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{SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 7 "Advice:" }{TEXT -1 26 "  R
eal values for a RootOf" }}{PARA 0 "" 0 "" {TEXT -1 73 " Maple often r
eturns solutions to various types of equations in terms of " }
{MPLTEXT 0 21 6 "RootOf" }{TEXT -1 20 " a polynomial.  The " }
{MPLTEXT 0 21 9 "allvalues" }{TEXT -1 37 " function can be used to rep
lace the " }{MPLTEXT 0 21 6 "RootOf" }{TEXT -1 462 " with the roots of
 the polynomial.  This will use symbolic solutions if that is possible
 (e.g. if the polynomial is of degree 4 or less), otherwise it uses fl
oating-point approximations.  In many cases this may be inconvenient b
ecause the symbolic solutions are very complicated.  Moreover, it incl
udes complex solutions, and you may wish to include only real solution
s.  An alternative, which always returns floating-point results for re
al solutions, is to use " }{MPLTEXT 0 21 6 "fsolve" }{TEXT -1 27 " as \+
follows.               " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Exampl
es:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "solve(\{ y^2+2*y+x=0,
 y = x^2 - 1 \});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/%\"yG-%'RootOf
G6#,,%#_ZG!\"\"*$)F*\"\"%\"\"\"\"\"\"*$)F*\"\"$F/F.*$)F*\"\"#F/F.F+F0/
%\"xG,$*&F&F0,&F&F0F6F0F0F+" }}}{PARA 0 "" 0 "" {TEXT -1 24 "Save this
 in a variable:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "q:= %:" }}
}{PARA 0 "" 0 "" {TEXT -1 12 "Isolate the " }{MPLTEXT 0 21 6 "RootOf" 
}{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ro:= op(in
dets(q,RootOf));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#roG-%'RootOfG6#
,,%#_ZG!\"\"*$)F)\"\"%\"\"\"\"\"\"*$)F)\"\"$F.F-*$)F)\"\"#F.F-F*F/" }}
}{PARA 0 "" 0 "" {TEXT -1 30 "Find a list of the real roots:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " rts:= [ fsolve(op(ro)) ];" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rtsG7$$!+8S6^Z!#5$\"+,7;-\\F(" }}
}{PARA 0 "" 0 "" {TEXT -1 30 "Substitute into the solutions:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "map(t -> subs(ro=t,q), rts);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$<$/%\"yG$!+8S6^Z!#5/%\"xG$\"+\"f
>\\C(F)<$/F&$\"+,7;-\\F)/F+$!+&3W2A\"!\"*" }}}{PARA 0 "" 0 "" {TEXT 
-1 58 "You could obtain complex solutions in the same way, using " }
{MPLTEXT 0 21 6 "fsolve" }{TEXT -1 10 " with the " }{MPLTEXT 0 21 7 "c
omplex" }{TEXT -1 8 " option:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 38 "rts:= [ fsolve(op(ro), _Z, complex) ];" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%$rtsG7&,&$!+fBb2?!\"*\"\"\"%\"IG$!+cz:J^!#5,&F'F*F+$
\"+cz:J^F.$!+8S6^ZF.$\"+,7;-\\F." }}}}{SECT 0 {PARA 0 "" 0 "" {TEXT 
26 9 "See also:" }{TEXT -1 1 " " }{HYPERLNK 17 "fsolve" 2 "fsolve" "" 
}{TEXT -1 2 ", " }{HYPERLNK 17 "RootOf" 2 "RootOf" "" }{TEXT -1 2 ", \+
" }{HYPERLNK 17 "allvalues" 2 "allvalues" "" }{TEXT -1 2 ", " }
{HYPERLNK 17 "allsolve" 2 "allsolve" "" }}}{PARA 0 "" 0 "" {TEXT 26 
22 "Maple Advisor Database" }{TEXT -1 18 "  R. Israel, 1997\n" }}}
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