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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 202 29 "Math 365D Lab One - Fal
l 2005" }{TEXT 203 0 "" }}{PARA 201 "" 0 "" {TEXT 203 0 "" }{TEXT 203 
216 "\nMaple contains thousands of mathematical commands in areas rang
ing from calculus to number theory to finance. We will begin with a fe
w basics, then concentrate on programming with specific attention to g
raph theory." }{TEXT 204 0 "" }{TEXT 204 1 "\n" }{TEXT 204 12 "\nSOME \+
BASICS" }{TEXT 203 0 "" }{TEXT 203 3 "\nA " }{TEXT 205 9 "semicolon" }
{TEXT 203 2 " (" }{TEXT 205 1 ";" }{TEXT 203 66 ") at the end of a com
mand causes the output to be printed while a " }{TEXT 205 5 "colon" }
{TEXT 203 2 " (" }{TEXT 205 1 ":" }{TEXT 203 29 ") suppresses the outp
ut. The " }{TEXT 205 5 "ditto" }{TEXT 203 42 " operator, represented b
y a percent sign (" }{TEXT 205 1 "%" }{TEXT 203 56 "), refers to the l
ast expression computed by Maple. The " }{TEXT 205 5 "sharp" }{TEXT 
203 9 " symbol (" }{TEXT 205 1 "#" }{TEXT 203 28 ") allows the user to
 put in " }{TEXT 205 8 "comments" }{TEXT 203 27 " that are ignored by \+
Maple." }{TEXT 203 0 "" }}{PARA 201 "" 0 "" {TEXT 203 0 "" }}{PARA 
202 "> " 0 "" {MPLTEXT 1 206 42 "13!; # compute and display 13*12*11*.
.*2*1" }{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#\"++3-F
i" }{TEXT 207 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 62 "is
prime(%); # ask if the previous expression is a prime number" }
{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I&falseGI*prote
ctedGF$" }{TEXT 207 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 61 "Exp
ressions, such as the previous one, that return values of " }{TEXT 
208 5 "true " }{TEXT 203 3 "or " }{TEXT 208 5 "false" }{TEXT 203 62 " \+
are called Boolean expressions - more on them in a later lab." }{TEXT 
203 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 19 "We use the symbols \+
" }{TEXT 205 2 ":=" }{TEXT 203 40 " to assign an expression to a varia
ble. " }{TEXT 203 0 "" }}{PARA 201 "" 0 "" {TEXT 203 102 "By pressing \+
SHIFT-ENTER instead of ENTER, we get a new line without displaying any
 output, as follows." }{TEXT 203 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 
1 206 70 "x:=(a+b)^8: # assign this to the variable x but don't displa
y anything" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 51 "\nexpand(x); # ex
pand this expression and display it" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 
206 1 "\n" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#,4*$I\"aG6\"\"\")\"\"\"*
&F%\"\"(I\"bGF&F(F'*&F%\"\"'F+\"\"#\"#G*&F%\"\"&F+\"\"$\"#c*&F%\"\"%F+
F5\"#q*&F%F2F+F1F3*&F%F.F+F-F/*&F%F(F+F*F'*$F+F'F(" }{TEXT 207 0 "" }}
}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 89 "y:=evalf[50](Pi); # a f
loating point evaluation of the expression to fifty decimal places" }
{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"S^P
*Rpr>%)G]zKQVEYQKz*e`EfTJ!#\\" }{TEXT 207 0 "" }}}{EXCHG {PARA 201 "" 
0 "" {TEXT 203 167 "It will often be useful (especially when using som
e of the built-in graph theory commands) to clear Maple's memory of th
e values of all variables. We do this with the " }{TEXT 205 7 "restart
" }{TEXT 203 9 " command." }{TEXT 203 0 "" }}{PARA 202 "> " 0 "" 
{MPLTEXT 1 206 8 "restart;" }{MPLTEXT 1 206 0 "" }}}{EXCHG {PARA 202 "
> " 0 "" {MPLTEXT 1 206 64 "y; # Maple will no longer remember what we
 assigned to y earlier" }{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" 
{XPPMATH 20 "6#I\"yG6\"" }{TEXT 207 0 "" }}}{EXCHG {PARA 201 "" 0 "" 
{TEXT 203 200 "When we open a Maple worksheet that has been saved, we \+
could execute the commands on an individual basis by hitting ENTER on \+
each line, but there is also a way to execute the entire worksheet at \+
