Questions tagged [functional]

Questions related to functional methods, e.g. functional differentiation and integration.

This tag is used for questions related to functional methods, e.g. functional differentiation and integration.

39 questions
6
votes
1 answer

How to define a functional by the way it acts on its own output

I want to define a functional E by using the property E[ E[f[x]] ] := E[f[x]] for some arbitrary function f[x]. Meaning, that I want Mathematica to evaluate every expression E[ E[f[x]] ] to E[f[x]] for all functions f[x]. How do I make this in…
Demoncracy
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6
votes
1 answer

How to compute symbolically the Legendre transform of a function?

Is it possible to compute symbolically the Legendre transform of a function in Mathematica? I find no LegendreTransform function.
a06e
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5
votes
4 answers

How do I define functionals in Mathematica?

When I write W[f_] := Integrate[f[x], {x, 0, π}] I may rightly conclude that W[Sin] = 2, W[Cos] = 0, W[Log] = π (-1 + Log[π]) etc. But I am unable to define W[Sin + Cos] or W[Sin[Sin]] etc. Please help.
Quasar Supernova
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2
votes
0 answers

Different delays in notebook and command-line?

I was surprised by the following sequence of expressions: Remove[foo$, bar$]; foo$ = Function[Set[bar$, 42]]; At this point, I expected foo$ to be defined and bar$ not to be defined, because I had not called the function named foo$ yet. Indeed, the…
Reb.Cabin
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1
vote
2 answers

Define a functional and nest it with its arguments

I'm looking for a definition of a functional f which works correctly with varying arguments t while it will be nested. For example, I've the following code f[g__[t__]] := g[t] + g[t - s] For an input function in[t] I'll…
Drakonomikon
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