error when evaluating symbolic expression involving cotangent of a complex number

[gh-DaveWitteMorris]

This issue is split off from #29400. The command cot(1 + I).n() gives a TypeError:

sage: cot(1 + I).n()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-6-8ad83d3021de> in <module>()
----> 1 cot(Integer(1) + I).n()

    [snip]

/Users/dmorris/Documents/misc/Programs/sage3/local/lib/python3.7/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:34715)()
   6054             res = x.pyobject()
   6055         else:
-> 6056             raise TypeError("cannot evaluate symbolic expression numerically")
   6057 
   6058         # Important -- the  we get might not be a valid output for numerical_approx in

TypeError: cannot evaluate symbolic expression numerically

There is no such error for sin, cos, tan, sec, or csc.

I believe this can be fixed by renaming the cotan method of the ComplexNumber class to cot, and I will upload a PR soon.

[gh-DaveWitteMorris]

I changed the name of the cotan method of the ComplexNumber class to cot. This eliminates the error:

sage: cot(1 + I).n()
0.217621561854403 - 0.868014142895925*I

For consistency, I made the same change to the class MPComplexNumber, which I think is the only other occurrence of a cotan function in the sage source. To preserve backwards compatibility, I added cotan as an alias for each of these methods.

---

New commits:

​9b59968

change cotan to tan

[slabbe]

Do we want to deprecate cotan? If so there is deprecated_function_alias that you may use. You will find example by doing search_src('deprecated_function_alias').

from sage.misc.superseded import deprecated_function_alias

[gh-DaveWitteMorris]

Yes, we should deprecate cotan. Thanks for the suggestion. I made a new ticket (#29412) for this, because cotangent is such a well known function that I don't feel comfortable making a possibly significant change to its behavior without announcing it, even though I don't think this will be controversial.

[klee]

This is not official, but we usually do

cotan = cot  # provide this alias for backwards compatibility in #29409

instead of

cotan = cot # provide this alias for backwards compatibility (2020-3-25)

[git]

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

​b941d30

include ticket number in comments

[gh-DaveWitteMorris]

Yes, that's better than what I wrote. Thanks for the correction.

[klee]

LGTM.

[gh-DaveWitteMorris]

Thanks for the review. Does the ticket need a reviewer name, or can that be left blank?