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{SECT 0 {PARA 0 "" 0 "" {TEXT 263 33 "Maple as a programming language \+
 " }{TEXT -1 32 "(Last updated by JR, 8/19/2004) " }}{PARA 0 "" 0 "" 
{TEXT -1 34 "Copyright 2000-2004, SUNY Buffalo." }}{PARA 0 "" 0 "" 
{TEXT -1 4 "The " }{TEXT 264 3 "for" }{TEXT -1 6 " loop:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "for i from 1 to 3 do\n   evalf(i*Pi
);\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+3`=$G'!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$\"+izxC%*!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 76 "Unfortunately Maple'
s authors have chosen to give a loop index global scope." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "i;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 137 "As the designers of C++ fina
lly concluded, this is almost always undesirable, \nso I recommend the
 practice of unassigning the loop index:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "for i from 1 to 3 do\n   evalf(i*Pi);\nod; unassign('
i'):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"+3`=$G'!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"+izxC%*!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 46 "One of the most useful data structures is the " }{TEXT 
257 8 "sequence" }{TEXT -1 40 ": a comma-separated list of expressions
:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "s:=1,seven,x^2;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6%\"\"\"%&sevenG*$)%\"xG\"\"#F&
" }}}{PARA 0 "" 0 "" {TEXT -1 36 "Elements can be accessed as follows:
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s[2];" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%&sevenG" }}}{PARA 0 "" 0 "" {TEXT -1 34 "My very fav
orite Maple command is " }{TEXT 258 3 "seq" }{TEXT -1 28 ":  for gener
ating sequences." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "seq(eval
f(i*Pi),i=1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+aEfTJ!\"*$\"+3
`=$G'F%$\"+izxC%*F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "seq(A[i],i=0..7);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6*&%\"AG6#\"\"!&F$6#\"\"\"&F$6#\"\"#&F$6#\"\"$&F$6#\"\"%&
F$6#\"\"&&F$6#\"\"'&F$6#\"\"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "seq(i^2,i=[2,10,-7]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"$+\"\"#\\" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plots[displa
y](seq(plot(sin(n*x),x=0..Pi/2),n=1..3));" }}{PARA 13 "" 1 "" 
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z'))3tqF=7$F`x$!3FeY3$ePJu(F=7$Fex$!3K%*f3a'G8L)F=7$Fjx$!3)*)G]\"fe$)*
z)F=7$F_y$!3!HH)3m'yoC*F=7$Fdy$!3jb+H6Zbh&*F=7$Fiy$!3_=Uo*[p_!)*F=7$F^
z$!3U3>m%*oiZ**F=7$Fcz$F][lF)Fgz-%+AXESLABELSG6%Q\"x6\"Q!Fi]m-%%FONTG6
#%(DEFAULTG-%%VIEWG6$;F($\"+Fjzq:!\"*F^^m" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "Associati
ve arrays can be created simply by assigning an element:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "for i from 0 to 3 do\n   A[i]:=i*x;
\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"AG6#\"\"!F'" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>&%\"AG6#\"\"\"%\"xG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"AG6#\"\"#,$*&F'\"\"\"%\"xGF*F*" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%\"AG6#\"\"$,$*&F'\"\"\"%\"xGF*F*" }}}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 50 "A sequence enclosed by square brackets is a Maple " }
{TEXT 256 4 "list" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "[%];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+aEfTJ!\"
*$\"+3`=$G'F&$\"+izxC%*F&" }}}{PARA 0 "" 0 "" {TEXT -1 98 "Lists can b
e used as vectors: simple arithmetic (usually) distributes over them a
s you might hope," }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "u:=[2,x
,y];\n7*u;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG7%\"\"#%\"xG%\"yG
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"#9,$*&\"\"(\"\"\"%\"xGF(F(,$*&
F'F(%\"yGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "v:=[3,4,5]
;\nu+v;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%\"\"$\"\"%\"\"&" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"&,&\"\"%\"\"\"%\"xGF',&F$F'%\"yG
F'" }}}{PARA 0 "" 0 "" {TEXT -1 33 "though sometimes you need to use \+
" }{TEXT 265 6 "expand" }{TEXT -1 34 " to get Maple to do what you wan
t:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "t*v;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*&%\"tG\"\"\"7%\"\"$\"\"%\"\"&F%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "expand(t*v);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7%,$*&\"\"$\"\"\"%\"tGF'F',$*&\"\"%F'F(F'F',$*&\"\"&F'F(F'F'" }}
}{PARA 0 "" 0 "" {TEXT -1 97 "and, there is a nasty bug in Maple 6, fi
xed in Maple 7, that gets the following just plain wrong:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "w:=[sin(t),4*t,5];\nexpand(2*w);\n[