once." }{TEXT 203 0 "" }{TEXT 203 1 "\n" }{TEXT 203 280 "\nGo back and
 comment out (with a #) the line with the restart command and then exe
cute the entire worksheet by using the pull-down menu sequence EDIT:EX
ECUTE:WORKSHEET. Maple will execute every command in this worksheet an
d thus should now know the expression assigned to y above." }{TEXT 
203 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 2 "y;" }{MPLTEXT 1 206 
0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#I\"yG6\"" }{TEXT 207 0 "" }}}
{EXCHG {PARA 201 "" 0 "" {TEXT 204 10 "PROCEDURES" }{TEXT 203 0 "" }
{TEXT 203 40 "\nWe will do our programming by creating " }{TEXT 205 
10 "procedures" }{TEXT 203 45 " as the following simple example illust
rates." }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 45 "\nraise:=proc(a::inte
ger,b::integer)::numeric;" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 50 "\n
description \"computes a raised to the bth power\";" }{MPLTEXT 1 209 
0 "" }{MPLTEXT 1 209 34 "\n        a^b;        # returns a^b" }
{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 10 "\nend proc:" }{TEXT 203 0 "" }
}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 11 "raise(3,5);" }
{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#\"$V#" }{TEXT 
207 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 12 "The objects " }
{TEXT 205 2 "a " }{TEXT 203 4 "and " }{TEXT 205 2 "b " }{TEXT 203 11 "
are called " }{TEXT 205 17 "formal parameters" }{TEXT 203 48 ", and it
 is considered good form to give each a " }{TEXT 205 16 "type declarat
ion" }{TEXT 203 68 " (integer in this case).  We have also given the p
rocedure itself a " }{TEXT 205 15 "type assertion " }{TEXT 203 10 "(nu
meric [" }{TEXT 208 5 "i.e.," }{TEXT 203 116 " integer or fraction or \+
floating(decimal)] here), which tells Maple what sort of object the pr
ocedure should return." }{TEXT 203 0 "" }{TEXT 203 1 "\n" }{TEXT 203 
57 "\nOnce the procedure is invoked (by executing the command " }
{TEXT 205 10 "raise(3,5)" }{TEXT 203 41 "), the formal parameters are \+
replaced by " }{TEXT 205 9 "arguments" }{TEXT 203 4 " or " }{TEXT 205 
17 "actual parameters" }{TEXT 203 11 " (3 and 5)." }{TEXT 203 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 77 "raise(3,sqrt(2)); # noti
ce what happens if we try to pass an invalid argument" }{MPLTEXT 1 
206 0 "" }}{PARA 204 "" 1 "" {TEXT 210 100 "Error, invalid input: rais
e expects its 2nd argument, b, to be of type integer, but received 2^(
1/2)" }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 56 "Now go
 back and change the procedure's type assertion to" }{TEXT 205 1 " " }
{TEXT 203 20 "integer and execute " }{TEXT 205 11 "raise(5,-1)" }
{TEXT 203 1 "." }{TEXT 203 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 
12 "raise(5,-1);" }{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" {XPPMATH 
20 "6##\"\"\"\"\"&" }{TEXT 207 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 
203 234 "So, why didn't this give an error? By default, Maple does not
 check for procedure type assertion. To activate such checking, we nee
d the following command, which you should get in the habit of executin
g at the start of each worksheet." }{TEXT 203 0 "" }}{PARA 202 "> " 0 
"" {MPLTEXT 1 206 28 "kernelopts(assertlevel=2);  " }{MPLTEXT 1 206 0 
"" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#\"\"!" }{TEXT 207 0 "" }}}
{EXCHG {PARA 201 "" 0 "" {TEXT 203 22 "We've now changed the " }{TEXT 
205 11 "assertlevel" }{TEXT 203 40 " to 2, and Maple has displayed wha
t the " }{TEXT 211 8 "previous" }{TEXT 203 163 " value of assertlevel \+
was. To confirm that we're now at level 2, we execute the following. (
For more details on kernelopts and assertlevel, please see Maple Help.
