Add non-offset logarithmic integral, Li

[sagetrac-myurko]

Add the logarithmic integral, Li, with integration starting at 0 rather than 2.

CC: @sagetrac-myurko @benjaminfjones

Component: calculus

Reviewer: Karl-Dieter Crisman

Issue created by migration from https://trac.sagemath.org/ticket/7357

[sagetrac-myurko]

comment:1

Attachment: li(x).patch.gz

[kcrisman]

comment:2

This is nice, but like #3401, should have some doctests indicating it works for complex input (I assume it does). The patch also depends on #3401.

[kcrisman]

comment:3

Attachment: non-offset-log-int.patch.gz

This patch adds these tests. It still depends on the (newest) patch at #3401, and in fact gets rid of one final thing which was only needed by the previous implementation of Li.

[kcrisman]

Author: Michael Yurko

[kcrisman]

Reviewer: Karl-Dieter Crisman

[burcin]

comment:5

This needs more work. See my comments about the prec parameter at #3401 comment:10.

Two different functions whose names differ only in capitalization (li and Li) is also very confusing. We need to come up with a better name for this.

[kcrisman]

comment:7

This seems to be addressed in the context of a much bigger overhaul by #11143. But there the name is... more complicated.

[benjaminfjones]

comment:8

Yes, this would duplicate work done in #11143. The function added there is a fully symbolic function with numerical evaluation handled by mpmath. I think that is superior to the one defined here which is just a wrapper for the mpmath call.

The function added in #11143 is really a class called Function_exp_integral_li and it has an alias exp_integral_li to match the other exponential integrals. #11143 also moves all the exponential integrals to a new module under sage/functions so this would conflict with that design decision too.

[kcrisman]

comment:9

So this can be closed as duplicate, correct? Except I really would love it to be called Li instead of something horribly long... either way, feel free to review this as positive; I'm changing the milestone.

[kcrisman]

comment:10

This is definitely and definitively duplicated by the much more comprehensive #11143.

[kcrisman]

Changed author from Michael Yurko to none