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

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Richard Fateman

Posts: 1,400
Registered: 12/7/04
Re: An independent integration test suite
Posted: Apr 24, 2013 2:11 PM
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I'm not sure what the relevance is of DERIVE's performance, since the
program is neither supported nor distributed at this time, but the
syntax looked almost identical to Macsyma (commercial, not supported or
distributed) so I tried to run it through Macsyma 2.4.0

textual changes ... LN -> LOG, PI -> %pi, #e-.%e, INT( -> integrate(,
removal of [ ].. downcasing of all trig functions and sqrt.

1. I found expressions in the test suite of the form

integrate(A,x) = B = C

which do not parse properly since B=C makes sense in Macsyma
if B and C are algebraic. It does not make sense in Macsyma
to ask (A=B) = C since A=B is logical not algebraic.

That is almost beside the point though. What is the test suite
supposed to be used for? Testing the simplification of B=C?
Is either answer, B or C supposed to be OK for the integration?
Is one supposed to verify the answer by differentiating B?

So I removed all the "answers" of several forms. I am optimistically
assuming that all results from integration of the forms in this chapter
will pass
some version of differentiation + simplification.

Running through the examples, Macsyma paused in a number of places
to ask (for example) is a*b pos or neg; is a nonzero; is x >0, is n+1
nonzero..

So I added assumptions such as assume(a>0, b>0, x>0 n>0) and ran the
test again.

The test went through without any burps that I noticed except for

integrate(asin(x/a)^(3/2)/sqrt(a^2-x^2),x)
which was not integrated. This appears to be the same as the first
clumsily restated expression in the original posting.

