#11143: define symbolic functions for exponential integrals
-----------------------------+----------------------------------------------
Reporter: kcrisman | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.1
Component: symbolics | Keywords: ei Ei special function maxima
Work_issues: | Upstream: N/A
Reviewer: Burcin Erocal | Author: Benjamin Jones
Merged: | Dependencies:
-----------------------------+----------------------------------------------
Comment(by benjaminfjones):
The patch now depends on #11513
Here are new timings for the ``_eval_`` method with
``_is_numerically_zero()``:
{{{
#!rst
.. code-block:: python
# special case: *quickly* test if (z == 0 and n > 1)
if isinstance(z, Expression):
if z._is_numerically_zero():
z_zero = True # for later
if n > 1:
return 1/(n-1)
else:
if not z:
z_zero = True
if n > 1:
return 1/(n-1)
====================================================== =======
Test Time
====================================================== =======
sage: timeit("f = exp_integral_e(n,z)") 535 µs
sage: timeit("f = exp_integral_e(n,0)") 482 µs
sage: assume(n > 1); timeit("f = exp_integral_e(n,0)") 3.56 ms
sage: timeit("f = exp_integral_e(0,z)") 968 µs
sage: timeit("f = exp_integral_e(1.0,1.0)") 160 µs
====================================================== =======
}}}
I realized that in row 2 of the previous timings I neglected to assume n >
1 so those timings aren't giving much information since the expression is
left unevaluated like in row 1. The new row 3 includes that assumption so
that the simplified result ``1/(n-1)`` is created and returned.
I'll update the timings above and move these tables to the wiki.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11143#comment:18>
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