#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 kcrisman):
> 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?
In this case, it is not an example of Eviatar's (good) point. `f` always
has the variables in the same order, so your first option is not possible.
The second option would be legitimate but I guess Sage just assumes the
[http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Schwarz.27_theorem
Clairaut/Schwarz Theorem] always holds for 'symbolic' functions.
> Interestingly, the following does not return `True` but two visually
indistinguishable expressions. To me, this looks like a bug.
> {{{
> sage: f.diff(x,y) == f.diff(y,x)
> D[0, 1](f)(x, y) == D[0, 1](f)(x, y)
> }}}
See above.
> It would be unambiguous and shorter. What is the advantage of the
D-notation again?
I'm still not 100% sold on it, especially since it doesn't LaTeX with
subscripts, but this would be a second issue.
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Questions:
* Is it worth trying to distinguish `D[0,1]` and `D[1,0]`?
* Would it be very hard to do so? (I have not looked at this code in a
long time.)
* Is it easy to have the LaTeX be subscripts?
* Alternately (or with that), would it be possible to just "read off" the
actual variable names and put those in, ala `D[x,y]` and `D[y,x]`? In
principle it should be, since all such functions now have ''ordered''
variable names. I don't know how that would combine with the whole
`D[0,1](f)(x,x+1)` thing, so maybe it's a bad idea.
--
Ticket URL: <http://trac.sagemath.org/ticket/17445#comment:12>
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