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]]
**********************************************************************