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{SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 8 "Advice: " }{TEXT -1 37 "Fr
actional powers of negative numbers" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 175 "Maple's mathematics is largely based on
 complex numbers rather than real numbers.  In particular, it uses the
 \"principal branch\" of fractional powers: the principal branch of " 
}{XPPEDIT 18 0 "z^(1/n)" ")%\"zG*&\"\"\"\"\"\"%\"nG!\"\"" }{TEXT -1 
22 " has argument between " }{XPPEDIT 18 0 "-Pi/n" ",$*&%#PiG\"\"\"%\"
nG!\"\"F'" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "Pi/n" "*&%#PiG\"\"\"%\"
nG!\"\"" }{TEXT -1 22 ", and the argument of " }{XPPEDIT 18 0 "(-1)^(1
/n)" "),$\"\"\"!\"\"*&\"\"\"\"\"\"%\"nGF%" }{TEXT -1 4 " is " }
{XPPEDIT 18 0 "Pi/n" "*&%#PiG\"\"\"%\"nG!\"\"" }{TEXT -1 17 ".\nSo for
 example:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalc((-1)^(1/5
));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$\"\"&#\"\"\"\"\"##F'\"\"%F)
F'*(%\"IGF'F(F&,&F%F'F$!\"\"F&F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+X*
p,4)!#5\"\"\"%\"IG$\"+?D&y(eF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 22 "evalf(argument(\")/Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
+)*******>!#5" }}}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{MPLTEXT 0 21 4 "
surd" }{TEXT -1 32 " function provides \"elementary\" " }{XPPEDIT 18 
0 "n" "I\"nG6\"" }{TEXT -1 19 "'th roots, i.e. if " }{XPPEDIT 18 0 "x
" "I\"xG6\"" }{TEXT -1 26 " is a negative number and " }{XPPEDIT 18 0 
"n" "I\"nG6\"" }{TEXT -1 14 " is odd, then " }{MPLTEXT 0 21 9 "surd(x,
n)" }{TEXT -1 24 " is the real (negative) " }{XPPEDIT 18 0 "n" "I\"nG6
\"" }{TEXT -1 12 "'th root of " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT 
-1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "surd(-8,3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"#" }}}{PARA 0 "" 0 "" {TEXT -1 149 
"In order to have a somewhat nicer syntax, as well as covering rationa
l exponents with numerators other than 1, I have defined an infix-form
 operator " }{MPLTEXT 0 21 2 "&^" }{TEXT -1 85 ".  This is part of the
 Maple Advisor Database, and must be read in before being used:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "readlib(`&^`);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "(-1)&^(2/5), (-1) &^ (3/5);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"!\"\"" }}}{PARA 0 "" 0 "" {TEXT 
-1 13 "For positive " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 2 ", " }
{XPPEDIT 18 0 "x &^ p" "-%#&^G6$%\"xG%\"pG" }{TEXT -1 16 " is the same
 as " }{XPPEDIT 18 0 "x^p" ")%\"xG%\"pG" }{TEXT -1 16 ".  For negative
 " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 5 ", if " }{XPPEDIT 18 0 "p
 =m/n" "/%\"pG*&%\"mG\"\"\"%\"nG!\"\"" }{TEXT -1 43 " is a fraction we
 have the following cases:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "assume(x<0); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 
18 0 "m" "I\"mG6\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "n" "I\"nG6\"" 
}{TEXT -1 11 " both odd: " }{XPPEDIT 18 0 "`&^`(x,(m/n)) = -(-x)^(m/n)
;" "/-%#&^G6$%\"xG*&%\"mG\"\"\"%\"nG!\"\",$),$F&F+*&F(F)F*F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x &^ (3/5);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*$,$%#x|irG!\"\"#\"\"$\"\"&F'" }}}{EXCHG {PARA 
0 "" 0 "" {XPPEDIT 18 0 "m" "I\"mG6\"" }{TEXT -1 7 " even, " }
{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 6 " odd: " }{XPPEDIT 18 0 "`&^`
(x,m/n) = (-x)^(m/n);" "/-%#&^G6$%\"xG*&%\"mG\"\"\"%\"nG!\"\"),$F&F+*&
F(F)F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x &^ (4/5);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,$%#x|irG!\"\"#\"\"%\"\"&" }}}
{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "m" "I\"mG6\"" }{TEXT -1 6 " odd,
 " }{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 7 " even: " }{XPPEDIT 18 0 
"`&^`(x,(m/n));" "-%#&^G6$%\"xG*&%\"mG\"\"\"%\"nG!\"\"" }{TEXT -1 12 "
 is complex." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x &^ (3/8);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&!\"\"#\"\"(\"\"),$%#x|irGF$#\"\"
$F'" }}}{PARA 0 "" 0 "" {TEXT -1 5 "When " }{XPPEDIT 18 0 "x" "I\"xG6
\"" }{TEXT -1 30 " is not known to be real, and " }{XPPEDIT 18 0 "p" "
I\"pG6\"" }{TEXT -1 16 " is a fraction, " }{XPPEDIT 18 0 "x&^p" "-%#&^
G6$%\"xG%\"pG" }{TEXT -1 87 " is written as a surd.  When p is given i
n decimal form, it is converted to a fraction." }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "x:= 'x': x &^ (3/8);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%%surdG6$*$%\"xG\"\"$\"\")" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "x &^ 0.375;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%s
urdG6$*$%\"xG\"\"$\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
plot(x &^ (2/3), x = -1 .. 1);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(x &^ (3/5), x = -1 .. 1
);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{SECT 0 {PARA 0 "" 0 "" 
{TEXT 26 9 "See also:" }{TEXT -1 1 " " }{HYPERLNK 17 "^" 2 "^" "" }
{TEXT -1 2 ", " }{HYPERLNK 17 "&^" 2 "&^" "" }{TEXT -1 2 ", " }
{HYPERLNK 17 "surd" 2 "surd" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 
24 "Maple Advisor Database  " }{TEXT -1 15 "R. Israel, 1998" }}}}
{MARK "2 0 0" 20 }{VIEWOPTS 1 1 0 1 1 1803 }