Improve printing of FDerivative by adapting the appropriate hook in PyNaC

[Nils Bruin]

As Bill Page points out on:

​https://github.com/pynac/pynac/issues/187

PyNaC does provide a special hook for printing FDerivative expressions. The relevant routine py_print_fderivative lives in src/sage/symbolic/pynac.pyx, on line 583 (or thereabouts).

It look likes an expression D[*params](f)(*args) would get printed using a call of the form

py_print_fderivative(<id of f>,params,args)

so we'd have enough information to decide if args consist of distinct simple variables, in which case we could print it as

diff(f(*args),[args[i] for i in params])

or something nicer.

[Nils Bruin]

After finally tracking down where the hook for this exists, the actual change only requires a few lines. With the attached POC branch:

sage: var('x,y'); function('f')
sage: diff(f(y,x),x, y)
diff(f(y, x), y, x)
sage: diff(f(x+y,x-y),x,y)
D[0, 0](f)(x + y, x - y) - D[1, 1](f)(x + y, x - y)

so we get more intuitive printing when argument positions are easily determined by variable names, and revert to unambiguous notation if not. For univariate we do have:

sage: diff(f(sin(x)),x)
cos(x)*diff(f(sin(x)), sin(x))

of course, actual printing styles can be adapted.

---

New commits:

​81ded03

trac 21286: Improved adaptive printing of FDerivative expressions

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5d234d6	trac 21286: improved latex typesetting of FDerivative
​bce16a2	trac 21286: fix doctests (and adjust some edge cases detected by doctests)

[Nils Bruin]

OK, I think this is a reasonable start that's ready to be merged. In many common cases, expressions containing an FDerivative operator will be printed in a way that's valid input (an appropriate "diff" expression). The latex should look nice in those cases as well.

Other options can be tried and bikeshedded later on follow-up tickets. This at least should alleviate the worst complaints about printing derivatives.

[Bill Page]

Thank you! I checked out this ticket and am just starting to look at it... already I like it. Great work.

[Eric Gourgoulhon]

I also gave a look at it; it looks very good (in particular I've checked the LaTeX output in this ​jupyter notebook). Thanks for this improvement! There remains to replace \partial by \mathrm{d} in the LaTeX output for the univariate case, but this might be deferred to some follow-up ticket.

A question: shouldn't the change be documentated by some doctest in src/sage/symbolic/pynac.pyx?

[Ralf Stephan]

Replying to egourgoulhon:

A question: shouldn't the change be documentated by some doctest in src/sage/symbolic/pynac.pyx?

The changed doctests with the new output suffice absolutely.

As the output is deemed satisfactory by reviewers, the pynac.pyx looks good, and make ptestlong passes, I'll set positive now. Thanks for the work.

[Nils Bruin]

Thanks for the quick review. Once this is merged, we can close #6344 and possibly some other tickets.

Concerning printing a "\mathrm{d}" rather than "\partial": yes, I think that's a nice refinement to make in a follow-up ticket. That might also be a place to start thinking about when function names can be safely put in the numerator and whether such behaviour should be subject to some global state.

[Eric Gourgoulhon]

Have you noticed that the patchbot next_method plugin failed on src/sage/symbolic/pynac.pyx? Probably the builtin function next should be used instead of .next() in line 653.

[Travis Scrimshaw]

While I doubt it will make a difference, it would be good to check that there are no conflicts with #21369.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​f3bfeb8	.next() -> next(..)
​807d77d	doc+test

[Nils Bruin]

OK, let's see if this fares better.

[Eric Gourgoulhon]

Replying to nbruin:

OK, let's see if this fares better.

Thanks for the changes!

[Bill Page]

Excellent. Thanks.