{VERSION 5 0 "IBM INTEL NT" "5.0" }
{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 271 "" 1 12 0 0 0 0 0 2 2 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 1 }1 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "
" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 
0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 
1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 
0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Bullet \+
Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 
0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 
1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }
{PSTYLE "" 18 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 }2 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {SECT 1 {PARA 256 "" 0 "" {TEXT -1 31 "Chapter 3\n\nVariables \+
and Names\n" }}{PARA 0 "" 0 "" {TEXT 271 31 "\251 Copyright 2003 by An
dr\351 Heck." }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 270 2 "1." }{TEXT -1 
52 " What is the difference in the use of the variables " }{XPPEDIT 
18 0 "a" "6#%\"aG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "b" "6#%\"bG" }
{TEXT -1 7 " in\n   " }{TEXT 0 44 "> a := 'a';   b := 'b';   a := b;  \+
 b := 10;" }{TEXT -1 8 "\nand\n   " }{TEXT 0 44 "> a := 'a';   b := 'b
';   b := 10;   a := b;" }{TEXT -1 213 "\nCan you add one extra assign
ment at the end of the sentence below, so that the total effect of car
rying out the instructions on the line is the same as the result of en
tering the first of the above sentences?\n   " }{TEXT 0 34 "> a := 'a'
;   b := 'b';   b := 10;" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 
57 "After executing the first command sequence, the variable " }{TEXT 
0 1 "a" }{TEXT -1 33 " evaluates to the same value as  " }{TEXT 0 1 "b
" }{TEXT -1 42 " does, no matter what value you assign to " }{TEXT 0 
1 "b" }{TEXT -1 106 " later on during the Maple session. After executi
ng the other command sequence, if we change the value of " }{TEXT 0 1 
"b" }{TEXT -1 2 ", " }{TEXT 0 1 "a" }{TEXT -1 66 " continues to evalua
te to 10, because, at the time of assignment, " }{TEXT 0 1 "a" }{TEXT 
-1 28 " only got the value to what " }{TEXT 0 1 "b" }{TEXT -1 26 " eva
luated at that moment." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "res
tart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "a := 'a';   b := '
b';   a := b;   b := 10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"aG%\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"
#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a, b;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$\"#5F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "b := 20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a, b;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$\"#?F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "a := 'a';  \+
 b := 'b';   b := 10;   a := b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"aGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"bG\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG
\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a, b;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$\"#5F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "b := 20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#?" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a, b;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"#5\"#?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "The as
signment at the end of the sentence can be " }{TEXT 0 8 "a := 'b'" }
{TEXT -1 71 ". The effect of using the aprostrophes is that Maple does
 not evaluate " }{TEXT 0 1 "b" }{TEXT -1 28 " as 10, but as the variab
le " }{TEXT 0 1 "b" }{TEXT -1 42 " itself. Everytime we change the val
ue of " }{TEXT 0 1 "b" }{TEXT -1 2 ", " }{TEXT 0 1 "a" }{TEXT -1 42 " \+
will automaticaly evaluate to this value." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 44 "a := 'a';   b := 'b';   b := 10;   a := 'b';" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"bGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#5" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"aG%\"bG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "a, b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#5F#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "b := 20;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"bG\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 
"a, b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#?F#" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 256 2 "2.