)" }{TEXT 203 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 24 "kernelopts
(assertlevel);" }{MPLTEXT 1 206 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "
6#\"\"#" }{TEXT 207 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 31 "Now
 go back and re-execute the " }{TEXT 205 12 "raise(5,-1) " }{TEXT 203 
46 "command, which should give an error this time." }{TEXT 203 0 "" }}
}{EXCHG {PARA 201 "" 0 "" {TEXT 204 15 "DECISION-MAKING" }{TEXT 203 0 
"" }{TEXT 203 5 "\nThe " }{TEXT 205 12 "if ... then " }{TEXT 203 81 "s
tatement allows us to perform an operation only when a certain conditi
on is met." }{TEXT 203 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 
206 21 "pos:=proc(a::integer)" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 
63 "\ndescription \"outputs 'positive' if and only if a is positive\";
" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 30 "\nif a>0 then print(\"Posit
ive\")" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 8 "\nend if;" }{MPLTEXT 
1 206 0 "" }{MPLTEXT 1 206 10 "\nend proc:" }{MPLTEXT 1 206 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 7 "pos(5);" }{MPLTEXT 1 206 
0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#Q)Positive6\"" }{TEXT 207 0 ""
 }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 43 "Note the distinction betwee
n the procedure " }{TEXT 205 5 "raise" }{TEXT 203 19 " and the procedu
re " }{TEXT 205 3 "pos" }{TEXT 203 2 ". " }{TEXT 205 5 "raise" }{TEXT 
203 1 " " }{TEXT 211 7 "returns" }{TEXT 203 36 " a value; this is simi
lar to making " }{TEXT 205 5 "raise" }{TEXT 203 122 " the name of a fu
nction which then takes on a certain value (243 above) after the proce
dure is called. On the other hand, " }{TEXT 205 3 "pos" }{TEXT 203 9 "
 doesn't " }{TEXT 211 6 "return" }{TEXT 203 199 " anything; instead, o
ne of the commands within this procedure displays the word \"Positive
\" under certain conditions.  This distinction will become more clear \+
as we see further examples in later labs." }{TEXT 203 0 "" }}}{EXCHG 
{PARA 201 "" 0 "" {TEXT 203 4 "The " }{TEXT 205 20 "if ... then ... el
se" }{TEXT 203 259 " statement gives additional flexibility. We can al
so \"nest\" if statements within if statements repeatedly if we need t
o examine several cases. We will look more fully at nesting in a later
 lab, but you can probably figure it out on your own today if you wish
." }{TEXT 203 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 77 "absoluteva
lue:=proc(x::float)::float; # the type 'float' lets us use decimals" }
{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 47 "\ndescription \"outputs the ab
solute value of x\";" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 18 "\nif x \+
>= 0 then x " }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 16 "\n        else \+
-x" }{MPLTEXT 1 206 0 "" }{MPLTEXT 1 206 8 "\nend if;" }{MPLTEXT 1 
206 0 "" }{MPLTEXT 1 206 10 "\nend proc:" }{MPLTEXT 1 206 0 "" }}}
{PARA 205 "" 0 "" {TEXT 212 0 "" }}{EXCHG {PARA 202 "> " 0 "" 
