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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT 256 5 "Solve" }}{PARA 0 "" 0 "" {TEXT -1 80 "This worksheet expl
ores the use of \"solve\".  We begin by reading the help pages." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 6 "?solve" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
26 "Now, some simple examples." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 24 "solve( x^2 + x - 1, x );" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "solve( x^3 + x - 1, x );" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 47 "That was a bit ugly.  What if we try a quartic?" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve( x^4 + x - 1, x );" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 168 "Maple's default is not to give y
ou the radical solution---it's generally very ugly.  If you really wan
t it, you can force Maple to give it to you, by using \"allvalues\"." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "### WARNING: allvalues n
ow returns a list of symbolic values instead of a sequence of lists of
 numeric values\nallvalues( \{%\} );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 182 "Ick!  \"Have you ever asked a computer algebra system a questi
on, and then when screens went whizzing past, said `I wish I hadn't as
ked'?\"  --- an impression of a quote from W. Kahan." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf( [ \+
% ] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Of course, for degree 5
 and higher, radicals are generally impossible anyway." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve( x^10 - x - 1, x );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf( \{%\} );" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve( x^10 - x - 1, x );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "fsolve( x^10 - x - 1, x, com
plex );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Now some non-polynomia
l examples." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve( w*exp
(w) - z, w );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve( w*e
xp(-p) - w - p, p );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "_En
vAllSolutions := true;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "s
olve( w*exp(-p) - w - p, p );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 
"For more information on W, see the web page http://www.apmaths.uwo.ca
/~rcorless and the pointers there." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 31 "Now some examples with systems:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "solve( \{x^2 + y^2 - 1, x*y \+
- 12/25\}, \{x,y\} );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "so
lve( \{x^3 + y^3 - 1, x*y - 12/25\}, \{x,y\} );" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 127 "Are those RootOf's independent?  No!  This can be s
een by examining the labels.  An alternative is to use the Groebner pa
ckage." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(Groebner):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "gbasis( \{x^3 + y^3 - 1, \+
x*y - 12/25\}, plex(x,y) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Exercises:" }}{PARA 0 "" 
0 "" {TEXT -1 88 "1. solve( x^4 - x + e, x ), and plot the results as \+
a function of \"e\", for -1 <= e <= 1." }}{PARA 0 "" 0 "" {TEXT -1 
115 "2. Investigate the routine \"discrim\" and find the exact value o
f \"e\" for which the roots of the above are multiple." }}{PARA 0 "" 
0 "" {TEXT -1 43 "3. solve the system x^4+y^4 - 1, x*y-12/25." }}
{PARA 0 "" 0 "" {TEXT -1 59 "4. solve y^2 + ln(y) = x for y.  Are the \+
solutions correct?" }}{PARA 0 "" 0 "" {TEXT -1 46 "5. solve the system
 ax^4 + by^4 - 1, d*xy = 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{MARK "31" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 
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