FYI,
This is update for the final summer 2024 edition of CAS integration tests
about the issue Fricas giving zero for non zero integrand.
There are 4 such cases found out of 107,000 integrals.
Here they are
>sqlite3 cas_integration_tests.db
sqlite> select COUNT(*) from main where fricas_anti="0";
6
But only 2 of these 6 cases should give zero. The rest should not.
sqlite> select command_in_fricas from main where fricas_anti="0";
integrate(1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/pi/(a*x-1)^(1/2),x,
algorithm="fricas")
integrate(0,x, algorithm="fricas")
integrate((1-x)^3+(-x^2+x)^3-3*(1-x)*(-x^2+x)*(x^2-1)+(x^2-1)^3,x,
algorithm="fricas")
integrate(a*(-3*c+2*2^(1/2)*c+6^(1/2)*a*x)/(c^2-3^(1/2)*a*c*x+2^(1/2)*a^2*x^2),x,
algorithm="fricas")
integrate((3*7^(1/2)+6*11^(1/2)+(-121*105^(1/2)-98*165^(1/2))*x^4)/(-12*15^(1/2)+10200*x^4-118580*15^(1/2)*x^8),x,
algorithm="fricas")
integrate((-36-2*6^(1/2)*x^2)/(9*3^(1/2)+3*2^(1/2)*x^2-x^4),x,
algorithm="fricas")
Here is the output from Fricas for the four cases:
FriCAS Computer Algebra System
Version: FriCAS 1.3.10 built with sbcl 2.3.11
Timestamp: Wed Jan 10 09:37:52 PM CST 2024
(4) -> setSimplifyDenomsFlag(true)
(5) ->
integrate(a*(-3*c+2*2^(1/2)*c+6^(1/2)*a*x)/(c^2-3^(1/2)*a*c*x+2^(1/2)*a^2*x^2),x)
(5) 0
Type:
Union(Expression(AlgebraicNumber),...)
(6) -> integrate(1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/pi/(a*x-1)^(1/2),x)
(6) 0
Type:
Union(Expression(Integer),...)
(7) ->
integrate((3*7^(1/2)+6*11^(1/2)+(-121*105^(1/2)-98*165^(1/2))*x^4)/(-12*15^(1/2)+10200*x^4-118580*15^(1/2)*x^8),x)
(7) 0
Type:
Union(Expression(AlgebraicNumber),...)
(8) -> integrate((-36-2*6^(1/2)*x^2)/(9*3^(1/2)+3*2^(1/2)*x^2-x^4),x)
(8) 0
Type:
Union(Expression(AlgebraicNumber),...)
--Nasser
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