differential operators

[Kai Ludwig]

> Hi!
>
> On Fri, Oct 24, 2003 at 12:59:48PM +0200, Kai Ludwig wrote:
>> > I'm new to GiNac. Is there a way to execute symbolic differentiation
>> > of expressions that includes differential operators ?
>> >
>> > e.g. suppose an expression
>> >
>> > ex F = u * dx*u
>> >
>> > When differentiate that expression F.diff(u)
>> > it should result in the expression
>>
>> dx*u + u*dx
>
> I'm still not sure what exactly the rules are that are in effect here,
> but it seems that "dx" and "u" are noncommutative?

Sorry - maybe my question was not precise enough. The shortcut
symbol dx means the differential operator d/dx. Applied to a
function u gives du/dx. The expression I mentioned
comes from functional analysis. F is an operator. I'm asking
for an automatic derived expression for the (Frechet-) differential
dF/du. I guess, the chain rule (thus, the product rule) also applies
to such differentials. Then,

dF/du = du/du * du/dx + u * d/du du/dx

thus, formally

dF/du = du/dx + u * d/dx

That's what I meant with

dx*u + u*dx


??Kai



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Kai Ludwig
Institut für Organische Chemie
Auf der Morgenstelle 18
72076 Tübingen
Tel.: 07071/29-73049
Mail: kai.ludwig at uni-tuebingen.de