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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-*$F*\"\"#F-F+F./%\"xG,$*&F&F.
,&F&F.F2F.F.F+" }}}{PARA 0 "" 0 "" {TEXT -1 24 "Save this in a variabl
e:" }}{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(indets(q,RootO
f));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#roG-%'RootOfG6#,,%#_ZG!\"\"
*$F)\"\"%\"\"\"*$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$\"+,7;-\\F(" }}}{PARA 0 "" 0 "" 
{TEXT -1 30 "Substitute into the solutions:" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 28 "map(t -> subs(ro=t,q), rts);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7$<$/%\"yG$!+8S6^Z!#5/%\"xG$\"+\"f>\\C(F)<$/F&$\"+,7;-
\\F)/F+$!+&3W2A\"!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 58 "You could obtai
n complex solutions in the same way, using " }{MPLTEXT 0 21 6 "fsolve
" }{TEXT -1 10 " with the " }{MPLTEXT 0 21 7 "complex" }{TEXT -1 8 " o
ption:" }}{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." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" 
}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See also:" }{TEXT -1 1 " " }
{HYPERLNK 17 "fsolve" 2 "fsolve" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "Ro
otOf" 2 "RootOf" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "allvalues" 2 "allv
alues" "" }}}{PARA 0 "" 0 "" {TEXT 26 22 "Maple Advisor Database" }
{TEXT -1 18 "  R. Israel, 1997\n" }}}{MARK "0 1 6" 202 }{VIEWOPTS 1 1 
0 1 1 1803 }