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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 0 "" 0 "" {TEXT 
26 9 "Bug fix: " }{TEXT -1 21 "Problems with unapply" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "The function " }
{MPLTEXT 0 21 7 "unapply" }{TEXT -1 154 ", which constructs a procedur
e from an expression, has three major shortcomings, listed below.  To \+
correct them, I have written the alternative procedure " }{MPLTEXT 0 
21 7 "vnapply" }{TEXT -1 1 "." }}{PARA 15 "" 0 "" {MPLTEXT 0 21 7 "una
pply" }{TEXT -1 106 " does not work with arrays (including matrices an
d vectors) or tables.  I'm not showing the result of the " }{MPLTEXT 
0 21 7 "unapply" }{TEXT -1 80 " command below, because that result can
 cause Maple to crash if you click on it." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "f:=unapply(vector([1,x,x^2]), x):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 5 "f(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'
VECTORG6#7%\"\"\"%\"xG*$F(\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 16 "Here \+
it is with " }{MPLTEXT 0 21 7 "vnapply" }{TEXT -1 2 ": " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "readlib(vnapply):\nf:= vnapply(vect
or([1,x,x^2]), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6
\"6$%)operatorG%&arrowGF(-%&arrayG6$;\"\"\"\"\"$7%/F1*$9$\"\"#/F0F0/F6
F5F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(t);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7%\"\"\"%\"tG*$F(\"\"#" }}}{PARA 
15 "" 0 "" {TEXT -1 86 "When the expression contains derivatives with \+
respect to the variables, we don't want " }{MPLTEXT 0 21 7 "unapply" }
{TEXT -1 28 " to return a result such as " }{XPPEDIT 18 0 "x -> diff(g
(x),x)" ":6#%\"xG7\"6$%)operatorG%&arrowG6\"-%%diffG6$-%\"gG6#F$F$F)F)
" }{TEXT -1 36 ", because that wouldn't work unless " }{MPLTEXT 0 21 
1 "x" }{TEXT -1 72 " is a name of a variable.  What we do want is to t
ake the derivative of " }{MPLTEXT 0 21 1 "g" }{TEXT -1 101 ", and then
 return the function that evaluates this at its argument.  This can be
 expressed using the " }{MPLTEXT 0 21 1 "D" }{TEXT -1 10 " operator." 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "unapply(diff(g(x),x), x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"DG6#%\"gG" }}}{PARA 0 "" 0 "" 
{TEXT -1 15 "Unfortunately, " }{MPLTEXT 0 21 7 "unapply" }{TEXT -1 61 
" fails to do this in slightly more complicated circumstances." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "unapply(2*diff(g(x),x), x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#:6#%\"xG6\"6$%)operatorG%&arrowGF&
,$-%%diffG6$-%\"gG6#9$F1\"\"#F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 16 "Her
e it is with " }{MPLTEXT 0 21 7 "vnapply" }{TEXT -1 1 ":" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "vnapply(2*diff(g(x),x), x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#:6#%\"xG6\"6$%)operatorG%&arrowGF&,$--
%\"DG6#%\"gG6#9$\"\"#F&F&" }}}{PARA 15 "" 0 "" {TEXT -1 1 " " }
{MPLTEXT 0 21 7 "unapply" }{TEXT -1 145 " has a rather strange feature
: if the expression is an integer power, then what is returned is the \+
power of a procedure rather than a procedure. " }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 23 "f:= unapply((x+1)^2,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG*$:6#%\"xG6\"6$%)operatorG%&arrowGF),&9$\"\"\"F/F
/F)F)\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whattype(f);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}{PARA 0 "" 0 "" {TEXT 
-1 51 "In most cases this behaviour is harmless: applying " }{MPLTEXT 
0 21 1 "f" }{TEXT -1 17 " to any argument " }{MPLTEXT 0 21 1 "v" }
{TEXT -1 16 " will result in " }{XPPEDIT 18 0 "(v+1)^2" "*$,&%\"vG\"\"
\"\"\"\"F%\"\"#" }{TEXT -1 16 ", as it should. " }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 7 "f(q+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&
%\"qG\"\"\"\"\"#F&F'" }}}{PARA 0 "" 0 "" {TEXT -1 46 "However, one pla
ce it will not work is in the " }{MPLTEXT 0 21 6 "evalhf" }{TEXT -1 
13 " environment:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalhf(
f(3));" }}{PARA 8 "" 1 "" {TEXT -1 48 "Error, unable to evaluate funct
ion `f` in evalhf" }}}{PARA 0 "" 0 "" {TEXT -1 17 "Here it is using " 
}{MPLTEXT 0 21 7 "vnapply" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "g:= vnapply((x+1)^2,x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"gG:6#%\"xG6\"6$%)operatorG%&arrowGF(*$,&9$\"\"\"F/F/\"\"#F(F
(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalhf(g(3));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#;\"\"!" }}}}{SECT 0 {PARA 0 "" 0 "
" {TEXT 26 9 "See also:" }{TEXT -1 1 " " }{HYPERLNK 17 "array" 2 "arra
y" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "D" 2 "D" "" }{TEXT -1 2 ", " }
{HYPERLNK 17 "diff" 2 "diff" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "evalhf
" 2 "evalhf" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "table" 2 "table" "" }
{TEXT -1 0 "" }{TEXT -1 2 ", " }{HYPERLNK 17 "unapply" 2 "unapply" "" 
}{TEXT -1 2 ", " }{HYPERLNK 17 "vnapply" 2 "vnapply" "" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 24 "Maple Adviso
r Database, " }{TEXT -1 15 " R. Israel 1998" }}}}{MARK "3 0" 0 }
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