Wrap Maxima's demoivre and exponentialize

[qed777]

Sage does not appear to have easily accesible analogues of Mathematica's TrigToExp and ExpToTrig. From AskSage:

sage: x = var('x')
sage: t1 = cos(x)
sage: t2 = e^(I * x) / 2 / I - e^(-I * x) / 2 / I
sage: sageobj(t1._maxima_().exponentialize())
1/2*e^(-I*x) + 1/2*e^(I*x)
sage: sageobj(t2._maxima_().demoivre())
sin(x)

CC: @kcrisman @sagetrac-fmaltey @slel

Component: symbolics

Keywords: expression tree

Author: Emmanuel Charpentier

Branch/Commit: e913bee

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/10038

[burcin]

comment:1

You can use maxima_methods() to access the maxima functions easily.

sage: x = var('x')
sage: t1 = cos(x)
sage: t2 = e^(I * x) / 2 / I - e^(-I * x) / 2 / I
sage: res = t1.maxima_methods().exponentialize(); res
1/2*e^(-I*x) + 1/2*e^(I*x)
sage: type(res)
<type 'sage.symbolic.expression.Expression'>
sage: t2.maxima_methods().demoivre()
sin(x)

I am very much against wrapping each maxima function for manipulating symbolic expressions individually from Sage. Even though maxima provides a lot of functionality, their user interface is far from intuitive.

IMHO, the user interface to these functions should be something like:

sage: t1.rewrite(exp)
1/2*e^(-I*x) + 1/2*e^(I*x)
sage: t2.rewrite(sin)
sin(x)

BTW, it would be great if we could think about how to provide basic functionality like this directly in Sage without relying on maxima. It's possible that this requires wrapping more of pynac's features, for example

• http://www.ginac.de/tutorial/Applying-a-function-on-subexpressions.html and
• http://www.ginac.de/tutorial/Visitors-and-tree-traversal.html

but it's well worth the effort.

[kcrisman]

comment:2

Replying to @burcin:

You can use maxima_methods() to access the maxima functions easily.

Yes, thanks for that reminder!

I am very much against wrapping each maxima function for manipulating symbolic expressions individually from Sage. Even though maxima provides a lot of functionality, their user interface is far from intuitive.

I don't see why we can't provide a more intuitive user interface for some of them, though. Just because a ticket is opened doesn't mean it will ever be fulfilled, but at least it's here now if enough people want it.

IMHO, the user interface to these functions should be something like:

sage: t1.rewrite(exp)
1/2*e^(-I*x) + 1/2*e^(I*x)
sage: t2.rewrite(sin)
sin(x)

This seems awkward, esp. if you don't know ahead of time whether it's sin or cos. I think that simplify_* makes sense, the way we have it now. For now it's not worth having the discussion - I doubt anyone has time to do this right now. But if someone does, maybe it's time to revisit that.

BTW, it would be great if we could think about how to provide basic functionality like this directly in Sage without relying on

Yes, of course. If only we could have that Sage Days solely about symbolics...

• http://www.ginac.de/tutorial/Applying-a-function-on-subexpressions.html and
• http://www.ginac.de/tutorial/Visitors-and-tree-traversal.html

but it's well worth the effort.

[slel]

Changed keywords from none to expression tree

[slel]

comment:7

Replying to @burcin:

BTW, it would be great if we could think about how to provide basic functionality like this directly in Sage without relying on maxima. It's possible that this requires wrapping more of pynac's features, for example

• http://www.ginac.de/tutorial/Applying-a-function-on-subexpressions.html and
• http://www.ginac.de/tutorial/Visitors-and-tree-traversal.html

but it's well worth the effort.

The links seem to have slightly changed:

• https://www.ginac.de/tutorial/#Applying-a-function-on-subexpressions
• https://www.ginac.de/tutorial/#Visitors-and-tree-traversal

[EmmanuelCharpentier]

Branch: u/charpent/dm2

[EmmanuelCharpentier]

comment:9

Replying to @EmmanuelCharpentier:

Eleven years later, it seems obvious that no one ever undertook to wrap Pynac's tree traversal utilities. However, the expressionTreeWalker class offers means to implement such utilities not too painfully.

This proposal passes ptestlong with no new failures.

==>needs_review

---

New commits:

22d0354

de Moivre/exponentialize methods for symbolic expressions (Sage)

[EmmanuelCharpentier]

Commit: 22d0354

[EmmanuelCharpentier]

comment:10

Wups. A nice typo : _init__ for __init__...

==> needs_work.

[sagetrac-git]

Changed commit from 22d0354 to 43bce84

[sagetrac-git]

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

43bce84

Exponentialize : typo.

[EmmanuelCharpentier]

comment:12

Typo fixed ==>needs_review.

[EmmanuelCharpentier]

Author: Emmanuel Charpentier

[EmmanuelCharpentier]

comment:14

One doctest (src/sage/doctest/sources.py) fails.

[sagetrac-git]

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

7810b80

deMoivre : reformatting doctests.

[sagetrac-git]

Changed commit from 43bce84 to 7810b80

[EmmanuelCharpentier]

comment:16

New patchbot attempt ==>needs_review

[tscrim]

comment:17

A few little things:

It would be good to use Sage's doc conventions:

-        """Returns this sumbolic expression with all circular and hyperbolic
+        """
+        Return this sumbolic expression with all circular and hyperbolic
         functions replaced by their respective exponential
         expressions.

Exponentialize.__init__ is missing a doctest.

The import here

    def demoivre(self, force=False):
        from sage.symbolic.expression_conversions import DeMoivre
        """

should go after the docstring (which probably is not being picked up as a docstring but instead just a string being created within the function).

-return op(*[self(_) for _ in ex.operands()])
+return op(*[self(oper) for oper in ex.operands()])

[sagetrac-git]

Changed commit from 7810b80 to 518361f

[sagetrac-git]

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

518361f

de Moivre/exponentialize : documentation fixes, code streamlining.

[EmmanuelCharpentier]

comment:20

Replying to @sagetrac-git:

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

518361f

de Moivre/exponentialize : documentation fixes, code streamlining.

Fixed doctests pass. setting needs_review to start the patchbots.

[tscrim]

Changed commit from 518361f to e913bee

[tscrim]

comment:21

I did a few more reviewer changes. If my changes are good, then positive review.

---

New commits:

751776b	Merge branch 'u/charpent/dm2' of git://trac.sagemath.org/sage into u/tscrim/demoivre_exp-10038
e913bee	Trac #10038: reviewer changes.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Changed branch from u/charpent/dm2 to u/tscrim/demoivre_exp-10038

[EmmanuelCharpentier]

comment:22

Thanks !

Okay with your cosmetics (notwithstanding the fact that I do not grasp their rationale) ==> positive_review.

[tscrim]

comment:23

Thank you.

Most of them are formatting corrections, so after a :: is needed to be indented (which becomes code) and the corresponding text needs to be at the base level. If something is followed by text, then it should be a single colon :. Convention says we should start docstrings with Return not Returns, and a few other small tweaks for that and PEP8.

[vbraun]

Changed branch from u/tscrim/demoivre_exp-10038 to e913bee