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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 16 "Introduction to " }
{TEXT 256 5 "Maple" }{TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 12 "Pr
ogramming " }{TEXT 280 44 "by Bob Bradshaw, Ohlone College, Fremont, C
A" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 154 "A c
omputer program allows a computer to do repetitive operations without \+
having a person constantly telling the computer what to do. The simple
st type of " }{TEXT 260 5 "Maple" }{TEXT -1 46 " program may consist o
f only a single command." }}{PARA 0 "" 0 "" {TEXT -1 39 "For example, \+
if you wanted to find the " }{XPPEDIT 18 0 "sum(1/x,x = 1 .. n);" "6#-
%$sumG6$*&\"\"\"F'%\"xG!\"\"/F(;F'%\"nG" }{TEXT -1 24 "  between for v
alues of " }{TEXT 257 1 "n" }{TEXT -1 62 " between 2 and  5, a person \+
would have to do the computations " }{XPPEDIT 18 0 "sum(1/x,x = 1 .. 2
);" "6#-%$sumG6$*&\"\"\"F'%\"xG!\"\"/F(;F'\"\"#" }{TEXT -1 4 "  , " }
{XPPEDIT 18 0 "sum(1/x,x = 1 .. 3);" "6#-%$sumG6$*&\"\"\"F'%\"xG!\"\"/
F(;F'\"\"$" }{TEXT -1 4 "  , " }{XPPEDIT 18 0 "sum(1/x,x = 1 .. 4);" "
6#-%$sumG6$*&\"\"\"F'%\"xG!\"\"/F(;F'\"\"%" }{TEXT -1 7 " , and " }
{XPPEDIT 18 0 "sum(1/x,x = 1 .. 5);" "6#-%$sumG6$*&\"\"\"F'%\"xG!\"\"/
F(;F'\"\"&" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 12 "We can have " }{TEXT 258 5 "Maple" }{TEXT -1 55 "
 perform all these computations by using a \"for\" loop. " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "\nfor n from 2 to 5 do \n      Sum(
1/x,x=1..n)=evalf(sum(1/x,x=1..n)) \n   od;" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 47 "\nTo compute sums for non-consecutive values of " }
{TEXT 259 1 "n" }{TEXT -1 19 ", use the following" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 81 "for n from 1  by 6 to 20 do \n      Sum(1/x,x=1..n)
=evalf(sum(1/x,x=1..n)) \n   od;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
113 "\nTo create a more elaborate program, we can use something called
 a procedure. A procedure is simply the lines of " }{TEXT 261 6 "Maple
 " }{TEXT -1 269 "that you would use to accomplish a task if you were \+
doing the task by yourself. For example, suppose you wanted to find th
e equation of the line that passes through two points. First, you woul
d determine the slope of the line and then you could use the equation \+
of the " }}{PARA 0 "" 0 "" {TEXT -1 5 "line " }{TEXT 262 1 "y" }{TEXT 
-1 3 " = " }{TEXT 263 1 "m" }{TEXT -1 1 "(" }{TEXT 264 1 "x" }{TEXT 
-1 3 " - " }{TEXT 265 1 "x" }{TEXT -1 5 "1) + " }{TEXT 266 1 "y" }
{TEXT -1 47 "1. We can write a procedure to do exactly that." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "In the lines th
at follow, p and q are points where p[1] is the " }{TEXT 267 1 "x" }
{TEXT -1 28 " value of p and p[2] is the " }{TEXT 268 1 "y" }{TEXT -1 
13 " value of p. " }}{PARA 0 "" 0 "" {TEXT -1 21 "The first line tells
 " }{TEXT 271 5 "Maple" }{TEXT -1 62 " that you are going to give the \+
procedure two points, p and q." }}{PARA 0 "" 0 "" {TEXT -1 37 "The sec
ond line of the program tells " }{TEXT 269 5 "Maple" }{TEXT -1 0 "" }
{TEXT 270 1 " " }{TEXT -1 62 "that the name \"slope\" has no meaning o
utside of the procedure." }}{PARA 0 "" 0 "" {TEXT -1 47 "The third and
 fourth lines do the calculations." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "line:=proc(p,q)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "local slope;
\nslope:=(q[2]-p[2])/(q[1]-p[1]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "y=slope*(x-p[1])+p[2];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 
"To use the procedure, first tell " }{TEXT 272 5 "Maple" }{TEXT -1 44 
" the points through which you want the line." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 18 "p:=[1,2];q:=[5,7];" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Next, ask " }
{TEXT 273 6 "Maple " }{TEXT -1 55 " to use the procedure to give the e
quation of the line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 
10 "line(p,q);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 55 "You can also give the points directly to the procedu
re." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 18 "line([3,5],[6,7
]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 125 "The next step is to modify the procedure to allow for the case
 where the slope of the line is undefined. To do this, use the " }
{TEXT 274 17 "if \311 then \311 else " }{TEXT -1 8 "command." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 178 "In the line \"
if q[1] - p[1] <> 0\", the procedure first asks if the denominator of \+
the slope is not equal to zero. If this is true, the procedure returns
 the equation of the line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 99 "If the denominator  does equal zero, the slope is
 undefined and the equation of the line is in the " }}{PARA 0 "" 0 "" 
{TEXT -1 5 "form " }{TEXT 275 1 "x" }{TEXT -1 8 " = p[1]." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 1 0 16 "line2:=proc(p,q)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
121 "local slope;\n  if (q[1]-p[1])<>0 then\n     slope:=(q[2]-p[2])/(
q[1]-p[1]);\n     y=slope*(x-p[1])+p[2];\n  else\n     x=p[1]" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "  fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 4 "end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 71 "We can now ask for the equation of the line through two
 points. If the " }{TEXT 276 1 "x" }{TEXT -1 90 " values are different
, the procedure returns the same result as would the first procedure.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "line2([3,4],[10,11]);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "If
 we ask for the equation of the line through two points with the same \+
" }{TEXT 278 2 "x " }{TEXT -1 64 "values, the procedure returns the eq
uation fo the vertical line." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "lin
e2([2,9],[2,11]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 274 "The next version of the procedure is more elabora
te. Instead of simply giving the equation of the line through the poin
ts, the procedure creates a graph of the points and the line through t
he points. The program then uses the equation of the line as the title
 of the graph. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 37 "Before starting the program, restart " }{TEXT 277 5 "Mapl
e" }{TEXT -1 14 " and load the " }{TEXT 279 5 "plots" }{TEXT -1 11 " s
ubroutine" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 
"The program below looks complicated but simply finds the equation of \+
the line and draws a graph." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 1 0 16 "line3:=proc(p,q)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
604 "local slope,y,Title,Line,Points;\n\nif (q[1]-p[1])<>0 then\nslope
:=(q[2]-p[2])/(q[1]-p[1]);\ny:=slope*(x-p[1])+p[2];\nTitle:=cat(\"y = \+
\",convert(y,string));     Line:=plot(slope*(x-p[1])+p[2],x=min(p[1],q
[1])-4..max(p[1],q[1])+4,color=blue,title=Title,titlefont=[HELVETICA,B
OLD,24]);\nPoints:=plot(\{p,q\},style=point,symbol=circle,color=red,ax
es=normal);\ndisplay(Line,Points);\n\nelse\nTitle:=textplot([p[1],max(
p[2],q[2])+3,cat(\"x = \",convert(p[1],string))],font=[HELVETICA,BOLD,
24]);\nLine:=plottools[line](p,q,color=blue);\nPoints:=plot(\{p,q\},st
yle=point,symbol=circle,color=red);\ndisplay(\{Line,Points,Title\});\n
fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "line3([8,5],[6,9]);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "line3([2,5],[2,-25]);" }}}}{MARK "0 1 1" 44 }
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