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Topic: An independent integration test suite
Replies: 128   Last Post: Dec 8, 2013 3:21 PM

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 Albert D. Rich Posts: 311 From: Hawaii Island Registered: 5/30/09
The A. F. Timofeev symbolic integration test suite
Posted: Oct 1, 2013 4:10 AM
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On Sunday, September 29, 2013 10:49:28 AM UTC-10, clicl...@freenet.de wrote:

> I have converted the 61 examples from Chapter 9 of Timofeev's book to
> Derive format and made a visual comparison of your evaluations with
> those in the book. Thus I discovered that two integrands (and their
> antiderivatives) must be corrected: in example #45 a misprinted
> (x^2-1)^(3/2) must be replaced by (x^2-1)^(5/2), and in example #46 your
> ACSC(x)^2 must be replaced by ACSC(x)^4, as is actually printed.
> Timofeev's evaluations correctly differentiate back to the revised
> integrands.
>
> For reasons of quality, uniformity, conciseness, and aesthetics, I also
> propose to:
> - replace 2*ATANH((1 + 2*x^2)) by LN(1 + 1/x^2) in examples #4, #33, #34
> and #35 to get rid of the imaginary offset.
> - replace 2*ATANH((1 - 2*x^2)) by LN(1 - 1/x^2) in example #42 for the
> same reason and to get rid of bad branch cuts.
> - express ACSC as ASEC in example #47 since this is the rule for all
> other examples.
> - change SQRT(2 - COSH(x)^2) to SQRT(1 - SINH(x)^2) in example #57
> because the second radicand looks more natural.
> - move the piecewise constant x/SQRT(x^2) into ATANH and simplify to
> ATANH(1/SQRT(x^2)) in examples #40, #41 (and the old #45).
> - move the piecewise constant x/SQRT(x^2) into ACOTH and simplify to
> ATANH(1/SQRT(x^2)) in example #43.
> - remove a constant term from the evaluation of example #36 as you see
> fit.
> - perhaps replace SQRT(x^2)/x by x/SQRT(x^2) in examples #37, #38, #43,
> #47 and #53, as the latter form is used elsewhere. In the same vain,
> simplify SQRT(x^2)/x^3 to 1/(x*SQRT(x^2)) in example #38, (simplify
> SQRT(x^2)/x^2 to 1/SQRT(x^2) in the old example #46), simplify
> SQRT(x^2)/x^3 to 1/(x*SQRT(x^2)) and SQRT(x^2)/x^5 to 1/(x^3*SQRT(x^2))
> in example #47, and simplify SQRT(x^2)/x^2 to 1/SQRT(x^2) and
> SQRT(x^2)/x^4 to 1/(x^2)^(3/2) in example #48.

Most of the changes you suggested for Chapter 9 of the Timofeev symbolic integration test suite are included in the revised test results file at

http://www.apmaths.uwo.ca/~arich/TimofeevChapter9TestResults.pdf

However I take issue with your assertion that Timofeev's antiderivatives for examples #45 and #46 differentiate back to the integrands. They are still off by piecewise constant factors.

I do not know what you mean by removing "a constant term from the evaluation of example #36".

Note that despite the more compact form of many of the optimal antiderivatives, the scores of the various systems on the Chapter 9 test suite did not change. This is justifiable because the post-integration simplifications required should be done automatically by the systems (but aren't...), and are not really the responsibility of the integrators.