" }{TEXT -1 82 " Explain in detail what happens when you enter the fol
lowing commands in sequence\n" }{TEXT 0 97 "  > p := 'p' ; q := 'q' ;
\n  > 7 * 5 ;\n  > p = 10 ;\n  > q : 3 ;\n  > %%% ; %%% ; %%% ;\n  > p
 ; q ;\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p := 'p' ; q := 'q' ;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pGF$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"qGF$" }}}{PARA 0 "" 0 "" {TEXT -1 41 "First, we simply uneva
lute the variables " }{TEXT 0 1 "p" }{TEXT -1 5 " and " }{TEXT 0 1 "q
" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "7 * 5 ;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#N" }}}{PARA 0 "" 0 "" {TEXT -1 
43 "Then Maple shows the result of the product " }{TEXT 0 8 "7*5 = 35
" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "p = 10 ;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"pG\"#5" }}}{PARA 0 "" 0 "" 
{TEXT -1 25 "Above, we write down the " }{TEXT 257 8 "equation" }
{TEXT -1 10 " in which " }{TEXT 0 1 "p" }{TEXT -1 52 " is equal to 10,
 but we do not assign that value to " }{TEXT 0 1 "p" }{TEXT -1 1 "." }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "q : 3 ;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 26 "We omitted the o
utput for " }{TEXT 0 1 "q" }{TEXT -1 74 " (which has no value) because
 of the colon, and we showed 3 as output for " }{TEXT 0 2 "3;" }{TEXT 
-1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "%%% ; %%% ; %%% \+
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"pG\"#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%\"qG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}
{PARA 0 "" 0 "" {TEXT -1 65 "Here, Maple shows the result of the third
 last executed command (" }{TEXT 20 6 "p = 10" }{TEXT -1 88 "). Then M
aple shows the third last result  taking into account that the last on
e now is " }{TEXT 0 4 "%%%;" }{TEXT -1 12 " (returning " }{TEXT 20 1 "
q" }{TEXT -1 32 "), and after that Maple returns " }{TEXT 20 1 "3" }
{TEXT -1 21 " for the same reason." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "p ; q ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"pG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"qG" }}}{PARA 0 "" 0 "" {TEXT -1 43 
"Finally, as we did not assign any value to " }{TEXT 0 1 "p" }{TEXT 
-1 5 " and " }{TEXT 0 1 "q" }{TEXT -1 21 ", Maple only returns " }
{TEXT 20 1 "p" }{TEXT -1 5 " and " }{TEXT 20 1 "q" }{TEXT -1 12 " them
selves." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 0 "" 0 "" {TEXT 258 2 "3." }{TEXT -1 66 " Explain the different \+
result of the following Maple commands:\n   " }{TEXT 0 4 "x*y;" }
{TEXT -1 3 ",  " }{TEXT 0 4 "x.y;" }{TEXT -1 1 "," }{TEXT 0 5 " x||y" 
}{TEXT -1 5 " and " }{TEXT 0 4 "x\\y;" }{TEXT -1 2 ".\n" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 4 "x*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"
\"%\"yGF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Here, we have a prod
uct of the variables " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 5 " and \+
" }{XPPEDIT 18 0 "y" "6#%\"yG" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 5 "x||y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#xyG" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x\\y;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%#xyG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Both expr
essions above, concatenate the variables " }{XPPEDIT 18 0 "x" "6#%\"xG
" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "y" "6#%\"yG" }{TEXT -1 1 "." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x.y;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%\".G6$%\"xG%\"yG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
45 "Here, the dot is an unknown operator to Maple" }}}}{SECT 1 {PARA 
0 "" 0 "" {TEXT 259 2 "4." }{TEXT -1 133 " Describe in detail the diff
erence between the two Maple sessions below (e.g., by drawing pictures
 of the internal data structures).\n" }{TEXT 0 50 "  > a := b;\n  > b \+
:= 3;\n  > a;\n  > b := 4;\n  > a;\n" }{TEXT -1 4 "and\n" }{TEXT 0 50 
"  > b := 3;\n  > a := b;\n  > a;\n  > b := 4;\n  > a;\n" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 7 "a := b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG%\"
bG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b := 3;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"bG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b := 4;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"bG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{PARA 0 "" 0 "" 
{TEXT -1 13 "The value of " }{TEXT 0 1 "a" }{TEXT -1 13 " is equal to \+
" }{TEXT 0 1 "b" }{TEXT -1 5 " and " }{TEXT 0 1 "a" }{TEXT -1 27 " eva
luates to the value of " }{TEXT 0 1 "b" }{TEXT -1 54 ". The next two s
tatements and results illustrate this." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "eval(a,1), eval(b,1); # values of a and b" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$%\"bG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "eval(a,2); # two-level evaluation" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 27 "Now we change \+
