On Fri, Apr 19, 2024 at 12:42:19AM -0700, 'Nasser M. Abbasi' via FriCAS -
computer algebra system wrote:
> 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.
>
> Here is the output from Fricas for the four cases:
>
> (4) -> setSimplifyDenomsFlag(true)
>
> (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),...)
Well,
(10) -> 1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/pi/(a*x-1)^(1/2)
+-------+
- 2 log(- \|a x - 1 ) + log(a x - 1)
(10) ------------------------------------
+-------+
2 pi\|a x - 1
Type: Expression(Integer)
(11) -> normalize(1/2*(log(a*x-1)-2*log(-(a*x-1)^(1/2)))/pi/(a*x-1)^(1/2))
(11) 0
Type: Expression(Integer)
Here there are 2 dependent logarithms which may combine to 0.
And FriCAS assumes that they will combine to 0. This is a
design choice: I think that current behaviour is more useful than
easy alternatives like signaling error in user input.
The other 3 are plain bugs.
--
Waldek Hebisch
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