Albert

Date Subject Author
2/24/13 clicliclic@freenet.de
3/19/13 clicliclic@freenet.de
3/21/13 Waldek Hebisch
3/22/13 clicliclic@freenet.de
3/26/13 Waldek Hebisch
3/26/13 clicliclic@freenet.de
4/20/13 clicliclic@freenet.de
4/20/13 Nasser Abbasi
4/20/13 Rouben Rostamian
4/20/13 clicliclic@freenet.de
4/20/13 Rouben Rostamian
4/20/13 Axel Vogt
4/20/13 clicliclic@freenet.de
4/20/13 Axel Vogt
4/21/13 Axel Vogt
4/21/13 clicliclic@freenet.de
4/21/13 Waldek Hebisch
4/22/13 clicliclic@freenet.de
4/22/13 Axel Vogt
4/22/13 clicliclic@freenet.de
4/23/13 Waldek Hebisch
4/24/13 clicliclic@freenet.de
4/25/13 Waldek Hebisch
4/26/13 clicliclic@freenet.de
4/27/13 Waldek Hebisch
4/24/13 Richard Fateman
4/24/13 clicliclic@freenet.de
4/25/13 Richard Fateman
4/26/13 clicliclic@freenet.de
4/26/13 Axel Vogt
4/27/13 clicliclic@freenet.de
4/25/13 Waldek Hebisch
4/25/13 Peter Pein
4/25/13 Nasser Abbasi
4/26/13 Peter Pein
4/26/13 clicliclic@freenet.de
4/26/13 Peter Pein
4/26/13 clicliclic@freenet.de
4/26/13 Richard Fateman
4/27/13 clicliclic@freenet.de
4/27/13 Richard Fateman
6/30/13 clicliclic@freenet.de
6/30/13 Axel Vogt
7/1/13 clicliclic@freenet.de
7/1/13 Axel Vogt
7/1/13 Waldek Hebisch
7/2/13 clicliclic@freenet.de
7/2/13 clicliclic@freenet.de
7/2/13 clicliclic@freenet.de
7/2/13 Nasser Abbasi
7/2/13 Nasser Abbasi
7/4/13 clicliclic@freenet.de
7/4/13 Nasser Abbasi
7/4/13 Nasser Abbasi
7/5/13 clicliclic@freenet.de
7/5/13 Nasser Abbasi
7/9/13 clicliclic@freenet.de
7/10/13 Nasser Abbasi
7/10/13 Richard Fateman
7/10/13 Nasser Abbasi
7/10/13 clicliclic@freenet.de
8/6/13 clicliclic@freenet.de
9/15/13 Albert D. Rich
9/15/13 clicliclic@freenet.de
9/15/13 clicliclic@freenet.de
9/21/13 Albert D. Rich
9/21/13 clicliclic@freenet.de
9/22/13 daly@axiom-developer.org
9/24/13 daly@axiom-developer.org
9/30/13 daly@axiom-developer.org
9/22/13 Albert D. Rich
9/25/13 Albert D. Rich
9/25/13 Albert D. Rich
9/25/13 clicliclic@freenet.de
9/25/13 Albert D. Rich
9/26/13 Albert D. Rich
9/26/13 clicliclic@freenet.de
9/26/13 Albert D. Rich
9/29/13 clicliclic@freenet.de
10/1/13 Albert D. Rich
10/1/13 clicliclic@freenet.de
10/1/13 Albert D. Rich
10/5/13 clicliclic@freenet.de
10/5/13 Albert D. Rich
10/6/13 clicliclic@freenet.de
10/10/13 Albert D. Rich
10/10/13 Nasser Abbasi
10/11/13 clicliclic@freenet.de
11/6/13 Albert D. Rich
11/6/13 Nasser Abbasi
11/7/13 did
11/7/13 clicliclic@freenet.de
11/7/13 clicliclic@freenet.de
11/7/13 Albert D. Rich
11/12/13 clicliclic@freenet.de
11/12/13 Albert D. Rich
11/13/13 clicliclic@freenet.de
11/13/13 Albert D. Rich
11/14/13 clicliclic@freenet.de
11/14/13 Albert D. Rich
11/15/13 clicliclic@freenet.de
11/15/13 Albert D. Rich
11/16/13 clicliclic@freenet.de
11/16/13 clicliclic@freenet.de
11/21/13 Albert D. Rich
11/21/13 clicliclic@freenet.de
11/21/13 Nasser Abbasi
11/21/13 Albert D. Rich
11/21/13 Albert D. Rich
11/22/13 clicliclic@freenet.de
11/14/13 Albert D. Rich
11/15/13 clicliclic@freenet.de
11/15/13 Nasser Abbasi
11/16/13 clicliclic@freenet.de
11/16/13 Nasser Abbasi
11/7/13 did
11/7/13 clicliclic@freenet.de
4/20/13 Richard Fateman
4/21/13 clicliclic@freenet.de
4/20/13 Axel Vogt
4/20/13 clicliclic@freenet.de
4/20/13 Waldek Hebisch
4/21/13 G. A. Edgar
12/8/13 clicliclic@freenet.de
10/5/13 Albert D. Rich
10/6/13 clicliclic@freenet.de

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