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{SECT 0 {SECT 1 {PARA 256 "" 0 "" {TEXT -1 57 "Chapter 6\n\nInternal D
ata Representation and Substitution\n" }}{PARA 0 "" 0 "" {TEXT 270 31 
"\251 Copyright 2003 by Andr\351 Heck." }}}{SECT 1 {PARA 0 "" 0 "" 
{TEXT 263 2 "1." }{TEXT -1 75 " Describe in detail the internal repres
entation in Maple of the polynomial " }{XPPEDIT 18 0 "2*x*(y^2+1)^2" "
6#*(\"\"#\"\"\"%\"xGF%,&*$%\"yGF$F%F%F%F$" }{TEXT -1 210 ". Draw the c
orresponding directed acyclic graph (DAG) and the representation tree.
 Write down all subexpressions that are recognized as such by Maple. E
nlarge your trust in your answer by use of the procedures " }{TEXT 0 
8 "whattype" }{TEXT -1 2 ", " }{TEXT 0 4 "nops" }{TEXT -1 6 ", and " }
{TEXT 0 2 "op" }{TEXT -1 27 ". By use of the procedures " }{TEXT 0 9 "
dismantle" }{TEXT -1 2 ", " }{TEXT 0 9 "addressof" }{TEXT -1 2 ", " }
{TEXT 0 7 "pointto" }{TEXT -1 2 ", " }{TEXT 0 11 "disassemble" }{TEXT 
-1 6 ", and " }{TEXT 0 8 "assemble" }{TEXT -1 39 " you can completely \+
check your answer.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta
rt;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "poly := 2*x*(y^2+1)^
2;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%%polyG,$*(\"\"#\"\"\"%\"xGF(),&*$)%\"yGF'F(F(F(F(F'F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "whattype(poly);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%\"*G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "n
ops(poly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "op(poly);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6%\"\"#%\"xG*$),&*$)%\"yGF#\"\"\"F+F+F+F#F+" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "op(3, poly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
*$),&*$)%\"yG\"\"#\"\"\"F*F*F*F)F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "op(%%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$,&*$)%\"yG\"\"#\"\"\"F(F(F(F'" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 11 "op(1, %%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*$)%\"yG\"\"#\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"+G" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "op(%%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$*$)%\"yG\"\"#\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "op(1, %%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"
yG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 7 "op(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"yG\"
\"#" }}}{PARA 0 "" 0 "" {TEXT -1 42 "So the representation tree look a
s follows" }}{PARA 0 "" 0 "" {TEXT 257 230 "  *--|--|--|\n     |  |  |
\n     2  x  ^--|--------------|\n              |              |\n    \+
          +--|--------|  2\n                 |        |      \n       \+
          ^--|--|  1\n                    |  |\n                    y \+
 2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "The
 real internal data structure as a DAG can be found as follows:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dismantle(poly);" }}{PARA 6 
"" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 6 "SUM(3)" }}{PARA 6 
"" 1 "" {TEXT -1 10 "   PROD(5)" }}{PARA 6 "" 1 "" {TEXT -1 16 "      \+
NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 1" }}
{PARA 6 "" 1 "" {TEXT -1 12 "      SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 
16 "         PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 22 "            NAME(
4): y" }}{PARA 6 "" 1 "" {TEXT -1 24 "            INTPOS(2): 2" }}
{PARA 6 "" 1 "" {TEXT -1 21 "         INTPOS(2): 1" }}{PARA 6 "" 1 "" 
{TEXT -1 21 "         INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 21 "   \+
      INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 2
" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INTPOS(2): 2" }}{PARA 6 "" 1 "" 
{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 85 "For example, it is clear
 that the internal data structure at top level is actually a " }{TEXT 
258 3 "SUM" }{TEXT -1 26 " data vector with summand " }{XPPEDIT 18 0 "
x*(y^2+1)^2" "6#*&%\"xG\"\"\"*$,&*$%\"yG\"\"#F%F%F%F*F%" }{TEXT -1 39 
" and coefficient 2. Let us verify this:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "addressof(poly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"(C*3E" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "d := disassemble
(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG6%\"#;\")g)=S\"\"\"&" }}
}{PARA 0 "" 0 "" {TEXT 0 1 "d" }{TEXT -1 6 " is a " }{TEXT 259 3 "SUM
" }{TEXT -1 13 " data vector." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "kernelopts(dagtag=d[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$SU
MG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "pointto(d[2]);  # sum
mand" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\"),&*$)%\"yG\"\"#F
%F%F%F%F+F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "pointto(d[3]
);  # coefficient" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{PARA 
0 "" 0 "" {TEXT -1 26 "You could go on like this:" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 23 "e := disassemble(d[2]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"eG6'\"#9\"(K8e#\"\"$\")[(>S\"\"\"&" }}}{PARA 0 "" 
0 "" {TEXT 0 1 "e" }{TEXT -1 6 " is a " }{TEXT 260 4 "PROD" }{TEXT -1 
13 " data vector." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "kernelo
pts(dagtag=e[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%PRODG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pointto(e[2]);  # base" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "pointto(e[3]);  # exponent" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "po
intto(e[4]);  # base" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"yG\"\"
#\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "pointto(e[
5]);  # exponent" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f := disassemble(e[4]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"fG6'\"#;\"(3*3E\"\"$F(F(" }}}{PARA 0 "" 
0 "" {TEXT 0 1 "f" }{TEXT -1 6 " is a " }{TEXT 261 3 "SUM" }{TEXT -1 
13 " data vector." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "kernelo
pts(dagtag=f[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$SUMG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "pointto(f[2]);  # summand" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"yG\"\"#\"\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "pointto(f[3]);  # coefficient" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "pointto(f[4]);  # summand" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "po
intto(f[5]);  # coefficient" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "g := disassemble(f[2]);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG6%\"#9\"(O7e#\"\"&" }}}
{PARA 0 "" 0 "" {TEXT 0 1 "g" }{TEXT -1 6 " is a " }{TEXT 262 4 "PROD
" }{TEXT -1 13 " data vector." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "kernelopts(dagtag=g[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%PR
ODG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pointto(g[2]);  # ba
se" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"yG" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 26 "pointto(g[3]);  # exponent" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{PARA 0 "" 0 "" {TEXT -1 52 "Subexpressions recognized as such by Map
le are: 2,  " }{XPPEDIT 18 0 "x*(y^2+1)^2" "6#*&%\"xG\"\"\"*$,&*$%\"yG
\"\"#F%F%F%F*F%" }{TEXT -1 12 ",   x,  1,  " }{XPPEDIT 18 0 "y^2+1" "6
#,&*$%\"yG\"\"#\"\"\"F'F'" }{TEXT -1 3 ",  " }{XPPEDIT 18 0 "y^2" "6#*
$%\"yG\"\"#" }{TEXT -1 108 ", and  y. You find them by inspection of t
he addresses that show up when you disassemble the subexpressions." }}
}{SECT 1 {PARA 0 "" 0 "" {TEXT 264 2 "2." }{TEXT -1 11 " Transform " }
{XPPEDIT 18 0 "(x+y)^2 + 1/(x+y)" "6#,&*$,&%\"xG\"\"\"%\"yGF'\"\"#F'*&
F'F',&F&F'F(F'!\"\"F'" }{TEXT -1 6 " into " }{XPPEDIT 18 0 "((x+y)^3+1
)/(x+y)" "6#*&,&*$,&%\"xG\"\"\"%\"yGF(\"\"$F(F(F(F(,&F'F(F)F(!\"\"" }
{TEXT -1 17 " and vice versa.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expr := \+
(x+y)^2 + 1/(x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG,&*$),&%
\"xG\"\"\"%\"yGF*\"\"#F*F**&F*F*F(!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 18 "subs(x+y=z, expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*$)%\"zG\"\"#\"\"\"F(*&F(F(F&!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "normal(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*
$)%\"zG\"\"$\"\"\"F)F)F)F)F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "subs(z=x+y,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,
&*$),&%\"xG\"\"\"%\"yGF)\"\"$F)F)F)F)F)F'!\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "expr := %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%%exprG*&,&*$),&%\"xG\"\"\"%\"yGF+\"\"$F+F+F+F+F+F)!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(x+y=z,%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,&*$)%\"zG\"\"$\"\"\"F)F)F)F)F'!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$)%\"zG\"\"#\"\"\"F(*&F(F(F&!\"\"F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "subs(z=x+y,%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$),&%\"xG\"\"\"%\"yGF(\"\"#F(F(*&F(F(F&!\"\"F(" }}}
{PARA 0 "" 0 "" {TEXT -1 51 "Alternatively, expand the expression whil
e keeping " }{XPPEDIT 18 0 "x+y" "6#,&%\"xG\"\"\"%\"yGF%" }{TEXT -1 8 
" intact:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "expand(expr, x+
y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"%\"yGF(\"\"#F
(F(*&F(F(F&!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 0 "" 0 "" {TEXT 265 2 "3." }{TEXT -1 37 " Tranform  \n  \+
                       " }{XPPEDIT 18 0 " x^2+2*x+1+1/(x^2+2*x+1)" "6#
,**$%\"xG\"\"#\"\"\"*&F&F'F%F'F'F'F'*&F'F',(*$F%F&F'*&F&F'F%F'F'F'F'!
