email@example.com wrote: > > Waldek Hebisch schrieb: > > > > Nasser M. Abbasi <firstname.lastname@example.org> wrote: > > > On 6/13/2013 5:04 PM, Waldek Hebisch wrote: > > > > > > > > > > > I tried sympy-0.7.2 on the ten. I got anwers for #2 and #10: > > > > > > If any one interested, I have screen shots from sympy up now. > > > > > > http://www.12000.org/my_notes/ten_hard_integrals/index.htm > > > > > > I used whatever my Linux installed for me via package manager, which > > > it says it is sympy 0.7.1-rc1-3. It gave result for #10 for > > > this version. > > > > > > > > > > > #4 did not finish after 35 min. > > > > > > For me, it was #5 which never finished, waited 1 hr. > > > > I gave wrong number: it was #5. In fact it is still > > runnig 2h 20min, 4.3GB RAM in use. > > > > Better late than never :). > > If my information is up-to-date, Sympy claims to field a complete > implementation the Risch procedures from Bronstein's volume 1, covering > everything elementary but non-algebraic,
I do not think so. IIUC they started working on such thing, but it is far from finished.
> supplemented by an > implementation of the extended Risch-Norman heuristic (something like > Bronsteins "Poor Man's Integrator") for cases where these procedures do > not apply.
AFAIK this is main integration procedure.
> Sympy also claims that it can automatically convert to and > determine the antiderivatives of Meijer G-functions.
Yes, they have such a routine.
> So, what you are suffering here must be the "extended Risch-Norman > heuristic" mostly.
Yes, that is the Risch-Norman part. I do not know why it is so slow. Risch-Norman heuristic (with few improvements due to Bronstein) implemented in FriCAS is much faster. The longest running example is #9 needing 9s. FriCAS version can only do #2. Risch-Norman heuristic can generate quite large systems of linear equations, for example #9 generates system of 1814 equations in 794 unknowns. FriCAS version treats algebraics like transcendentals, which means it is expected to fail on integrals involving algebraics. Still, properly handling algebraics should only moderately increase size of linear systems (and sometimes may lead to smaller system).