exp(x) is broken at x=Infinity and x=-Infinity

[golam-m-hossain]

exponetial function exp(x) is broken at both x=-Infinity
and x=Infinity

sage: exp(-Infinity)
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
....
RuntimeError: x*Infinity with non real x encountered.

sage: exp(Infinity)
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
....
RuntimeError: x*Infinity with non real x encountered.

Component: symbolics

Keywords: symbolic exp

Author: Burcin Erocal

Reviewer: Golam Mortuza Hossain

Merged: Sage 4.1.1.rc1

Issue created by migration from https://trac.sagemath.org/ticket/6377

[burcin]

comment:1

Good catch! After adding support for infinity in pynac, I forgot to add cases to handle infinity in the eval functions of special functions.

The fix for exp() needs to go into pynac. I don't know what other functions are effected by this. It would be good to try other special functions defined by Sage to see if they handle infinity, or other constants defined by Sage properly.

[burcin]

Attachment: trac_6377-exp_infinity.patch.gz

doctests for the fix

[burcin]

Author: Burcin Erocal

[burcin]

comment:2

I have a fix for this in my local pynac tree. I will make a new pynac package available soon.

I checked all the functions defined in inifcns_trans.cpp in pynac. The remaining functions still need to be fixed.

[burcin]

comment:3

This now depends on the package linked from #6404.

Please follow the instructions on that ticket to apply & test.

[golam-m-hossain]

comment:4

Hi Burcin,

I tested this out. It looks fine to me.

I guess, it would be good if we could follow some standard convention for
values of these functions at their poles, brunch cuts. For example, following
looks odd to me

sage: arctan(-Infinity)
-1/2*pi
sage: tan(-pi/2)
Infinity

May be we should discuss this in sage-devel for adopting a convention for
these special values.

There are some other issues that would need future work. For example, you have
fixed values of log at 0

sage: SR(0).log()
-Infinity

However, following still raises error

sage: log(0)
ValueError ...

In any case, this patch fixes lot of issues and should be included.
The remaining issues should be fixed later. I am going to give a positive
review shortly.

[golam-m-hossain]

comment:5

Note: I am giving partial positive review because I tested this patch against my stable sage-4.1. So if it applies cleanly on Sage-4.1.1.rc1 then that would be full positive from me.

[golam-m-hossain]

Reviewer: Golam Mortuza Hossain

[sagetrac-mvngu]

Merged: Sage 4.1.1.rc1

[sagetrac-mvngu]

comment:6

I applied patches in the following order:

1. the spkg pynac-0.1.8.p2.spkg at Typeseting for conjugate() of symbolic function is inadequate #6404
2. trac_6404-conjugate_typesetting.patch
3. trac_6401-real_imag_typesetting.patch
4. trac_6377-exp_infinity.patch
5. trac_6243-fderivative_hash.patch
   All doctests pass in my merge tree. So I'm changing Typeseting for conjugate() of symbolic function is inadequate #6404, Typesettings of real() and imag() are broken #6401, exp(x) is broken at x=Infinity and x=-Infinity #6377 and hashes for derivatives of symbolic functions w.r.t. different variables are the same #6243 to positive review as per Golam's request.