\"\"F'" }{TEXT -1 31 " \ninto\n                        " }{XPPEDIT 18 
0 "((x+1)^4+1)/(x+1)^2" "6#*&,&*$,&%\"xG\"\"\"F(F(\"\"%F(F(F(F(*$,&F'F
(F(F(\"\"#!\"\"" }{TEXT -1 25 "       \nand vice versa.\n " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 32 "expr := x^2+2*x+1+1/(x^2+2*x+1);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%exprG,**$)%\"xG\"\"#\"\"\"F**&F)F*F(F*F*F*F**&F*F*
,(F&F**&F)F*F(F*F*F*F*!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "algsubs(x^2+2*x+1=z, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&
\"\"\"F%%\"zG!\"\"F%F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 
"normal(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&\"\"\"F%*$)%\"zG\"
\"#F%F%F%F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(z=
factor(x^2+2*x+1), %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&\"\"\"F%
*$),&%\"xGF%F%F%\"\"%F%F%F%F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "expr := %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%expr
G*&,&\"\"\"F'*$),&%\"xGF'F'F'\"\"%F'F'F'F*!\"#" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "expand(expr, x+1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&\"\"\"F%*$),&%\"xGF%F%F%\"\"#F%!\"\"F%*$F'F%F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "map(normal, %, expanded);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"#\"\"\"F(*&F'F(F&F(F(F(
F(*&F(F(,(F$F(*&F'F(F&F(F(F(F(!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 268 2 "4." }{TEXT 
-1 51 " Explain the result of the following substitution:\n" }{TEXT 0 
22 "   > x^2-x+1/x-1/x^2;\n" }{TEXT -1 56 "                           \+
                             " }{XPPEDIT 18 0 "x^2-x+1/x-1/x^2;" "6#,*
*$%\"xG\"\"#\"\"\"F%!\"\"*&F'F'F%F(F'*&F'F'*$F%F&F(F(" }{TEXT -1 1 "\n
" }{TEXT 0 19 "   > subs(-1=1,%);\n" }{TEXT -1 57 "                   \+
                                      " }{XPPEDIT 18 0 "x^2+2*x+1/x^2
" "6#,(*$%\"xG\"\"#\"\"\"*&F&F'F%F'F'*&F'F'*$F%F&!\"\"F'" }{TEXT -1 1 
"\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "x^2-x+1/x-1/x^2;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,**$)%\"xG\"\"#\"\"\"F(F&!\"\"*&F(F(F&F)F(*&F(F(*$F%F
(F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(-1=1,%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(*&F'F(F&F(F(*&F
(F(*$F%F(!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 125 "Because of Maple's internal representati
on, with the command lines above, we substitute all the occurrences of
 the structure " }{TEXT 266 8 "intneg 1" }{TEXT -1 4 " by " }{TEXT 
267 8 "intpos 1" }{TEXT -1 17 ". So,  the terms " }{XPPEDIT 18 0 "-x" 
"6#,$%\"xG!\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "-1/x^2" "6#,$*&\"
\"\"F%*$%\"xG\"\"#!\"\"F)" }{TEXT -1 17 " turn into x and " }{XPPEDIT 
18 0 "1/x^2" "6#*&\"\"\"F$*$%\"xG\"\"#!\"\"" }{TEXT -1 26 ", respectiv
ely. Moreover, " }{XPPEDIT 18 0 "1/x" "6#*&\"\"\"F$%\"xG!\"\"" }{TEXT 
-1 19 " is represented by " }{XPPEDIT 18 0 "x^(-1)" "6#)%\"xG,$\"\"\"!
\"\"" }{TEXT -1 47 "and the exponent changes  into 1, resulting in " }
{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 29 ". So the final expression is
 " }{XPPEDIT 18 0 "x^2+x+x+1/x^2" "6#,**$%\"xG\"\"#\"\"\"F%F'F%F'*&F'F
'*$F%F&!\"\"F'" }{TEXT -1 8 ", i.e., " }{XPPEDIT 18 0 "x^2+2x+1/x^2" "
6#,(*$%\"xG\"\"#\"\"\"*&F&F'F%F'F'*&F'F'*$F%F&!\"\"F'" }{TEXT -1 1 ".
" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 269 2 "5." }{TEXT -1 38 " Transform
\n                           " }{XPPEDIT 18 0 "((x+1)^10-2*y)/(x+y)^10
+1/(x+y)^9-x/(x+y)^10" "6#,(*&,&*$,&%\"xG\"\"\"F)F)\"#5F)*&\"\"#F)%\"y
GF)!\"\"F)*$,&F(F)F-F)F*F.F)*&F)F)*$,&F(F)F-F)\"\"*F.F)*&F(F)*$,&F(F)F
-F)F*F.F." }{TEXT -1 58 " \ninto\n                                    \+
               " }{XPPEDIT 18 0 "((x+1)^10-y)/(x+y)^10" "6#*&,&*$,&%\"
xG\"\"\"F(F(\"#5F(%\"yG!\"\"F(*$,&F'F(F*F(F)F+" }{TEXT -1 5 " .\n  " }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 58 "expr := ((x+1)^10-2*y)/(x+y)^10\n + 1/(x+y)
^9 - x/(x+y)^10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG,(*&,&*$),
&%\"xG\"\"\"F,F,\"#5F,F,*&\"\"#F,%\"yGF,!\"\"F,,&F+F,F0F,!#5F,*&F,F,*$
)F2\"\"*F,F1F,*&F+F,F2F3F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "subs(\{x+1=a, x+y=b\}, expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
(*&,&*$)%\"aG\"#5\"\"\"F**&\"\"#F*%\"yGF*!\"\"F*%\"bG!#5F**&F*F**$)F/
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