Re: [fricas-devel] fyi, the problem of zero result for antiderivative instead of not solved

[Qian Yun]

I tested some of the integrals, not all.

It seems that for integrals contain only x (no a/b), failure is caused
by commit 1f42999f91ce516a8d027a61be4ecbf32ad2ada4 on Jun 13 2022,
"Handle some elliptic integrals".
BTW, for FriCAS, pi is typed as "%pi", is the usage correct in your
other tests?

- Qian

On 8/27/22 17:17, 'Nasser M. Abbasi' via FriCAS - computer algebra 
system wrote:
Fyi,

I think I mentioned this before at a different forum.

This is just FYI, that Fricas still gives zero for some integrals instead
of returning the input if it can't solve it. This confuses the  CAS
integration test program, as it thinks it solved the integral.  I will try
to add special check for Fricas to filter these results as not solved. The
only legal antiderivative of zero should be when the integrand itself is
zero, and there is only one such integral in the whole test suite.

fricas
Checking for foreign routines
FRICAS="/usr/local/lib/fricas/target/x86_64-linux-gnu"
spad-lib="/usr/local/lib/fricas/target/x86_64-linux-gnu/lib/libspad.so"
                        FriCAS Computer Algebra System
                             Version: FriCAS 1.3.8
(1) -> integrate(x/sqrt(1-x^3),x)
    (1)  0
1) -> integrate(x/(-x^3+1)^(1/2),x)
    (1)  0
(2) -> integrate(x/(-x^3+1)^(1/2),x)
    (2)  0
(3) -> integrate(1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/pi/(a*x-1)^(1/2),x)
    (3)  0

etc.. The following is partial list of such integrands.


sqlite> select command_in_sage,fricas_anti from main where fricas_anti="0";

integrate(x/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x,
algorithm="fricas")|0
integrate(1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/pi/(a*x-1)^(1/2),x,
algorithm="fricas")|0
integrate(0,x, algorithm="fricas")|0
integrate(1/(-2-3*x)^(1/2)/(2+3*x)^(1/2),x, algorithm="fricas")|0
integrate(1/(-b*x-2)^(1/2)/(b*x+2)^(1/2),x, algorithm="fricas")|0
integrate(x^2*(b*x+a)^(1/2)/(-b*x-a)^(1/2),x, algorithm="fricas")|0
integrate(x*(b*x+a)^(1/2)/(-b*x-a)^(1/2),x, algorithm="fricas")|0
integrate((b*x+a)^(1/2)/(-b*x-a)^(1/2),x, algorithm="fricas")|0
integrate((b*x+a)^(1/2)/x/(-b*x-a)^(1/2),x, algorithm="fricas")|0
integrate((b*x+a)^(1/2)/x^2/(-b*x-a)^(1/2),x, algorithm="fricas")|0
integrate((b*x+a)^(1/2)/x^3/(-b*x-a)^(1/2),x, algorithm="fricas")|0
integrate(1/x^(1/2)/(-b*x+a)^(1/2)/(b*x+a)^(1/2),x, algorithm="fricas")|0
integrate(1/x^(1/2)/(-b*x+2)^(1/2)/(b*x+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(2-3*x)^(1/2)/x^(1/2)/(2+3*x)^(1/2),x, algorithm="fricas")|0
integrate(1/(1-x)^(1/2)/x^(1/2)/(1+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(1+x)^(1/2)/(-x^2+x)^(1/2),x, algorithm="fricas")|0
integrate((1+x)^(1/2)/(1-x)^(1/2)/x^(1/2),x, algorithm="fricas")|0
integrate((1+x)^(1/2)/(-x^2+x)^(1/2),x, algorithm="fricas")|0
integrate((1-x)^(1/2)/x^(1/2)/(1+x)^(1/2),x, algorithm="fricas")|0
integrate((-1+1/x)^(1/2)*(1/x)^(1/2)*x^(1/2)/(1+x)^(1/2),x,
algorithm="fricas")|0
integrate((1-2*x)^(1/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm="fricas")|0
integrate((3+5*x)^(1/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm="fricas")|0
integrate(1/(3-x)^(1/2)/(1+x)^(1/2)/(2+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(2-x)^(1/2)/(1+x)^(1/2)/(3+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(1-x)^(1/2)/(2+x)^(1/2)/(3+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(1-x)^(1/2)/(2-x)^(1/2)/(3-x)^(1/2),x, algorithm="fricas")|0
integrate(1/(-3-x)^(1/2)/(-2+x)^(1/2)/(-1+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(-2-x)^(1/2)/(-3+x)^(1/2)/(-1+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(-1-x)^(1/2)/(-3+x)^(1/2)/(-2+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(-3-x)^(1/2)/(-2-x)^(1/2)/(-1-x)^(1/2),x, algorithm="fricas")|0
integrate((2+3*x)^(1/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm="fricas")|0
integrate(1/(1-2*x)^(1/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x,
algorithm="fricas")|0
integrate(1/(6-x)^(1/2)/(-2+x)^(1/2)/(-1+x)^(1/2),x, algorithm="fricas")|0
integrate(1/((6-x)*(-2+x))^(1/2)/(-1+x)^(1/2),x, algorithm="fricas")|0
integrate(1/(-1+x)^(1/2)/(-x^2+8*x-12)^(1/2),x, algorithm="fricas")|0
integrate((2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x,
algorithm="fricas")|0
integrate((7+5*x)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x,
algorithm="fricas")|0
integrate(1/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x,
algorithm="fricas")|0
integrate(1/x^(1/2)/(-a^2*x^2+1)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^2-1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^2-1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^2-1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^2-1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^2-1)^(1/2)/(x^2+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(-x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(-3*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(-4*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(-5*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^2-1)^(1/2)/(7+x^2-4*3^(1/2))^(1/2),x, algorithm="fricas")|0
integrate(1/(3+x^2*(-3+3^(1/2)))^(1/2)/(3-3*3^(1/2)+2*3^(1/2)*x^2)^(1/2),x,
algorithm="fricas")|0
integrate(1/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate(x/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate(1/(-x^3-1)^(1/2),x, algorithm="fricas")|0
integrate(x/(-x^3-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(x^4-1)^(1/2),x, algorithm="fricas")|0
integrate((1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate((1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm="fricas")|0
integrate((1-x-3^(1/2))/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate((1+x-3^(1/2))/(-x^3-1)^(1/2),x, algorithm="fricas")|0
integrate((-1+x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate((-1-x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm="fricas")|0
integrate((d*x+c)/(-x^3+1)^(1/2),x, algorithm="fricas")|0
integrate((d*x+c)/(-x^3-1)^(1/2),x, algorithm="fricas")|0
integrate(1/(3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x, algorithm="fricas")|0
integrate((3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x, algorithm="fricas")|0
integrate((3+5*x)^(1/2)/(-12*x^2+5*x+2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4+5*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4+4*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4+3*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4+2*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4+x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4-x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4-2*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4-3*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4-4*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(3*x^4-5*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+7*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+6*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+5*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+4*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+3*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+2*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4+x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4-x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4-2*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4-3*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4-4*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(2*x^4-5*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(-2*x^4+7*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(-2*x^4+6*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(-2*x^4+5*x^2-3)^(1/2),x, algorithm="fricas")|0
integrate(1/(-3*x^4+6*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(-3*x^4+5*x^2-2)^(1/2),x, algorithm="fricas")|0
integrate(1/(-x^4+5*x^2-1)^(1/2),x, algorithm="fricas")|0
etc..


--Nasser


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