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{SECT 0 {EXCHG {PARA 18 "" 0 "top_s02_3" {TEXT -1 22 "2.3  Solving Equ
ations" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmonte, Summer 1996" }}
{PARA 0 "" 0 "" {TEXT -1 63 "These are the shaded gray examples which \+
appear in Section 2.3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "r
estart; x^2 + 2*x - 1 = 0;\nsol:=solve(\", x); " }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/,(*$%\"xG\"\"#\"\"\"F&F'!\"\"F(\"\"!" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%$solG6$,&*$\"\"##\"\"\"F(F*!\"\"F*,&F+F*F'F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sol[1]; sol[2];" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,&*$\"\"##\"\"\"F%F'!\"\"F'" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,&!\"\"\"\"\"*$\"\"##F%F'F$" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 17 "f:=x^2 + 2*x - 1;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"fG,(*$%\"xG\"\"#\"\"\"F'F(!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 14 "solve(f=0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
,&*$\"\"##\"\"\"F%F'!\"\"F',&F(F'F$F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "eq:=x^2 + 2*x - 1 = 0;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#eqG/,(*$%\"xG\"\"#\"\"\"F(F)!\"\"F*\"\"!" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "solve(eq, x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$,&*$\"\"##\"\"\"F%F'!\"\"F',&F(F'F$F(" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 37 "eq1:=3*x + 2*y = 1; eq2:=x + 2*y = 3;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%$eq1G/,&%\"xG\"\"$%\"yG\"\"#\"\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,&%\"xG\"\"\"%\"yG\"\"#\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(\{eq1, eq2\}, \{x, y\}
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"yG\"\"#/%\"xG!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assign(\"); x, y;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$!\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "unassign('x', 'y');\neq:=x^3 - 2*x^2 + x - 3 = 0;\nso
lve(eq, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,**$%\"xG\"\"$\"
\"\"*$F(\"\"#!\"#F(F*!\"$F*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,(
*$,&\"$;$\"\"\"*$\"#x#F'\"\"#\"#O#F'\"\"$#F'\"\"'*$F%#!\"\"F.#F+F.F4F'
,*F$#F3\"#7F1F2F4F'*(%\"IGF'F.F*,&F$F/F1#!\"#F.F'F*,*F$F6F1F2F4F'F8#F3
F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "eq:=x^3 - 2.0*x^2 + x
 - 3.0 = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,**$%\"xG\"\"$\"
\"\"*$F(\"\"#$!#?!\"\"F(F*$!#IF/F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "solve(eq, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,&$!
+:0(zs)!#6\"\"\"%\"IG$!+6@Jr6!\"*,&F$F'F($\"+6@Jr6F+$\"+5%fX<#F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "eq:=x^7 + 3*x^4 + 2*x - 1 = \+
0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,**$%\"xG\"\"(\"\"\"*$F(
\"\"%\"\"$F(\"\"#!\"\"F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 13 "solve(eq, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6#,**
$%#_ZG\"\"(\"\"\"*$F(\"\"%\"\"$F(\"\"#!\"\"F*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 14 "fsolve(eq, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$\"+!4xTT%!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eq:=x^2 \+
+ 1/x - 1/x^2 = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,(*$%\"xG
\"\"#\"\"\"*$F(!\"\"F**$F(!\"#F,\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "fsolve(eq, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+
&3W2A\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(lhs(eq)
, x=-2..2, y=-20..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f
solve(eq, x, x=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!f>\\C(!#
5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Example of a parabola passin
g through three specified points." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "p:=x->a*x^2 + b*x + c;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"pG:6#%\"xG6\"6$%)operatorG%&arrowGF(,(*&%\"aG\"\"\"9$\"\"#F/
*&%\"bGF/F0F/F/%\"cGF/F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
41 "eq1:=p(-1)=2; eq2:=p(1)=3/2; eq3:=p(4)=7;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$eq1G/,(%\"aG\"\"\"%\"bG!\"\"%\"cGF(\"\"#" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,(%\"aG\"\"\"%\"bGF(%\"cGF(#\"\"$\"
\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/,(%\"aG\"#;%\"bG\"\"%%
\"cG\"\"\"\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "sol:=sol
ve(\{eq1, eq2, eq3\}, \{a, b, c\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$solG<%/%\"cG#\"\"%\"\"$/%\"bG#!\"\"F)/%\"aG#\"\"&\"#7" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<%/%\"cG$\"+LLLL8!\"*/%\"bG$!+++++D!#5/%\"aG$\"+nmmmTF-
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "f:=subs(sol, p(x)); eva
lf(\"); plot(f, x=-2..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*
$%\"xG\"\"##\"\"&\"#7F'#!\"\"\"\"%#F.\"\"$\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$%\"xG\"\"#$\"+nmmmT!#5F%$!+++++DF)$\"+LLLL8!\"*\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#7S%(animateG%*animate3dG%-changecoords
G%,complexplotG%.complexplot3dG%*conformalG%,contourplotG%.contourplot
3dG%*coordplotG%,coordplot3dG%-cylinderplotG%,densityplotG%(displayG%*
display3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradplot3dG%-implicit
plotG%/implicitplot3dG%(inequalG%-listcontplotG%/listcontplot3dG%0list
densityplotG%)listplotG%+listplot3dG%+loglogplotG%(logplotG%+matrixplo
tG%(odeplotG%'paretoG%*pointplotG%,pointplot3dG%*polarplotG%,polygonpl
otG%.polygonplot3dG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG
%+setoptionsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+spherepl
otG%)surfdataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 54 "eq:=x^2 + y^2 = 1; implicitplot(eq, x=-1..1,
 y=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,&*$%\"xG\"\"#\"
\"\"*$%\"yGF)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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