Re: Re: Derivative of Dot[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg91156] Re: [mg91106] Re: [mg91055] Derivative of Dot[]*From*: "Eitan Grinspun" <eitan at grinspun.com>*Date*: Thu, 7 Aug 2008 04:43:16 -0400 (EDT)*References*: <200808050759.DAA09628@smc.vnet.net>

On Wed, Aug 6, 2008 at 5:06 AM, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > I think the rule for D[X[t] . Y[t], t] is necessary, rather than > "useful". Compare these two > > > > In[1]:= D[Dot[X[t] , Y[t]], t] > Out[1]= X[t] . Derivative[1][Y][t] + Derivative[1][X][t] . Y[t] > > In[2]:= D[dot[X[t], Y[t]], t] > Out[2]= Derivative[1][Y][t]*Derivative[0, 1][dot][X[t], > Y[t]] + Derivative[1][X][t]*Derivative[1, 0][dot][ > X[t], Y[t]] > > If there was no built-in rule for D and Dot, then exactly the same > thing that happens for dot would happen for Dot, which would be > somewhat less convenient (you would need to define Derivative[1, 0] > [Dot] and Derivative[0, 1][Dot] yourself). > Other than that, I do not know of any obvious application. Note > however, that Derivative is always first converted to D[ ], so any > rules that are applied to Derivative and Dot are actually derived from > rules for D and Dot. I don't see any direct use for them and actually > I think they are basically an slightly unfortunate side effect. If I understand correctly, what you are saying is that if Dot' had not been defined, I would have to do the work of defining it. What I am saying is that the way it is defined, it does not seem to be useful, and I am assuming that this means that I am misunderstanding something (i.e., that it must have a useful definition). As far as I can see, Dot' = #1.1 + 1.#1& is useful iff 1 is interpreted as the identity map, and not useful if 1 is a scalar (which mathematica refuses to treat as the identity map). I could write rules/patterns to manipulate this, but I was assuming that the developers had something in mind. Eitan

**References**:**Derivative of Dot[]***From:*"Eitan Grinspun" <eitan@grinspun.com>

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**Re: Derivative of Dot[]**