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.