On Thu, Jun 23, 2022 at 09:06:13PM -0700, 'Nasser M. Abbasi' via FriCAS - computer algebra system wrote:
> And on the subject of using Fricas integrate in sagemath, I've just
> reported a new bug to sagemath due
> to interface issues. This causes few integrals to fail running Fricas
^^^
> integrate in sagemath, when they should not have failed because Fricas can
> do them. But this is out of my control.
AFAICS in Rubi testsuite there is more than 7000 integrals that
are expressible in terms of ellipic integrals and can not be
done otherwise. That is about 10% of Rubi testsuite and about
40% of what 1.3.7 could not do. I do not know how many of
them 1.3.8 can do, but I would expect more than half.
> Hopefully when these are fixed, will re-run CAS integration tests again for
> Fricas 1..3.8. It is due to translation of elliptic special function names.
>
>
https://trac.sagemath.org/ticket/34058
I wonder if Weierstrass function translate to Sage:
(10) -> integrate(x/sqrt(4*x^3 + x), x)
(10) - weierstrassZeta(- 1,0,weierstrassPInverse(- 1,0,x))
Type: Union(Expression(Integer),...)
Note that translating elliptic functions and integrals is
tricky, as there are many notations and each system uses its own.
You can see FriCAS definitions below:
(11) -> D(ellipticE(x, m), x)
+----------+ +--------+
| 2 | 2
\|- m x + 1 \|- x + 1
(11) - ------------------------
2
x - 1
Type: Expression(Integer)
(12) -> D(ellipticF(x, m), x)
+----------+ +--------+
| 2 | 2
\|- m x + 1 \|- x + 1
(12) ------------------------
4 2
m x + (- m - 1)x + 1
Type: Expression(Integer)
Actually, definition of E and F has both roots in denominator, but
with setSimplifyDenomsFlag(true) FriCAS puts roots in numerator.
--
Waldek Hebisch