{MPLTEXT 1 206 20 "absolutevalue(-5.6);" }{MPLTEXT 1 206 0 "" }}{PARA 
203 "" 1 "" {XPPMATH 20 "6#$\"#c!\"\"" }{TEXT 207 0 "" }}}{EXCHG 
{PARA 201 "" 0 "" {TEXT 203 24 "What happens if you try " }{TEXT 205 
17 "absolutevalue(-5)" }{TEXT 203 1 "?" }{TEXT 203 0 "" }}}{PARA 205 "
" 0 "" {TEXT 213 9 "EXERCISES" }{TEXT 212 0 "" }}{PARA 205 "" 0 "" 
{TEXT 214 98 "In the exercises for this and future labs, you will some
times be asked to write a procedure that \"" }{TEXT 214 8 "returns\"" 
}{TEXT 214 117 " an object and sometimes asked to \"display\" or \"ind
icate\" something. This is the difference that was mentioned above." }
{TEXT 212 0 "" }{TEXT 212 1 "\n" }}{PARA 205 "" 0 "" {TEXT 214 47 "1. \+
Write a procedure that takes three integers " }{TEXT 215 1 "x" }{TEXT 
214 2 ", " }{TEXT 215 1 "y" }{TEXT 214 6 ", and " }{TEXT 215 1 "z" }
{TEXT 214 43 " as its arguments and returns the value of " }{TEXT 215 
4 "xy+z" }{TEXT 214 1 "." }{TEXT 214 0 "" }{TEXT 214 60 "\n2. Write a \+
procedure that takes two floating-point numbers " }{TEXT 215 1 "a" }
{TEXT 214 5 " and " }{TEXT 215 1 "b" }{TEXT 214 34 " as its arguments \+
and returns the " }{TEXT 215 1 "b" }{TEXT 214 11 "th root of " }{TEXT 
215 1 "a" }{TEXT 214 1 "." }{TEXT 214 0 "" }{TEXT 214 35 "\n3. Write a
 procedure that takes a " }{TEXT 216 6 "string" }{TEXT 214 156 " (any \+
sequence of characters enclosed in double quotes, such as \"walrus\") \+
as its argument and returns the third character of that string. Hint: \+
look up the " }{TEXT 216 9 "substring" }{TEXT 214 26 " command in the \+
Help menu." }{TEXT 214 0 "" }{TEXT 214 143 "\n4. Write a procedure tha
t takes a floating-point number as its argument and then indicates whe
ther that number is positive, negative, or zero." }{TEXT 214 0 "" }
{TEXT 214 110 "\n5. Write a procedure that takes two integers as its a
rguments and returns the value of the larger of the two." }{TEXT 214 
0 "" }{TEXT 214 216 "\n6. Write a procedure that takes three floating-
point numbers as its arguments and returns the value of the largest of
 the three. Note: this may require some techniques slightly beyond tho
se taught in the lab so far." }{TEXT 214 0 "" }{TEXT 214 67 "\n7. Writ
e a procedure that takes a positive integer (variable type " }{TEXT 
216 6 "posint" }{TEXT 214 81 ") as its argument and then displays eith
er \"prime\" or \"composite\" as appropriate." }{TEXT 212 0 "" }}
{PARA 205 "" 0 "" {TEXT 212 0 "" }}{PARA 205 "" 0 "" {TEXT 212 0 "" }}
{PARA 205 "" 0 "" {TEXT 212 0 "" }}{PARA 205 "" 0 "" {TEXT 212 0 "" }}
{PARA 205 "" 0 "" {TEXT 212 0 "" }}{PARA 205 "" 0 "" {TEXT 212 0 "" }}
{PARA 205 "" 0 "" {TEXT 212 0 "" }}{PARA 205 "" 0 "" {TEXT 212 0 "" }}
{PARA 205 "" 0 "" {TEXT 212 8 "        " }{TEXT 212 0 "" }}{PARA 205 "
" 0 "" {TEXT 212 0 "" }}{PARA 205 "" 0 "" {TEXT 212 0 "" }}{PARA 205 "
" 0 "" {TEXT 212 0 "" }}{PARA 205 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 \+
0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }