" BTW, for FriCAS, pi is typed as "%pi", is the usage correct in your
other tests?"
I just copied the result as given to sagemath interface which uses pi and
not %pi ofcourse, and just forgot to use %pi when I used the command
directly inside fricas to confirm.
1) -> integrate(1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/%pi/(a*x-1)^(1/2),x)
(1) 0
Type:
Union(Expression(Integer),...)
(2) ->
Yes, all in the list are correct, they are called from sagemath, not
fricas, so syntax might need to be manually adjusted as needed to run them
inside Fricas as you showed.
Thanks
--Nasser
On Saturday, August 27, 2022 at 5:55:13 AM UTC-5 oldk1331 wrote:
> 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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