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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 22 "Basic Algebra in Maple" }
}{PARA 19 "" 0 "" {TEXT -1 21 "Original by Dave Hart" }}{PARA 19 "" 0 
"" {TEXT -1 24 "Updated by Clinton Wolfe" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 29 "Basic Polynomial Manipulation" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "z:=(x+y)^2 + 9*(2+x)*(x+y);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"zG,&*$),&%\"xG\"\"\"%\"yGF*\"\"#\"\"\"F**&,&F,F*F)F
*F*F(F*\"\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 632 "Here an algebrai
c expression has been typed. Maple reads in the\nstatement, assigns th
e right hand side to the variable z, and\n\"prettyprints\" it. The let
ters x, y, and z are here considered\nvariables; legal variables start
 with a letter and have at most 494\ncharacters. Examples of legal var
iable names are: g, G, new_term,\nx13a, and the_answer_is. Maple is ca
se sensitive, so the variables g\nand G are distinct. \n\nNotice also \+
that the line ends with a semicolon. All commands entered \nin Maple m
ust end in with a semicolon. If one is not entered at the \nend of the
 line, then Maple will wait for one to be entered on the \nnext line.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(z);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\"\"#\"\"\"\"#5*&F&\"\"\"%\"yGF+\"#6*
$)F,F'F(F+F&\"#=F,F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "This comm
and expanded the algebraic expression assigned to z." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 4 "%^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$
),,*$)%\"xG\"\"#\"\"\"\"#5*&F(\"\"\"%\"yGF-\"#6*$)F.F)F*F-F(\"#=F.F2\"
\"$F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 231 "Here, this command tell
s Maple to take the previous result and cube\nit. (The percent sign re
fers to the most recent result.) \nMaple does not expand the result. T
o see the\nmultiplication explicitly, the following command is issued:
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#,N*$)%\"xG\"\"'\"\"\"\"%+5*&)F&\"\"&F(%\"yG
\"\"\"\"%+L*&)F&\"\"%F()F-\"\"#F(\"%IR*&)F&\"\"$F()F-F8F(\"%\"*>*&)F&F
4F()F-F2F(\"$$R*&F&F.)F-F,F(\"#L*$)F-F'F(F.*$F+F(\"%+a*&F1F(F-F(\"&!G<
*&F7F(F3F(\"&%\\>*&F<F(F9F(\"%-))*&F&F(F=F(\"%U7*$F@F(\"#a*$F1F(\"%?(*
*&F7F(F-F(\"&K,$*&F<F(F3F(\"&w?$*&F&F(F9F(\"&OE\"*$F=F(\"$s**$F7F(\"%K
e*&F<F(F-F(\"&'\\<*&F&F(F3F(Fgn*$F9F(Fen" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 68 "Notice that Maple does not list the elements in any speci
fic order. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sort(%);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#,N*$)%\"xG\"\"'\"\"\"\"%+5*&)F&\"\"&F(
%\"yG\"\"\"\"%+L*&)F&\"\"%F()F-\"\"#F(\"%IR*&)F&\"\"$F()F-F8F(\"%\"*>*
&)F&F4F()F-F2F(\"$$R*&F&F.)F-F,F(\"#L*$)F-F'F(F.*$F+F(\"%+a*&F1F(F-F(
\"&!G<*&F7F(F3F(\"&%\\>*&F<F(F9F(\"%-))*&F&F(F=F(\"%U7*$F@F(\"#a*$F1F(
\"%?(**&F7F(F-F(\"&K,$*&F<F(F3F(\"&w?$*&F&F(F9F(\"&OE\"*$F=F(\"$s**$F7
F(\"%Ke*&F<F(F-F(\"&'\\<*&F&F(F3F(Fgn*$F9F(Fen" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 52 "Use the \"sort\" command to see it in a prettier for
m." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"$\"\"\"),(F&\"#5F
(F'\"#=F'F)F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 195 "Here Maple fact
ors the previous result. Notice that the result does \nnot look like t
he expressions previously entered. Maple will not \nalways be able to \+
return an expression to its previous form." }}}}{SECT 0 {PARA 3 "" 0 "
" {TEXT -1 25 "Operations on Polynomials" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "integrate(x/(1-x^3), x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(-%#lnG6#,&%\"xG\"\"\"!\"\"F)#F*\"\"$-F%6#,(*$)F(\"\"#
\"\"\"F)F(F)F)F)#F)\"\"'*&-%%sqrtG6#F,F3-%'arctanG6#,$*&,&F(F2F)F)F)F7
F3#F)F,F)F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 208 "Maple integrates \+
x/(1-x^3) with respect to x. Because any letter used\nin a Maple sessi
on is considered a variable, you must specify with\nrespect to what va
riable differentiation and integration should \noccur." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "diff(%, x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&\"\"\"F%,&%\"xG\"\"\"!\"\"F(!\"\"#F)\"\"$*&,&F'\"\"
#F(F(F%,(*$)F'F/F%F(F'F(F(F(F*#F(\"\"'*&F%F%,&F(F(*$)F.F/F%#F(F,F*#!\"
#F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Differentiation." }}{PARA 
0 "" 0 "" {TEXT -1 170 "The result is not exactly like the integrand, \+
but it is in a form \nsimilar enough to recognize that they are the sa
me expression.  \nSimplification is a difficult problem." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "series(exp(-x)*sin(2*x), x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#+/%\"xG\"\"#\"\"\"!\"#\"\"##!\"\"\"\"$
\"\"$\"\"\"\"\"%#!#>\"#g\"\"&-%\"OG6#F-\"\"'" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 269 "The command will find a series (either Taylor, Laurent
, or \ngeneralized) around the point x=0 if no value is given. General
ly, \nthe last term of the series will be the order term, where the or
der \nis decided by a global Maple variable which can be defined by th
e \nuser." }}}}}{MARK "2 6 0 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 }