The resulting symbolic expression must contain a different sort of information. For example
∂²f/[∂J(x1)∂J(x2)] does not have a analogon, if you try to dervive it in terms of ordinary differentiation with subsequent substitution. Structurally, for the functional derivative, you must basically be able to differentiate a function of infinitely many arguments (thus on an infinitely dimensional space) with regard to one of those arguments. The ordinary partial derivative obviously does not capture this kind of operation. I was contemplating that, perhaps, such an operation could be implemented on top of a function *f: ℂ∞ ⊕ … ⊕ ℂ∞ → ℂ* * * for f[J(x)] that would just be f: ℂ∞ → *ℂ. *But even if I'm able to express that function in SAGE, we'd still need some notion of a derivative on that. Perhaps there are other cathegorically similar structures which can be used to implement it, I don't know, On Sunday, April 21, 2013 2:03:31 PM UTC+2, adsmith wrote: > > On Saturday, April 20, 2013 2:03:07 PM UTC-4, ManDay wrote: > >> I'd like to be able to derive in the following manner: >> >> x = var( "x" ); >> J = function( "g",x ); >> f = function( "f",g ); >> >> # like so >> >> x1 = var( "x1" ); >> >> f.diff( J( x1 ) ); >> >> which is the functional f derivate with respect to the value of J at x1. >> Is this possible in a fashion at least similar to what I demonstrate above? >> I'm not understanding enough of the internal workings of symbolic >> expressions to modify "diff" so that it would do what I suggest, perhaps >> someone has a clever idea. >> >> Thanks. >> > > How do you see this as being different than a substitution? > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