2. The results were the same with MAXIMA.




RJF


The test suite as used



integrate(1/(a^2-b^2*x^2),x);
integrate(1/(a^2+b^2*x^2),x);
integrate(sec(2*a*x),x);
integrate(1/(4*sin(x/3)),x);
integrate(1/cos(3/4*%pi-2*x),x);
integrate(sec(x)*tan(x),x);
integrate(csc(x)*cot(x),x);
integrate(tan(x)/sin(2*x),x);
integrate(1/(1+cos(x)),x);
integrate(1/(1-cos(x)),x);
integrate(sin(x)/(a-b*cos(x)),x);
integrate(cos(x)/(a^2+b^2*sin(x)^2),x);
integrate(cos(x)/(a^2-b^2*sin(x)^2),x);
integrate(sin(2*x)/(b^2*sin(x)^2+a^2),x);
integrate(sin(2*x)/(b^2*cos(x)^2+a^2),x);
integrate(sin(2*x)/(b^2*cos(x)^2-a^2),x);
integrate(1/(4-cos(x)^2),x);
integrate(%w^x/(%w^(2*x)-1),x);
integrate(1/(x*log(x)),x);
integrate(1/(x*(1+log(x)^2)),x);
integrate(1/(x*(1-log(x))),x);
integrate(1/(x*(1+log(x/a))),x);
integrate(((1-sqrt(x)+x)/x)^2,x);
integrate((2-x^(2/3))*(x+sqrt(x))/x^(3/2),x);
integrate((2*x-1)/(2*x+3),x);
integrate((2*x-5)/(3*x^2-2),x);
integrate((2*x-5)/(3*x^2+2),x);
integrate(sin(x)*sin(x/4),x);
integrate(cos(3*x)*cos(4*x),x);
integrate(tan(x)*tan(x-a),x);
integrate(sin(x)^2,x);
integrate(cos(x)^2,x);
integrate(sin(x)*cos(x)^3,x);
integrate(cos(x)^3/sin(x)^4,x);
integrate(1/(sin(x)^2*cos(x)^2),x);
integrate(cot(3/4*x)^2,x);
integrate((1+tan(2*x))^2,x);
integrate((tan(x)-cot(x))^2,x);
integrate((tan(x)-sec(x))^2,x);
integrate(sin(x)/(1+sin(x)),x);
integrate(cos(x)/(1-cos(x)),x);
integrate((%w^(x/2)-1)^3*%w^(-x/2),x);
integrate(1/(x^2-6*x+5),x);
integrate(x^2/(13-6*x^3+x^6),x);
integrate((x+2)/(x^2-4*x-1),x);
integrate(1/(1+(x+1)^(1/3)),x);
integrate(1/((a*x+b)*sqrt(x)),x);
integrate(x^3*sqrt(1+x^2),x);
integrate(x/sqrt(a^4-x^4),x);
integrate(1/(x*sqrt(x^2-a^2)),x);
integrate(1/(x*sqrt(a^2-x^2)),x);
integrate(1/(x*sqrt(x^2+a^2)),x);
integrate(1/sqrt(2+x-x^2),x);
integrate(1/sqrt(3*x^2-4*x+5),x);
integrate(1/sqrt(x-x^2),x);
integrate((2*x+1)/sqrt(2+x-x^2),x);
integrate(1/(x*sqrt(2+x-x^2)),x);
integrate(1/((x-2)*sqrt(2+x-x^2)),x);
integrate((2+3*sin(x))/(sin(x)*(1-cos(x))),x);
integrate(1/(2+3*cos(x)^2),x);
integrate((1-tan(x))/sin(2*x),x);
integrate((1+tan(x)^2)/(1-tan(x)^2),x);
integrate((a^2-4*cos(x)^2)^(3/4)*sin(2*x),x);
integrate(sin(2*x)/(a^2-4*sin(x)^2)^(1/3),x);
integrate(1/sqrt(a^(2*x)-1),x);
integrate(%w^(x/2)/sqrt(%w^x-1),x);
integrate(atan(x)^n/(1+x^2),x);
integrate(asin(x/a)^(3/2)/sqrt(a^2-x^2),x);
integrate(1/(acos(x)^3*sqrt(1-x^2)),x);
integrate(log(x)^2*x,x);
integrate(log(x)/x^5,x);
integrate(x^2*log((x-1)/x),x);
integrate(cos(x)^5,x);
integrate(sin(x)^2*cos(x)^4,x);
integrate(1/sin(x)^5,x);
integrate(sin(x)/%w^x,x);
integrate(%w^(2*x)*sin(3*x),x);
integrate(a^x*cos(x),x);
integrate(cos(log(x)),x);
integrate(sec(x)^2*log(cos(x)),x);
integrate(x*tan(x)^2,x);
integrate(asin(x)/x^2,x);
integrate(asin(x)^2,x);
integrate(x^2*atan(x)/(1+x^2),x);
integrate(acos(sqrt(x/(x+1))),x);


Date Subject Author
2/24/13
Read An independent integration test suite
clicliclic@freenet.de
3/19/13
Read where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/21/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/22/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/26/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/26/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Nasser Abbasi
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/21/13
Read Re: An independent integration test suite
Waldek Hebisch
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/22/13
Read Re: An independent integration test suite
Axel Vogt
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/23/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
Richard Fateman
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Richard Fateman
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Axel Vogt
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/25/13
Read Re: An independent integration test suite
Peter Pein
4/25/13
Read Re: An independent integration test suite
Nasser Abbasi
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Richard Fateman
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Richard Fateman
6/30/13
Read Re: An independent integration test suite
clicliclic@freenet.de
6/30/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite / Chap 3
clicliclic@freenet.de
7/1/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite
Waldek Hebisch
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/5/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/5/13
Read Re: An independent integration test suite
Nasser Abbasi
7/9/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/10/13
Read Re: An independent integration test suite
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite/ Klerer?
Richard Fateman
7/10/13
Read Re: An independent integration test suite/ Klerer?
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite
clicliclic@freenet.de
8/6/13
Read Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/24/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/30/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/26/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/29/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
10/1/13
Read The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
10/11/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/22/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Richard Fateman
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Waldek Hebisch
4/21/13
Read Re: An independent integration test suite
G. A. Edgar
12/8/13
Read Re: An independent integration test suite
clicliclic@freenet.de
10/5/13
Read Re: An independent integration test suite
Albert D. Rich
10/6/13
Read Re: An independent integration test suite
clicliclic@freenet.de

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