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Bypassing built-in functions in differentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg62577] Bypassing built-in functions in differentiation
• From: "Ofek Shilon" <ofek at simbionix.com>
• Date: Tue, 29 Nov 2005 04:44:07 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup.

consider the following statement:

Dt[Transpose[a]]

which evaluates to

Dt[a] Transpose`[a]

that is, mathematica treats Transpose as a function and uses the chain
rule. i can try and bypass this behaviour manually:

Unprotect[Dt];
Dt[Transpose[x_]] := Transpose[Dt[x]]

but now consider expressions like -

Dt[Transpose[a].b]

which still produces:

Transpose[a].Dt[b] + Dt[a] Transpose`[a] b

which is a bit surprising. i can of course bypass this behaviour
manually as well:

Dt[Transpose[x_].y_] := Transpose[Dt[x]].y + Transpose[x].Dt[y]

which gives the desired result, but then check the following -
Dt[(Transpose[a].b)^2]

etc. etc.

i tried also to define -
Dt[Transpose[x_]] =1

which produces readable results, but discards the (correct, and needed)
'Transpose' head over a factor in the differentiation.

There has to be a general solution. is there a 'hook' where i can
interfere with the derivative computation? (i thought user definitions
would suffice, but apparently not)


thanks,

Ofek

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