#17445: Missing documentation of derivative operator/notation
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Reporter: schymans | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.5
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: schymans | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:10 schymans]:
> I was expecting the second to give either `D[0, 1](f)(y, x)` or `D[1,
0](f)(x, y)`. What is going on, is the order of differentiations not
honoured in the notation?
Correct. Rewriting of differentials apparently assumes symmetry. That's
not such a big issue, since in any reasonable application environment it
holds anyway (if your functions aren't continuously differentiable you
tend to have to use other things, such as distributions, anyway.
Illustration:
{{{
sage: D(f,[1,0])
D[1, 0](f)
sage: D(f,[0,1])
D[0, 1](f)
sage: D(f,[0,1])(x,y)
D[0, 1](f)(x, y)
sage: D(f,[1,0])(x,y)
D[0, 1](f)(x, y)
}}}
As you can see, the reordering happens on evaluation. It's not an
ambiguity in notation, it's an assumption that's been programmed into
sage. Perhaps it's already in Pynac?
--
Ticket URL: <http://trac.sagemath.org/ticket/17445#comment:15>
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