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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 257 25 "SUMalg-symbolic summatio
n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 23 "Loading the packages..." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 70 "Directory below should be the directory where the
 source code file is." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "re
ad(\"SUMalg.txt\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
258 8 "Examples" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "E:=u[n+1
]-u[n];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG,&&%\"uG6#,&%\"nG\"\"
\"F+F+F+&F'6#F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "SUM
alg(E,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#&%\"uG6#,&%\"nG\"\"\"F(F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "E:=2*u[n+3]^2*u[n+2]-u[
n+1]^2*u[n]+u[n+2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG,(*(\"\"#
\"\"\")&%\"uG6#,&%\"nGF(\"\"$F(F'F(&F+6#,&F.F(F'F(F(F(*&)&F+6#,&F.F(F(
F(F'F(&F+6#F.F(!\"\"F0F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"SUMalg(E,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*(\"\"#\"\"\")&%\"u
G6#,&%\"nGF&\"\"$F&F%F&&F)6#,&F,F&F%F&F&F&*(F%F&)F.F%F&&F)6#,&F,F&F&F&
F&F&F.F&F3F&-%$sumG6$,&*&)F3F%F&&F)6#F,F&F&F<F&F,F&" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "E:=expand((n+1)^3*u[n+2]*v[n+1]^5-n^3*u[n
+1]*v[n]^5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG,,*(&%\"uG6#,&%
\"nG\"\"\"\"\"#F,F,)&%\"vG6#,&F+F,F,F,\"\"&F,)F+\"\"$F,F,**F5F,F'F,F.F
,)F+F-F,F,**F5F,F'F,F.F,F+F,F,*&F'F,F.F,F,*(F4F,&F(F1F,)&F06#F+F3F,!\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "SUMalg(E,n);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,**(&%\"uG6#,&%\"nG\"\"\"\"\"#F*F*)&%
\"vG6#,&F)F*F*F*\"\"&F*)F)\"\"$F*F***F3F*F%F*F,F*)F)F+F*F***F3F*F%F*F,
F*F)F*F**&F%F*F,F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "E:=
u[n+2]/u[n+1]^p-u[n+1]/u[n]^p;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
EG,&*&&%\"uG6#,&%\"nG\"\"\"\"\"#F,F,)&F(6#,&F+F,F,F,%\"pG!\"\"F,*&F/F,
)&F(6#F+F2F3F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "SUMalg(E,
n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&&%\"uG6#,&%\"nG\"\"\"\"\"#F)F
))&F%6#,&F(F)F)F)%\"pG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
63 "E:=(u[n+5]+u[n+1])/(u[n+2]+u[n+1])-(u[n+4]+u[n])/(u[n+1]+u[n]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG,&*&,&&%\"uG6#,&%\"nG\"\"\"\"\"
&F-F-&F)6#,&F,F-F-F-F-F-,&&F)6#,&F,F-\"\"#F-F-F/F-!\"\"F-*&,&&F)6#,&F,
F-\"\"%F-F-&F)6#F,F-F-,&F/F-F>F-F7F7" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "SUMalg(E,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,
&&%\"uG6#,&%\"nG\"\"\"\"\"#F+F+&F'6#,&F*F+F+F+F+!\"\"&F'6#,&F*F+\"\"&F
+F+F+*&F%F0F-F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 181 "The form of
 the summand can effect the summation proceedure for expressions which
 contain non-monomial terms in the denominator. Though the result is c
orrect, it may not be optimal." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 37 "E:=1/(u[n+2]+u[n+1])-1/(u[n+1]+u[n]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"EG,&*&\"\"\"F',&&%\"uG6#,&%\"nGF'\"\"#F'F'&F*6#,&F-
F'F'F'F'!\"\"F'*&F'F',&F/F'&F*6#F-F'F2F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "SUMalg(E,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"
\"\"F$,&&%\"uG6#,&%\"nGF$\"\"#F$F$&F'6#,&F*F$F$F$F$!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "19 0 0" 0 }{VIEWOPTS 1 
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