" I wonder if Weierstrass function translate to Sage:" Currently it does not translate this output as it does not know about these
sage: r=integrate(x/sqrt(4*x^3 + x), x,algorithm="fricas") -weierstrassZeta(-1, 0, weierstrassPInverse(-1, 0, x)) sage: ?weierstrassZeta Object `weierstrassZeta` not found. sage: ?weierstrassPInverse Object `weierstrassPInverse` not found. This sagemath page <https://doc.sagemath.org/html/en/reference/arithmetic_curves/sage/schemes/elliptic_curves/ell_wp.html> mentions support for The Weierstrass ℘ function and examples. But I do not use the output of Fricas in sage in any way. I just translate it to Latex and save the result. So as long as it does not crash or throws an exception, I am ok. This is its latex output for the above sage: latex(r) -{\rm weierstrassZeta}\left(-1, 0, {\rm weierstrassPInverse}\left(-1, 0, x\right)\right) The problem happens if one tries to use the output inside sagemath to do something with since it does not know these functions. The problem with ellipticE and ellipticF in the bug track I linked to above, is much more serious. Because these functions take 2 arguments, and sage for some reason translate them to elliptic_ec which takes one argument not two, and it then throws exception. So CAS integration test calls these integrals as failed for Fricas and there are few of them, which reduces Fricas score. I do not know by how much. --Nasser On Friday, June 24, 2022 at 4:12:46 AM UTC-5 Waldek Hebisch wrote: > 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 > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/7010cd84-e296-4fb0-81a6-13a55ab36113n%40googlegroups.com.
