Add left and right directions to limits

[DanaErnst]

1. Add from_left and from_right for dir keyword.
   
2. Improve error message dir keyword.
   
3. Add doctests and tests.

[DanaErnst]

Patch passes tests in sage/calculus. Need to test full Sage library.

[DanaErnst]

stand alone patch

[DanaErnst]

Rebased for version 4.5.1, apply only v2 patch.

[DanaErnst]

• All tests passed on version 4.5.1 (running OSX 10.6)
• HTML & PDF reference built without problem

[rbeezer]

Applies, builds, passes all tests, and docs look fine; on 4.5.2.alpha0. So this is a positive review.

Nice job on your first contribution!

[burcin]

Do we really need new keywords for this? And if we do, should it be from_{right,left}?

I think a user interface decision like this needs more input from other developers. I'll post to sage-devel with this question.

[DanaErnst]

The idea for this came up during one of the online sessions for the MAA PREP Workshop for Sage (organized by Rob Beezer, Jason Grout, and Karl-Dieter Crisman) that I am currently enrolled in. While we were discussing calculus during one of our workshop sessions, one of the participants remarked that most students learn one-sided limits as "from the left" and "from the right." Rob, Jason, and Karl-Dieter knew that I was interested in getting involved in Sage development and remarked that I could add that this terminology to Sage if I was interested. I figured that it was an easy way to get my feet wet.

I have been using Sage for almost a year, so I would consider myself a newbie. I'm not personally attached to this patch and if others feel that it is unnecessary bloat, then my feelings won't be hurt.

[burcin]

add deprecation warnings

[burcin]

This was discussed in the thread:

 http://groups.google.com/group/sage-devel/t/9dd6dfe26f09be93

The resulting decision was to deprecate 'above' and 'below' and add support for '+', '-', 'right', and 'left'.

attachment:trac_9200-deprecation.patch makes the necessary changes, on top of Dana's patch.

Patches to be applied in this order:

• attachment:trac_9200-left-right-limits-v2.patch
• attachment:trac_9200-deprecation.patch

[DanaErnst]

Burcin,

Thanks for picking up the ball on this. I was planning on attacking this in a few weeks after the initial craziness of my semester settled down. Now, I get to cross something off my todo list:)

Dana

[rbeezer]

I noticed while reviewing this that there are two "TEST" headers in the docstring for limit(). So I removed the second one and uploaded a new version of the "documentation" patch - only change is the removal of the header (still has Burcin's name on it too).

I'm running tests overnight and then plan to give this a positive review.

Burcin - I'll wait for you to check-off on the one change to your patch.

Rob

[burcin]

Thanks for taking care of the TEST headers Rob. I'm ok with your change. Looking forward to that positive review. :)

[rbeezer]

Thanks, Burcin, for the go-ahead and for prompting the discussion on this one. Builds (on 4.5.2), docs look good, passes all tests (sage -testall) and is consistent with discussion on sage-devel. Positive review.

Congrats to Dana Ernst on his first contribution. Next one will probably engender less discussion. ;-)

Release Manager

Patches to be applied in this order:

• attachment:trac_9200-left-right-limits-v2.patch
• attachment:trac_9200-deprecation-v2.patch

Dana Ernst is first-time contributor (for release notes).