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{SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "Function:" }{TEXT -1 53 " \+
fixD - prepare a function for differentiation with D" }}{PARA 0 "" 0 "
" {TEXT 26 17 "Calling sequence:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{MPLTEXT 0 21 7 "fixD(f)" }}{PARA 0 "" 0 "" {TEXT 26 11 "Parameters:" 
}}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "f" }{TEXT -1 20 " - a procedure nam
e " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 12 "Description:" }{TEXT -1 0 
"" }{TEXT 26 0 "" }}{PARA 15 "" 0 "" {TEXT -1 79 "This procedure is a \+
work-around for a weakness in the differentiation operator " }
{MPLTEXT 0 21 1 "D" }{TEXT -1 18 ": when a function " }{MPLTEXT 0 21 
1 "f" }{TEXT -1 49 " is defined using a second user-defined function \+
" }{MPLTEXT 0 21 1 "g" }{TEXT -1 2 ", " }{MPLTEXT 0 21 4 "D(f)" }
{TEXT -1 52 " doesn't work.  What is needed is a procedure named " }
{MPLTEXT 0 21 8 "`diff/g`" }{TEXT -1 38 " that performs the differenti
ation of " }{MPLTEXT 0 21 1 "g" }{TEXT -1 1 "." }}{PARA 15 "" 0 "" 
{TEXT -1 12 "The command " }{MPLTEXT 0 21 7 "fixD(f)" }{TEXT -1 9 " ap
plies " }{MPLTEXT 0 21 8 "makediff" }{TEXT -1 32 " to all user-defined
 procedures " }{MPLTEXT 0 21 1 "g" }{TEXT -1 15 " referenced in " }
{MPLTEXT 0 21 1 "f" }{TEXT -1 23 ", defining a procedure " }{MPLTEXT 
0 21 8 "`diff/g`" }{TEXT -1 37 " for each of them, and thus allowing \+
" }{MPLTEXT 0 21 4 "D(f)" }{TEXT -1 11 " to work.  " }}{PARA 15 "" 0 "
" {TEXT -1 78 "This works only for global procedures, not local proced
ures or module exports." }}{PARA 15 "" 0 "" {TEXT -1 26 "If some of th
e procedures " }{MPLTEXT 0 21 1 "g" }{TEXT -1 15 " referenced in " }
{MPLTEXT 0 21 1 "f" }{TEXT -1 102 " can't be differentiated with respe
ct to all their arguments, you should use the two-argument form of " }
{MPLTEXT 0 21 8 "makediff" }{TEXT -1 22 " on those procedures. " }}
{PARA 15 "" 0 "" {TEXT -1 29 "This function is part of the " }{TEXT 
256 23 "Maple Advisor Database." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 
9 "Examples:" }}{PARA 0 "" 0 "" {TEXT -1 9 "Defining " }{MPLTEXT 0 21 
1 "f" }{TEXT -1 24 " using defined function " }{MPLTEXT 0 21 1 "g" }
{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "f:= x -> x*
g(x^2);\ng:= x -> 1 + x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6
#%\"xG6\"6$%)operatorG%&arrowGF(*&9$\"\"\"-%\"gG6#*$)F-\"\"#F.F.F(F(F(
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"xG6\"6$%)operatorG%&ar
rowGF(,&\"\"\"F-*$)9$\"\"#F-F-F(F(F(" }}}{PARA 0 "" 0 "" {MPLTEXT 0 
21 4 "D(f)" }{TEXT -1 15 " does not work:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"DG6#%\"fG
" }}}{PARA 0 "" 0 "" {TEXT -1 6 "Using " }{MPLTEXT 0 21 7 "fixD(f)" }
{TEXT -1 19 " to make this work:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "fixD(f); D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"xG6\"6
$%)operatorG%&arrowGF&,&-%\"gG6#*$)9$\"\"#\"\"\"F2*&\"\"%F2)F0F4F2F2F&
F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 17 "Another function " }{MPLTEXT 0 
21 1 "h" }{TEXT -1 20 " defined using both " }{MPLTEXT 0 21 1 "f" }
{TEXT -1 5 " and " }{MPLTEXT 0 21 1 "g" }{TEXT -1 1 "." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "h:= (x,y) -> f(x) + g(y); D[1](h);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGR6$%\"xG%\"yG6\"6$%)operator
G%&arrowGF),&-%\"fG6#9$\"\"\"-%\"gG6#9%F2F)F)F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-&%\"DG6#\"\"\"6#%\"hG" }}}{PARA 0 "" 0 "" {TEXT -1 6 "
Using " }{MPLTEXT 0 21 7 "fixD(h)" }{TEXT -1 9 " to make " }{MPLTEXT 
0 21 7 "D[1](h)" }{TEXT -1 6 " work:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "fixD(h); D[1](h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
R6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF',&\"\"\"F,*&\"\"&F,)9$\"\"%F,F,
F'F'F'" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "See also:" }}{PARA 0 "
" 0 "" {HYPERLNK 17 "D" 2 "D" "" }{TEXT -1 3 ",  " }{HYPERLNK 17 "diff
" 2 "diff" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "makediff" 2 "makediff" "
" }{TEXT -1 2 ", " }{HYPERLNK 17 "Problems with D" 2 "Problems_with_D
" "" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT 26 24 "Maple Advisor Database  \+
" }{TEXT -1 15 "R. Israel, 2001" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}
{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{MARK "3 1 6" 0 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }