-,&FjoF-FBF@F-,&FjoF-F>F@F-,&**F6F-FhoF -F7F-FRF-F-F-F@F-F6F-,&*&FFF-FIF-F-F\\oF@F--F)6$F+,&FboF-F-F-F-F-*4F7F -,&F6F-F-F@F-,&F\\oF@**FFF-F6F-FhoF-F7F-F-F-,&F@F-*(F3F-FhoF-F7F-F-F-, &F-F-FipF-F-FhoF-,&F^oF-F?F@F-,&F^oF-FBF@F-,&F^oF-F>F@F-F@F@2FaoF+" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%,time=12.517G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Hence~f(n)~equalsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 $*&*,,&!\"\"\"\"\"*&)%\"aG\"\"#F')%\"qG%\"nGF'F'F',&F(F'*&%\"bGF'%\"cG F'F&F',&F(F'*&%\"dGF'F1F'F&F',&F(F'*&F5F'F2F'F&F'-%\"fG6#,&F.F'F'F&F'F '**,&F(F'F1F&F',&F(F'F2F&F',&F(F'F5F&F',&F(F'*(F1F'F2F'F5F'F&F'F&2\"\" !F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Hence~f(n)~equalsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&**-%%qfacG6%*&*&%\"qG\"\"\")%\"aG\"\"#F+F+ *&%\"bGF+%\"cGF+!\"\"F*%\"nGF+-F&6%*&F*F+F,F+F*F3F+-F&6%*&*&F*F+F,F+F+ *&%\"dGF+F1F+F2F*F3F+-F&6%*&*&F*F+F,F+F+*&F " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10 0 0" 5 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }