Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Richard Fateman Posts: 1,539 Registered: 12/7/04
Re: An independent integration test suite
Posted: Apr 24, 2013 2:11 PM

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 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