the value of " }{TEXT 0 1 "b" }{TEXT -1 41 ". Since we have not change
d the value of " }{TEXT 0 1 "a" }{TEXT -1 25 ", the full evaluation of
 " }{TEXT 0 1 "a" }{TEXT -1 40 " will still result in the evaluation o
f " }{TEXT 0 1 "b" }{TEXT -1 25 ", i.e., the new value of " }{TEXT 0 
1 "b" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b := \+
4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "Next w
e discuss the second Maple session in which the assignment of " }
{TEXT 0 4 "b:=3" }{TEXT -1 29 " comes before the assignment " }{TEXT 
0 4 "a:=b" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "b := 3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"$" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 7 "a := b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"
\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "The val
ue of  " }{TEXT 0 1 "a" }{TEXT -1 41 " is equal to 3 because in the as
signment " }{MPLTEXT 1 0 7 "a := b;" }{TEXT -1 92 ", the righ-hand sid
e first evaluates to the integer 3. We verify this in the next stateme
nt." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"$" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 11 "eval(a, 1);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 27 "If you change the value o
f " }{TEXT 0 1 "b" }{TEXT -1 42 ", this has no effect on the evaluatio
n of " }{TEXT 0 1 "a" }{TEXT -1 118 " because this variable refers to \+
the integer 3 and has no kowledge about the way it was once created vi
a the variable " }{TEXT 0 1 "b" }{TEXT -1 1 ";" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "b := 4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG
\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 260 2 "5." }{TEXT -1 91 " Predict
 the results of entering the following commands and check your answers
 with Maple.\n" }{TEXT 0 75 "  > X1 := 5;  j := 1;\n  > X || j;\n  > '
X || j';\n  > 'X' || j;\n  > `X || j`;" }{TEXT -1 1 "\n" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "X1 := 5; j:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%#X1G\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"jG\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "X||j;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 26 "This command concatenates
 " }{TEXT 0 1 "X" }{TEXT -1 25 " with the evaluation of  " }{TEXT 0 1 
"j" }{TEXT -1 11 ".  Because " }{TEXT 0 1 "j" }{TEXT -1 70 " has recei
ved the value 1, Maple shows the evaluation of the variable " }{TEXT 
0 2 "X1" }{TEXT -1 44 ", which has received the value 5 previously." }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "'X||j';" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#(%\"XG%\"jG" }}}{PARA 0 "" 0 "" {TEXT -1 85 "Because th
e expression is surrounded by apostrophes, Maple only peels off the qu
otes." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "`X`||j;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 97 "The left
 quotes (reverse apostrophes) have no effect on the evaluation: the co
mmand concatenates " }{TEXT 0 1 "X" }{TEXT -1 25 " with the evaluation
 of  " }{TEXT 0 1 "j" }{TEXT -1 11 ".  Because " }{TEXT 0 1 "j" }
{TEXT -1 70 " has received the value 1, Maple shows the evaluation of \+
the variable " }{TEXT 0 2 "X1" }{TEXT -1 44 ", which has received the \+
value 5 previously." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "`X||j`
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%X|gr|grjG" }}}{PARA 0 "" 0 "" 
{TEXT -1 109 "Here, the left quotes (reverse apostrophes) mark a name \+
with special characters, viz., the two vertical bars " }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 264 2 
"6." }{TEXT -1 28 " Suppose that the variables " }{TEXT 0 2 "v1" }
{TEXT -1 2 ", " }{TEXT 0 2 "v2" }{TEXT -1 6 ", and " }{TEXT 0 2 "v3" }
{TEXT -1 103 " are bound. Why can't you unassign these variables by th
e following repetition statement (or do-loop)?\n" }{TEXT 0 37 "   > fo
r i to 3 do v||i := 'v||i' od:" }{TEXT -1 68 "\nFind two ways for havi
ng the intended unassignment done in a loop.\n" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 26 "v1 := 1; v2 := 2; v3 := 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#v1G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v2G\"\"#" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#v3G\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "for i to 3 do v||i := 'v||i' od;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v1G(%\"vG%\"iG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#v2G(%\"vG%\"iG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v3G(%\"vG%\"iG" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "v3;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%#v4G" }}}{PARA 0 "" 0 "" {TEXT -1 27 "When Maple tries
 to assign " }{TEXT 0 4 "v||i" }{TEXT -1 4 " as " }{TEXT 0 6 "'v||i'" 
}{TEXT -1 174 ", it only does the intended concatentation in the left-
hand side of the statement. The right-hand side of it envolves apostro
