Riemann sums, added trapezoid option

[sagetrac-gagansekhon]

For piecewise functions, added trapezoid option to riemann_sum and riemann_sum_integral_approximation to already existing option of left, right and midpoint.

Deprecated, trapezoid_integral_approximation and trapezoid

Component: calculus

Keywords: riemann sums, trapezoid

Author: Gagan Sekhon

Reviewer: Dmitrii Pasechnik, Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/10597

[sagetrac-gagansekhon]

Attachment: riemann_sums.patch.gz

Attachment: trac_10597.patch.gz

[sagetrac-gagansekhon]

comment:1

changed file name and commit message to reflect trac number. Pleases use trac_10597.patch only.

[jdemeyer]

Reviewer: Dmitrii Pasechnik

[jdemeyer]

comment:6

There is a doctest failure:

sage -t  -force_lib devel/sage/doc/en/constructions/calculus.rst
**********************************************************************
File "/mnt/usb1/scratch/jdemeyer/merger/sage-4.6.2.alpha2/devel/sage-main/doc/en/constructions/calculus.rst", line 204:
    sage: f.trapezoid(4)
Expected:
    Piecewise defined function with 4 parts, [[(0, 1/2), 1/2*x],
    [(1/2, 1), 9/2*x - 2], [(1, 3/2), 1/2*x + 2],
    [(3/2, 2), -7/2*x + 8]]
Got:
    doctest:1: DeprecationWarning: _word_content is deprecated, use riemann_sum instead
    Piecewise defined function with 4 parts, [[(0, 1/2), 1/2*x], [(1/2, 1), 9/2*x - 2], [(1, 3/2), 1/2*x + 2], [(3/2, 2), -7/2*x + 8]]
**********************************************************************

[jdemeyer]

comment:7

A further small comment: in the docstrings, you should use OUTPUT: instead of Output:.

[jdemeyer]

Changed reviewer from Dmitrii Pasechnik to Dmitrii Pasechnik, Jeroen Demeyer

[sagetrac-gagansekhon]

comment:8

There is a discussion regarding this ticket on sage-devel.
http://groups.google.com/group/sage-devel/browse_thread/thread/c2c196ea37c753ae/bacb7b1fc3042d56?lnk=gst&q=gagan#bacb7b1fc3042d56

Until we come to a consensus, I think we should not merge it.

[dimpase]

comment:9

Replying to @sagetrac-gagansekhon:

There is a discussion regarding this ticket on sage-devel.
http://groups.google.com/group/sage-devel/browse_thread/thread/c2c196ea37c753ae/bacb7b1fc3042d56?lnk=gst&q=gagan#bacb7b1fc3042d56

Until we come to a consensus, I think we should not merge it.

Do you refer to the objection that trapezoid rule is not a Riemann sum? IMHO it is moot.

[sagetrac-khalasz]

comment:11

While helping a high school Calculus student with basic integration I tried to use Sage to do some computational examples, and when it didn't work as I expected it to I came across this ticket. The student's textbook considered a trapezoidal sum to be a Riemann sum, so I think pushing this ticket through would be helpful from the standpoint of wanting Sage to be a useful educational tool.

It seems that only minor updates are needed to get this patch to a point where it would be acceptable. I would be willing to make these small changes. However, based on the discussion cited above, which didn't seem to come to any sort of conclusion, I am hesitant to do so. Any thoughts on whether this patch is worth cleaning up and adding to the Sage source? I vote yes, but of course I am no Sage guru.

[mkoeppe]

comment:15

Patch is outdated after replacement of the piecewise implementation in #14801.

[davidlowryduda]

comment:16

I was asked about this ticket recently by a beginner, since it has the beginner keyword. But after looking at the ticket, I think this is not a good beginner ticket, especially now that the underlying code has been completely rewritten since this was first proposed.

I'm removing the beginner tag. But I also suggest that this ticket be closed --- there are no longer any Riemann sums here, so the discussion as to whether a trapezoidal sum should be considered no longer applies.