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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 79 "1. Write a Maple program
 that prints the first 10 squares (i.e. 1^2, 2^2, ...)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "for i from 1 to 10 do print (i^2) o
d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#\\" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#k" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
$+\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Or, as a procedure:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "first_squares := proc ()\n  \+
local i:\n\n  for i from 1 to 10 do print (i^2) od;\nend;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%.first_squaresG:6\"6#%\"iGF&F&?(8$\"\"\"F+\"#
5%%trueG-%&printG6#*$F*\"\"#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "first_squares ();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#\\" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#\")" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$+\"" }}}{EXCHG {PARA 257 "" 0 "" 
{TEXT -1 78 "2. Write a Maple program that tests whether two integers \+
are relatively prime." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "r
el_prime := proc (m, n)\n  if gcd(m,n)=1 then print (`Relatively prime
`) else print (`Not relatively prime`) fi;\nend;" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%*rel_primeG:6$%\"mG%\"nG6\"F)F)@%/-%$gcdG6$9$9%\"\"\"
-%&printG6#%1Relatively~primeG-F36#%5Not~relatively~primeGF)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "rel_prime (5,13);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%1Relatively~primeG" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "rel_prime (21, 9);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%5Not~relatively~primeG" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 
115 "3. Write a Maple program that tests whether a number is prime (do
n't use Maple's built in prime testing procedure)." }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 142 "prime_test := proc (n)\n  local i;\n\n  fo
r i from 2 to trunc(sqrt (n)) do\n    if n mod i = 0 then RETURN (fals
e) fi;\n  od;\n  RETURN (true);\nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#>%+prime_testG:6#%\"nG6#%\"iG6\"F*C$?(8$\"\"#\"\"\"-%&truncG6#-%%sq
rtG6#9$%%trueG@$/-%$modG6$F6F-\"\"!-%'RETURNG6#%&falseG-F?6#F7F*F*" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "prime_test(5);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "prime_test(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}
}{EXCHG {PARA 259 "" 0 "" {TEXT -1 121 "4. Check your program from the
 previous question by comparing it with Maple's isprime function for t
he first 100 numbers." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "c
heck := proc ()\n  local i;\n\n  for i from 2 to 100 do\n    if not (i
sprime(i)=prime_test(i)) then RETURN (false) fi;\n  od;\n  RETURN (tru
e);\nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&checkG:6\"6#%\"iGF&F&C
$?(8$\"\"#\"\"\"\"$+\"%%trueG@$4/-%(isprimeG6#F+-%+prime_testGF5-%'RET
URNG6#%&falseG-F96#F/F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 
"check ();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG 
{PARA 260 "" 0 "" {TEXT -1 84 "5. Write a program which, given a piece
 of text, returns the text written backwards." }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 66 "There are many ways to do this.  Here is one way, usin
g recursion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 282 "backwards \+
:= proc (text)\n  local last_letter, all_except_last;\n\n  if length (
text) <= 1 then RETURN (text) fi;\n\n  last_letter := substring (text,
 length(text));\n  all_except_last := substring (text, 1..length(text)
-1);\n  RETURN (cat (last_letter, backwards (all_except_last)));\nend:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "backwards (`Does it wor
k? Of course!`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%9!esruoc~fO~?krow
~ti~seoDG" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 230 "6. Write a progra
m which, given a piece of text, returns a list of the characters occur
ring in the text, along with the number of times they occur, in order \+
of decreasing frequency.  (Eg: given ``eep'', would return (e,2), (p,1
))." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Again, there are many ways
 of doing this.  Here is one way:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 263 "count := proc (text)\n  local counts, nums;\n\n  num
s := convert(text, 'bytes');\n  counts := map ((x,y) -> [convert([x], \+
'bytes'), numboccur (y,x)], nums, nums);\n  counts := convert (convert
 (counts, set), list);\n  op (sort (counts, (x,y) -> evalb(x[2]>y[2]))
);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "count (`How man
y roads must a man walk down?`);" }}{PARA 12 "" 1 "" {XPPMATH 20 "627$
%\"~G\"\"(7$%\"aG\"\"&7$%\"nG\"\"$7$%\"mGF+7$%\"wGF+7$%\"oGF+7$%\"sG\"
\"#7$%\"dGF47$%\"kG\"\"\"7$%\"lGF97$%\"tGF97$%\"uGF97$%\"rGF97$%\"yGF9
7$%\"HGF97$%\"?GF9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 99 "7. Write a
 Maple program which, given an RSA public key [n,a], finds the corresp
onding private key." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with
(numtheory):" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition f
or order" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "crack := proc \+
(key)\n  local phi_n;\n\n  phi_n := phi (key [1]);\n  [key[1], modp (1
/key[2], phi_n)];\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&crackG:6
#%$keyG6#%&phi_nG6\"F*C$>8$-%$phiG6#&9$6#\"\"\"7$F1-%%modpG6$*$&F26#\"
\"#!\"\"F-F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "crack ([5
2824610493623, 751]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"/BO\\5Y#G
&\".RO0?5^)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "time (crack \+
([25697821673947, 757]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%]r!\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "29 0 0" 0 
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