phes which are peeled off in the evaluation. So, " }{TEXT 0 2 "v1" }
{TEXT -1 2 ", " }{TEXT 0 2 "v2" }{TEXT -1 5 " and " }{TEXT 0 2 "v3" }
{TEXT -1 17 " are assigned as " }{TEXT 0 4 "v||i" }{TEXT -1 38 ". Then
, when you enter the expression " }{TEXT 0 2 "v3" }{TEXT -1 18 ", it e
valuates to " }{TEXT 0 2 "v4" }{TEXT -1 28 " because after the for-loo
p " }{TEXT 0 1 "i" }{TEXT -1 56 " has the value 4 (condition for quitt
ing the procedure)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "
" {TEXT 261 15 "First solution:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "v1 := 1;
 v2 := 2; v3 := 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G\"\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v2G\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v3G\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
45 "for i to 3 do \n  v||i := evaln(v||i) \nend do;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#v1GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v2GF$
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v3GF$" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 11 "v1;\nv2;\nv3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#%#v1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v2G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%#v3G" }}}{PARA 15 "" 0 "" {TEXT 262 16 "Second solutio
n:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "v1 := 1; v2 := 2; v3 := 3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v2G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v3G\"
\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "for i to 3 do \n  v|
|i := cat(v,i)\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1GF$" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v2GF$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v3GF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "
v1;\nv2;\nv3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v1G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%#v2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v3G" }}
}{PARA 0 "" 0 "" {TEXT 263 26 "Alternative solutions via " }{TEXT 0 8 
"unassign" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "v1 := 1; v2 := 2; v3 := 3;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v2G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v3G\"
\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "for i to 3 do \n  un
assign(evaln(v||i))\nend do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "v1;\nv2;\nv3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v1G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%#v2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v
3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "v1 := 1; v2 := 2; v3 := 3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v2G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v3G\"
\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "for i to 3 do \n  un
assign(cat(v,i))\nend do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
11 "v1;\nv2;\nv3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v1G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%#v2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#v
3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 
"" 0 "" {TEXT 265 2 "7." }{TEXT -1 63 " Explain what goes wrong when y
ou enter the following commands\n" }{TEXT 0 33 "  > gcd( x^2-1, x-1, x
 );\n  > x;\n" }}{PARA 0 "" 0 "" {TEXT -1 26 "The third argument of th
e " }{TEXT 0 3 "gcd" }{TEXT -1 130 " procedure must be a variable whic
h will be assigned the quotient of the first argument divided by the c
omputed gcd. In our case, " }{TEXT 0 1 "x" }{TEXT -1 13 " is assigned \+
" }{TEXT 0 3 "x+1" }{TEXT -1 47 ". So, we end up with a recursive defi
nition of " }{TEXT 0 1 "x" }{TEXT -1 93 ". When you enter x, infinite \+
recursive evaluation (until Maple runs short of memory) occurs.\n" }}}
{SECT 1 {PARA 0 "" 0 "" {TEXT 266 2 "8." }{TEXT -1 122 " Carry out the
 following instructions, predict the Maple results and compare these w
ith the actual answers of the system.\n" }{TEXT 0 5 "  > i" }{TEXT -1 
0 "" }{TEXT 0 231 ":= 3:  x:= 4:\n  > sum( x^i, i=1..5 );\n  > sum( x^
i, 'i'=1..5 );\n  > sum( 'x^i', 'i'=1..5 );\n  > sum( 'x'^i, 'i'=1..5 \+
);\n  > sum( x^'i', 'i'=1..5 );\n  > sum( 'x'^`i`, 'i'=1..5 );\n  > su
m( `x^i`, 'i'=1..5 );\n  > 'sum( x^i, i=1..5 )';" }{TEXT -1 1 "\n" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 15 "i := 3: x := 4:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "sum( x^i, i = 1..5);" }}{PARA 8 "" 1 "" {TEXT -1 
96 "Error, (in sum) summation variable previously assigned, second arg
ument evaluates to 3 = 1 .. 5\n" }}}{PARA 0 "" 0 "" {TEXT -1 68 "Here,
 Maple returns an error message because the summation variable " }
{TEXT 0 1 "i" }{TEXT -1 142 " has been previously assigned the value 3
. So, Maple evaluates the summation index to 3 and because of this it \+
cannot carry out the summation." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 22 "sum( x^i, 'i' = 1..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$?
$" }}}{PARA 0 "" 0 "" {TEXT -1 101 "Now, Maple does the summation beca
use the apostrophes delay the evaluation of the summation variable " }
{TEXT 0 1 "i" }{TEXT -1 8 ". Since " }{TEXT 0 1 "x" }{TEXT -1 35 " has
 been assigned the value 4 and " }{TEXT 0 1 "i" }{TEXT -1 33 " the val
ue 3, the first argument " }{TEXT 0 3 "x^i" }{TEXT -1 81 " evaluates t
o 64. What we get is the summation of five terms 64, which gives 320.
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum( 'x^i', 'i' = 1..5);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%k8" }}}{PARA 0 "" 0 "" {TEXT 
-1 138 "The summation process has two distinct steps: in the first one
, Maple creates the expressions to be summed varying the summation var
iable " }{TEXT 0 1 "i" }{TEXT -1 97 ". In this case, because of the de
lay of evaluation caused by the apostrophes, it returns the sum " }}
{PARA 0 "" 0 "" {XPPEDIT 18 0 "x+x^2+x^3+x^4+x^5" "6#,,%\"xG\"\"\"*$F$
\"\"#F%*$F$\"\"$F%*$F$\"\"%F%*$F$\"\"&F%" }{TEXT -1 39 ", without subs
tituting the value 4 for " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 118 
". Then, the second part consists on evaluating the intermediate expre
ssion and yields the result for this evaluation: " }{XPPEDIT 18 0 "4+4
^2+4^3+4^4+4^5=1364" "6#/,,\"\"%\"\"\"*$F%\"\"#F&*$F%\"\"$F&*$F%F%F&*$
F%\"\"&F&\"%k8" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "sum( 'x'^i, 'i' = 1..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&
\"\"&\"\"\")%\"xG\"\"$F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 11 "Maple sums
 " }{XPPEDIT 18 0 "x^3" "6#*$%\"xG\"\"$" }{TEXT -1 82 " five times bec
ause of the apostrophes (the first argument evaluates to a summand " }
{XPPEDIT 18 0 "x^3" "6#*$%\"xG\"\"$" }{TEXT -1 34 " because of the apo
strophs around " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 2 ")." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum( x^'i', 'i' = 1..5);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%k8" }}}{PARA 0 "" 0 "" {TEXT -1 11 
"Maple sums " }{XPPEDIT 18 0 "4+4^2+4^3+4^4+4^5" "6#,,\"\"%\"\"\"*$F$
\"\"#F%*$F$\"\"$F%*$F$F$F%*$F$\"\"&F%" }{TEXT -1 35 " because of the a
postrophes around " }{TEXT 0 1 "i" }{TEXT -1 23 " in the first argumen
t." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sum( 'x'^`i`, 'i' = 1.
