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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