1,2,3]+2*w;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG7%-%$sinG6#%\"tG,
$*&\"\"%\"\"\"F)F-F-\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,$*&\"
\"#\"\"\"-%$sinG6#%\"tGF'F',$*&\"\")F'F+F'F'\"#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%,&*&\"\"#\"\"\"-%$sinG6#%\"tGF'F'F'F',&*&\"\")F'F+F'F
'F&F'\"#8" }}}{PARA 0 "" 0 "" {TEXT -1 10 "and while " }{TEXT 260 4 "d
iff" }{TEXT -1 25 " distributes over lists, " }{TEXT 259 3 "int" }
{TEXT -1 10 " does not:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "r
:=[t,t^2,t^3];\ndiff(r,t);\nint(r,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"rG7%%\"tG*$)F&\"\"#\"\"\"*$)F&\"\"$F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%\"\"\",$*&\"\"#F$%\"tGF$F$,$*&\"\"$F$)F(F'F$F$" }}
{PARA 8 "" 1 "" {TEXT -1 52 "Error, (in int) wrong number (or type) of
 arguments\n" }}}{PARA 0 "" 0 "" {TEXT -1 43 "Conditional execution is
 achieved with the " }{TEXT 261 3 "if " }{TEXT -1 10 "construct:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "a:=3;\nif(a=3) then\n   prin
t(hello);\nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%&helloG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "if(a>3) then\n   print(hello);\nelse\n   print(goodby
e);\nfi;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(goodbyeG" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "Sometimes, it's  c
onvenient to use expressions as functions in the following way:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f:=x^2-x*y^2;\ng:=diff(f,x);
\nsubs(x=2,y=3,g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$)%\"xG
\"\"#\"\"\"F**&F(F*)%\"yGF)F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"gG,&%\"xG\"\"#*$)%\"yGF'\"\"\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#!\"&" }}}{PARA 0 "" 0 "" {TEXT -1 67 "Other times, you may find \+
it more convenient to use true functions:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "f:=(x,y)->x^2-x*y^2;\ng:=D[1](f);\ng(2,3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowG
F),&*$)9$\"\"#\"\"\"F2*&F0F2)9%F1F2!\"\"F)F)F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF),&9$\"\"#
*$)9%F/\"\"\"!\"\"F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"&" }}}
{PARA 0 "" 0 "" {TEXT -1 45 "Functions can be made from expressions us
ing " }{TEXT 262 7 "unapply" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 32 "F:=x^2-x*y^2;\nf:=unapply(F,x,y);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"FG,&*$)%\"xG\"\"#\"\"\"F**&F(F*)%\"yGF)F*!\"\"" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG
%&arrowGF),&*$)9$\"\"#\"\"\"F2*&F0F2)9%F1F2!\"\"F)F)F)" }}}{PARA 0 "" 
0 "" {TEXT -1 98 "Procedures are similar to functions, and are suitabl
e for functions that require multiple lines of" }}{PARA 0 "" 0 "" 
{TEXT -1 94 "code for their evaluation. The last-evaluated expression \+
is the return value of the procedure." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 68 "f:=proc(x,y)\n   foo;\n   bar;\n   x^2-x*y^2;\nend;\n
g:=D[1](f);\ng(2,3);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%
\"xG%\"yG6\"F)F)C%%$fooG%$barG,&*$)9$\"\"#\"\"\"F2*&F0F2)9%F1F2!\"\"F)
F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"yG6\"F)F),&9
$\"\"#*$)9%F,\"\"\"!\"\"F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"&
" }}}{PARA 0 "" 0 "" {TEXT -1 120 "Avoiding the annoying \"cannot dete
rmine if this expression is true or false\" error  in functions that h
ave conditionals:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "g1:=pr
oc(x,xi)  \n   if x < xi then cos(xi)*sin(x) else sin(xi)*cos(x) end i
f\nend proc:\ng1(1,2),g1(1,Pi);" }}{PARA 8 "" 1 "" {TEXT -1 78 "Error,
 (in g1) cannot determine if this expression is true or false: -Pi < -
1\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g1(a,b);" }}{PARA 8 "
" 1 "" {TEXT -1 77 "Error, (in g1) cannot determine if this expression
 is true or false: a-b < 0\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 320 "g2:=proc(x,xi)  # (avoids \"cannot determine if this expression
 is true or false\" error)\n  if type(evalf(x),numeric) and type(evalf
(xi),numeric) then\n     if evalf(x)< evalf(xi) then cos(xi)*sin(x) el
se sin(xi)*cos(x) end if\n  else\n     'g'(x,xi)    # return function \+
unevaluated\n  fi:\nend proc:\ng2(1,2),g2(1,Pi),g2(a,b);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6%*&-%$cosG6#\"\"#\"\"\"-%$sinG6#F(F(,$F)!\"\"-%\"
gG6$%\"aG%\"bG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 266 12 "One la
st tip" }}{PARA 0 "" 0 "" {TEXT -1 127 "When typing nested commands, I
 find it saves a great deal of tedious debugging if I always close my \+
 parentheses before typing " }}{PARA 0 "" 0 "" {TEXT -1 86 "the thing \+
enclosed by them. E.g. type \"seq()\", then backspace and put in the c
ontents." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0
" 8 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }