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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 35 "A Very Brief Introducti
on to Maple " }}{PARA 257 "" 0 "" {TEXT 257 43 " for Math 581: Foundat
ions in Combinatorics" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Basic O
perations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart;   ## c
lears all variables" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "2+3+5
+7;" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 3 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "7*6!;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "%=7!;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "evalb(7*6!=7!);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "Pi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eval
f(Pi,200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "32/4" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "5 a+3^b;" }}}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 20 " Assigning variables" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 5 "y:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 6 "x:=10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x+y;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a+b;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "c[1]:=3; c[2]:=17; c[3]:=4;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 6 "op(c);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 
24 "Polynomial Manipulations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "myeq:=(x+3*y)^3;" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 52 "unassign('x'); unassign('y');#can also use >restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "myeq:=(x+3*y)^3;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "y:=5;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "myeq:=(x+3*y)^3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "expand(myeq);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "subs(x=3,myeq);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "
subs(x=3*x, myeq) + myeq;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "myeq;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(myeq, \{x\});" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unassign('y');" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "collect((x+3*y+z)^3,x); " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "diff(myeq, x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "add(x[i], i=1..4);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sum(binomial(n,i), i=0..n);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "add(binomial(n,i), i=0..n);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "mul((1-x^i), i=1..4);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "product((1-x^i), i=1..4);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 32 "Plotting functions and Animation" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 6 "?plot;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 
"plot([sin(4*x),x,x=0..2*Pi],coords=polar,thickness=3);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "implicitplot(y^2=sin(x), x=-2*Pi..2
*Pi, y=-2*Pi..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "imp
licitplot(y^2=sin(x), x=-2*Pi..2*Pi, y=-2*Pi..2*Pi,numpoints=2000);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot3d(sin(x+y), x=-3..3, \+
y=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "animate(t*x^2,
 x=-2..2, t=-2..2);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 26 "Sequence
s, Lists, and Sets" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 
1 0 65 "These are 3 different ways to represent a collection of elemen
ts." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a:=seq(2*i mod 5, i=
1..10);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "b:=[seq(2*i mo
d 5, i=1..10)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "c:=\{seq
(2*i mod 5, i=1..10)\};\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "It i
s very easy to concatenate sequences. " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "a,a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "b,b;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "c,c;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 18 "c union \{3,4,5,6\};" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 92 "Counting the number of elements i
n a list or set is possible.  It doesn't work on sequences." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "nops(b),nops(c);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(a);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 88 "Lists and sequences are best if you ne
ed a fixed order or want to find the ith element:\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "b[3];" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "b[4..-1];#negative numbers count from the end of the \+
list back\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[4];" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "The null sequence, list and set ar
e three different objects:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 25 "a:=NULL;  #empty sequence" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 4 "a,1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a,2;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b:=[];" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "nops(b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 6 "c:=\{\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "c:= c un
ion \{4,5\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 11 "Proceedures" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "There are t
wo ways to define proceedures in Maple.  The first method is quick, th
e second has more flexibility." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 40 "catalan_nums:=n->binomial(2*n, n)/(n+1);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 30 "seq(catalan_nums(t), t=1..20);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "catalan:= proc(n) \n            op
tion remember; \n            if n=1 then 1; \n              else ((4*n
-2)/(n+1)) * catalan(n-1);  \n            fi; \n          end; " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "seq(catalan(t), t=1..20);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "add(catalan(t), t=1..20);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sum(catalan(t), t=1..20
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "catmatrix:=proc(i,j) \+
catalan(i+j); end;  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "wit
h(linalg);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "matrix(5,5,ca
tmatrix);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(%);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 
"" {TEXT -1 12 "Getting Help" }}{PARA 0 "" 0 "" {TEXT -1 109 "To get h
elp, either click on \"Help\" in upper right hand corner of your Maple
 window or use the question mark." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1 "?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?produc
t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?intro" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?index" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 " Sample Pro
blems" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 150 "1.  Define a function to
 compute the length generating function for the permutations in S_n us
ing the product formula.  Test your function on n=2,3,4." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 97 "2.  Define a function to compute the number of inversions in a \+
permutation.   Test your function." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 197 "3.  Define a function to compute \+
the length generating function for the permutations in S_n using your \+
function in Problem 2.   TIME your function using the time command.   \+
Which version is faster?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "9" 0 }
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