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

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clicliclic@freenet.de

Posts: 997
Registered: 4/26/08
Re: An independent integration test suite
Posted: Apr 20, 2013 12:16 PM
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clicliclic@freenet.de schrieb:
>
> The Russian book "Integration of Functions" [...] published by A.F.
> Timofeev [...] in 1948 provides [...] 533 integration examples [...].
> I believe the whole would make a good independent integration test
> suite because the book antedates all automated integrators and because
> the author claims to cover the field thoroughly [...].
>
> There are the usual misprints in the book, but with both the integrand
> and antiderivative available, the original meaning can be
> reconstructed for all (or almost all) examples I think. Timofeev's
> antiderivatives are usually close to the most compact form possible
> (an exception is his consistent use of logarithms for inverse
> hyperbolic functions), but they have to be checked for validity over
> the complex plane, and be corrected if necessary [...]. Apart from
> compactness, continuity (and reality) on the real axis might be worth
> checking and repairing too.
>
> So, if 5 to 10 people were found willing to type in and check (and
> perhaps correct or improve) 50 to 100 integrals and evaluations each,
> a digitization of this corpus could be an almost pleasant task, and
> surely quite useful. [...]
>


Although no interest has been shown in this integration test suite, I
have entered, checked, and amended all 81 integrals from chapter 1; the
integrals are appended below. Occasional multiple evaluations illustrate
alternatives worth pointing out, and integrals collected in vectors
represent examples involving sub-cases. Suggestions how to format the
integrals for easy testing of as systems as possible are welcome.

The antiderivatives hold on the entire complex plane and exhibit no
artificial discontinuities on the real axis (assuming the function
definitions of Derive). This does not apply to poles that cannot
sensibly be integrated over; thus logarithmic poles introduce imaginary
steps whose systematic removal via LN(x) <- 1/2*LN(x^2) would have been
awkward in many cases.

On these integrals, the performance of Derive 6.10 has been measured
with the integration variable limited to real values (the default mode
around which the system was built) - to declare the variable complex
should be considered unfair:

ch. ex's Der. Mpl MMA etc. etc.
6.10 ... ...
---------------------------------------
1 81 79 ?? ??
2 90 - - -
3 14 - - -
4 132 - - -
5 120 - - -
6 26 - - -
7 11 - - -
8 59 - - -
-------------------------------------
100% 97.5% ????% ????%

Derive 6.10 fails on examples 42 and 65; it automatically integrates
example 29 only with the Trigonometry simplification flag set to
Collect, which is not the default. When the integration variable is
declared complex, Derive additionally fails on integrals 44, 64, and 81.

Perhaps other systems (and/or chapters) can be added here by and by. I
am currently working on chapter 4 (132 integrals) in which I am
expecially interested, but not expecting to finish this before some
months have passed. I am not likely to enter the integrals from other
chapters too (particularly not the remaining massive ones 2, 5, and 8).

Martin.


" Timofeev (1948) Ch. 1, examples 1 - 21 (p. 25-26) ... "

INT(1/(a^2-b^2*x^2),x)=1/(a*b)*ATANH(b*x/a)

INT(1/(a^2+b^2*x^2),x)=1/(a*b)*ATAN(b*x/a)

INT(SEC(2*a*x),x)=1/(4*a)*LN((CSC(2*a*x)+1)/(CSC(2*a*x)-1))=-1/(~
2*a)*LN(TAN(pi/4-a*x))

INT(1/(4*SIN(x/3)),x)=3/8*LN((1-COS(x/3))/(1+COS(x/3)))=3/4*LN(T~
AN(x/6))

INT(1/COS(3/4*pi-2*x),x)=1/4*LN((1-SIN(3/4*pi-2*x))/(1+SIN(3/4*p~
i-2*x)))=1/2*LN(TAN(pi/8-x))

INT(SEC(x)*TAN(x),x)=SEC(x)

INT(CSC(x)*COT(x),x)=-CSC(x)

INT(TAN(x)/SIN(2*x),x)=1/2*TAN(x)

INT(1/(1+COS(x)),x)=SIN(x)/(1+COS(x))=TAN(x/2)

INT(1/(1-COS(x)),x)=SIN(x)/(COS(x)-1)=-COT(x/2)

INT(SIN(x)/(a-b*COS(x)),x)=1/b*LN(a-b*COS(x))

INT(COS(x)/(a^2+b^2*SIN(x)^2),x)=1/(a*b)*ATAN(b*SIN(x)/a)

INT(COS(x)/(a^2-b^2*SIN(x)^2),x)=1/(a*b)*ATANH(b*SIN(x)/a)

[INT(SIN(2*x)/(b^2*SIN(x)^2+a^2),x)=1/b^2*LN(a^2+b^2*SIN(x)^2),I~
NT(SIN(2*x)/(b^2*SIN(x)^2-a^2),x)=1/b^2*LN(a^2-b^2*SIN(x)^2)]

[INT(SIN(2*x)/(b^2*COS(x)^2+a^2),x)=-1/b^2*LN(a^2+b^2*COS(x)^2),~
INT(SIN(2*x)/(b^2*COS(x)^2-a^2),x)=-1/b^2*LN(a^2-b^2*COS(x)^2)]

INT(1/(4-COS(x)^2),x)=SQRT(3)/6*(ATAN(SIN(x)*COS(x)/(2*SQRT(3)+4~
-COS(x)^2))+x)

INT(#e^x/(#e^(2*x)-1),x)=-ATANH(#e^x)

INT(1/(x*LN(x)),x)=LN(LN(x))

INT(1/(x*(1+LN(x)^2)),x)=ATAN(LN(x))

INT(1/(x*(1-LN(x))),x)=-LN(1-LN(x))

INT(1/(x*(1+LN(x/a))),x)=LN(1+LN(x/a))

" Timofeev (1948) Ch. 1, examples 22 - 40 (p. 27-28) ... "

INT(((1-SQRT(x)+x)/x)^2,x)=3*LN(x)+x-4*SQRT(x)+4/SQRT(x)-1/x

INT((2-x^(2/3))*(x+SQRT(x))/x^(3/2),x)=2*LN(x)-6/7*x^(7/6)-3/2*x~
^(2/3)+4*SQRT(x)

INT((2*x-1)/(2*x+3),x)=x-2*LN(2*x+3)

INT((2*x-5)/(3*x^2-2),x)=1/3*LN(2-3*x^2)+5/SQRT(6)*ATANH(SQRT(6)~
*x/2)=(4-5*SQRT(6))/12*LN(SQRT(3)*x-SQRT(2))+(5*SQRT(6)+4)/12*LN~
(SQRT(3)*x+SQRT(2))

INT((2*x-5)/(3*x^2+2),x)=1/3*LN(3*x^2+2)-5/SQRT(6)*ATAN(SQRT(6)*~
x/2)

INT(SIN(x)*SIN(x/4),x)=2/3*SIN(3*x/4)-2/5*SIN(5*x/4)

INT(COS(3*x)*COS(4*x),x)=1/14*SIN(7*x)+1/2*SIN(x)

INT(TAN(x)*TAN(x-a),x)=1/TAN(a)*LN(1+TAN(a)*TAN(x))-x

[INT(SIN(x)^2,x)=1/2*(x-SIN(x)*COS(x)),INT(COS(x)^2,x)=1/2*(x+SI~
N(x)*COS(x))]

INT(SIN(x)*COS(x)^3,x)=-1/4*COS(x)^4

INT(COS(x)^3/SIN(x)^4,x)=1/SIN(x)-1/(3*SIN(x)^3)

INT(1/(SIN(x)^2*COS(x)^2),x)=TAN(x)-COT(x)

INT(COT(3/4*x)^2,x)=-4/3*COT(3*x/4)-x

INT((1+TAN(2*x))^2,x)=1/2*TAN(2*x)-LN(COS(2*x))

INT((TAN(x)-COT(x))^2,x)=TAN(x)-COT(x)-4*x

INT((TAN(x)-SEC(x))^2,x)=2*(TAN(x)-SEC(x))-x=2*TAN(x/2-pi/4)-x

INT(SIN(x)/(1+SIN(x)),x)=COS(x)/(1+SIN(x))+x=TAN(pi/4-x/2)+x

INT(COS(x)/(1-COS(x)),x)=SIN(x)/(COS(x)-1)-x=-COT(x/2)-x

INT((#e^(x/2)-1)^3*#e^(-x/2),x)=-6*#e^(x/2)+2*#e^(-x/2)+#e^x+3*x

" Timofeev (1948) Ch. 1, examples 41 - 65 (p. 35-37) ... "

INT(1/(x^2-6*x+5),x)=1/4*LN((x-5)/(x-1))

INT(x^2/(13-6*x^3+x^6),x)=1/6*ATAN((x^3-3)/2)

INT((x+2)/(x^2-4*x-1),x)=1/2*LN(1+4*x-x^2)+4/SQRT(5)*ATANH((2-x)~
/SQRT(5))=1/10*((4*SQRT(5)+5)*LN(x-SQRT(5)-2)+(5-4*SQRT(5))*LN(x~
+SQRT(5)-2))

INT(1/(1+(x+1)^(1/3)),x)=3/2*(x+1)^(2/3)-3*(x+1)^(1/3)+3*LN(1+(x~
+1)^(1/3))

INT(1/((a*x+b)*SQRT(x)),x)=2/(SQRT(a)*SQRT(b))*ATAN(SQRT(a)*SQRT~
(x)/SQRT(b))

INT(x^3*SQRT(1+x^2),x)=1/15*(3*x^4+x^2-2)*SQRT(x^2+1)

INT(x/SQRT(a^4-x^4),x)=1/2*ASIN(x^2/a^2)

[INT(1/(x*SQRT(x^2-a^2)),x)=1/a*ATAN(SQRT(x^2-a^2)/a),INT(1/(x*S~
QRT(a^2-x^2)),x)=-1/a*ATANH(SQRT(a^2-x^2)/a),INT(1/(x*SQRT(x^2+a~
^2)),x)=-1/a*ATANH(a/SQRT(x^2+a^2))]

INT(1/SQRT(2+x-x^2),x)=ASIN((2*x-1)/3)

INT(1/SQRT(3*x^2-4*x+5),x)=1/SQRT(3)*LN(SQRT(3)*SQRT(3*x^2-4*x+5~
)+3*x-2)

INT(1/SQRT(x-x^2),x)=ASIN(2*x-1)

INT((2*x+1)/SQRT(2+x-x^2),x)=2*ASIN((2*x-1)/3)-2*SQRT(-x^2+x+2)

INT(1/(x*SQRT(2+x-x^2)),x)=1/SQRT(2)*LN((2*SQRT(2)*SQRT(-x^2+x+2~
)-x-4)/x)

INT(1/((x-2)*SQRT(2+x-x^2)),x)=2*SQRT(2+x-x^2)/(3*(x-2))

INT((2+3*SIN(x))/(SIN(x)*(1-COS(x))),x)=1/2*LN((1-COS(x))/(1+COS~
(x)))+(3*SIN(x)+1)/(COS(x)-1)

INT(1/(2+3*COS(x)^2),x)=1/SQRT(10)*(x-ATAN(3*SIN(x)*COS(x)/(SQRT~
(10)+2+3*COS(x)^2)))

INT((1-TAN(x))/SIN(2*x),x)=1/4*LN((1-COS(2*x))/(1+COS(2*x)))-1/2~
*TAN(x)=1/2*(LN(TAN(x))-TAN(x))

INT((1+TAN(x)^2)/(1-TAN(x)^2),x)=1/2*LN((1+TAN(x))/(1-TAN(x)))

INT((a^2-4*COS(x)^2)^(3/4)*SIN(2*x),x)=1/7*(a^2-4*COS(x)^2)^(7/4)

INT(SIN(2*x)/(a^2-4*SIN(x)^2)^(1/3),x)=-3/8*(a^2-4*SIN(x)^2)^(2/~
3)

INT(1/SQRT(a^(2*x)-1),x)=1/LN(a)*ATAN(SQRT(a^(2*x)-1))=1/LN(a)*A~
SEC(SQRT(a^(2*x)))

INT(#e^(x/2)/SQRT(#e^x-1),x)=2*LN(SQRT(#e^x-1)+#e^(x/2))

INT(ATAN(x)^n/(1+x^2),x)=1/(n+1)*ATAN(x)^(n+1)

INT(ASIN(x/a)^(3/2)/SQRT(a^2-x^2),x)=2/5*(a/SQRT(a^2-x^2))*SQRT(~
1-(x/a)^2)*ASIN(x/a)^(5/2)

INT(1/(ACOS(x)^3*SQRT(1-x^2)),x)=1/(2*ACOS(x)^2)

" Timofeev (1948) Ch. 1, examples 66 - 81 (p. 41-42) ... "

INT(LN(x)^2*x,x)=x^2/2*(LN(x)^2-LN(x)+1/2)

INT(LN(x)/x^5,x)=-(4*LN(x)+1)/(16*x^4)

INT(x^2*LN((x-1)/x),x)=x^3/3*LN((x-1)/x)-1/3*LN(x-1)-x*(x+2)/6

INT(COS(x)^5,x)=SIN(x)/15*(3*COS(x)^4+4*COS(x)^2+8)

INT(SIN(x)^2*COS(x)^4,x)=1/6*SIN(x)^3*COS(x)^3+1/8*SIN(x)^3*COS(~
x)-1/16*SIN(x)*COS(x)+x/16

INT(1/SIN(x)^5,x)=3/16*LN((1-COS(x))/(1+COS(x)))-3*COS(x)/(8*SIN~
(x)^2)-COS(x)/(4*SIN(x)^4)

INT(SIN(x)/#e^x,x)=-(COS(x)+SIN(x))/(2*#e^x)

INT(#e^(2*x)*SIN(3*x),x)=1/13*#e^(2*x)*(2*SIN(3*x)-3*COS(3*x))

INT(a^x*COS(x),x)=a^x/(LN(a)^2+1)*(LN(a)*COS(x)+SIN(x))

INT(COS(LN(x)),x)=x/2*(COS(LN(x))+SIN(LN(x)))

INT(SEC(x)^2*LN(COS(x)),x)=TAN(x)*LN(COS(x))+TAN(x)-x

INT(x*TAN(x)^2,x)=LN(COS(x))+x*TAN(x)-1/2*x^2

INT(ASIN(x)/x^2,x)=-ASIN(x)/x+LN((1-SQRT(1-x^2))/x)

INT(ASIN(x)^2,x)=x*ASIN(x)^2+2*SQRT(1-x^2)*ASIN(x)-2*x

INT(x^2*ATAN(x)/(1+x^2),x)=x*ATAN(x)-1/2*ATAN(x)^2-1/2*LN(x^2+1)

INT(ACOS(SQRT(x/(x+1))),x)=(x+1)*(ACOS(SQRT(x/(x+1)))+SQRT(1/(x+~
1))*SQRT(x/(x+1)))

" ... end of Timofeev Ch. 1 "


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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