.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"&\"\"\")%\"xG\"\"$F&F&
" }}}{PARA 0 "" 0 "" {TEXT -1 122 "The left quatoes (reverse apostroph
es) around the i in the first argument have no effect. So we get the s
ame result as in " }{TEXT 0 23 "sum( 'x'^i, 'i'=1..5 );" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum( `x^i`, 'i' = 1..5);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"&\"\"\"%$x^iGF&F&" }}}{PARA 0 "" 0 "
" {TEXT -1 20 "Maple sums the noun " }{TEXT 0 3 "x^i" }{TEXT -1 95 " f
ive times, because the left quates (reverse apostrophes) mark a name w
ith special characters." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "'
sum( x^i, i = 1..5)';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sumG6$)%\"
xG%\"iG/F(;\"\"\"\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 112 "Because of th
e apostrophes around the whole expression, Maple only peels off these \+
quotes in the evalution step." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 267 2 "9." }{TEXT -1 39 " Suc
cessively transform the expression " }{XPPEDIT 18 0 "a+b+c" "6#,(%\"aG
\"\"\"%\"bGF%%\"cGF%" }{TEXT -1 6 " into " }{XPPEDIT 18 0 "a*b*c" "6#*
(%\"aG\"\"\"%\"bGF%%\"cGF%" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "[a,b,
c]" "6#7%%\"aG%\"bG%\"cG" }{TEXT -1 2 ".\n" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
6 "a+b+c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\"\"\"%\"bGF%%\"cG
F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "convert(%, `*`);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"aG\"\"\"%\"bGF%%\"cGF%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "convert(%, list);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7%%\"aG%\"bG%\"cG" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT 268 3 "10." }
{TEXT -1 55 " Use Maple to find the continued fraction expansion of " 
}{XPPEDIT 18 0 "sqrt(2)" "6#-%%sqrtG6#\"\"#" }{TEXT -1 2 ", " }
{XPPEDIT 18 0 "e-1" "6#,&%\"eG\"\"\"F%!\"\"" }{TEXT -1 23 ", and the g
olden ratio " }{XPPEDIT 18 0 "(1+sqrt(5))/2" "6#*&,&\"\"\"F%-%%sqrtG6#
\"\"&F%F%\"\"#!\"\"" }{TEXT -1 16 ", respectively.\n" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "with(numtheory):" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warn
ing, the protected name order has been redefined and unprotected\n" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "cfrac(sqrt(2));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"F$*&F$F$,&\"\"#F$*&F$F$,&F'F$*&F$F$,
&F'F$*&F$F$,&F'F$*&F$F$,&F'F$*&F$F$,&F'F$*&F$F$,&F'F$*&F$F$,&F'F$*&F$F
$,&F'F$*&F$F$,&F'F$%$...GF$!\"\"F$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 16 "cfrac(exp(1)-1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"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$,&F$F$*&F$F$,&
\"\"'F$*&F$F$,&F$F$*&F$F$,&F$F$%$...GF$!\"\"F$F=F$F=F$F=F$F=F$F=F$F=F$
F=F$F=F$F=F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "cfrac(exp(1
)-1, 50, 'quotients');    " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7V\"\"\"
F$\"\"#F$F$\"\"%F$F$\"\"'F$F$\"\")F$F$\"#5F$F$\"#7F$F$\"#9F$F$\"#;F$F$
\"#=F$F$\"#?F$F$\"#AF$F$\"#CF$F$\"#EF$F$\"#GF$F$\"#IF$F$\"#KF$F$\"#M%$
...G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "cfrac((1+sqrt(5))/2
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"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$*&F$F$,&F$F$*&F$F$,&
F$F$*&F$F$,&F$F$*&F$F$,&F$F$%$...GF$!\"\"F$F:F$F:F$F:F$F:F$F:F$F:F$F:F
$F:F$F:F$" }}}{PARA 0 "" 0 "" {TEXT -1 184 "The general structures of \+
the above continued fraction expansions are obvious. In fact, for the \+
first and last number Maple can determine the period of the continued \+
fraction expansion" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "cfrac(
sqrt(2), 'periodic');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"F$*&F
$F$,&\"\"#F$*&F$F$,&F'F$%$...GF$!\"\"F$F+F$" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 40 "cfrac(sqrt(2), 'periodic', 'quotients');" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7$7#\"\"\"7#\"\"#" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 33 "cfrac((1+sqrt(5))/2, 'periodic');" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&\"\"\"F$*&F$F$,&F$F$%$...GF$!\"\"F$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "cfrac((1+sqrt(5))/2, 'periodic', 'q
uotients');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7\"7#\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }