There is this issue about making functions like degree() handle polynomials in factored form https://github.com/sympy/sympy/issues/6322. Most things aren't implemented yet. If you do want just a specific term, your best bet is to use series(), as this works quite well on polynomials without expanding them.
Aaron Meurer On Mon, Nov 22, 2021 at 8:14 AM Paul Royik <distantjob...@gmail.com> wrote: > > Thank you. Yes, in some cases I just need a degree or a leading term. > > On Monday, November 22, 2021 at 3:34:17 PM UTC+2 Oscar wrote: >> >> On Mon, 22 Nov 2021 at 09:18, Paul Royik <distan...@gmail.com> wrote: >> > >> > `(x-2)**9000` takes much time, but `(x-6)**100*(2-x)**9000` takes forever. >> >> It's slow because it involves explicit coefficient calculations with >> very large polynomials. Note that if you don't use Poly and you don't >> expand the expressions then it's very fast. This kind of example >> pushes towards the limit where the Poly representation is not useful >> any more. In other words it's better not to expand these powers and >> products but just work with those expressions as they are (which SymPy >> can do just fine). I think that it would be useful to have a kind of >> Poly representation that does not expand everything but still enables >> other Poly methods like `degree`, `coeff` etc to work but that isn't >> available so Poly always has to expand everything. >> >> The fastest library I know of for this sort of thing is flint which >> can do this in about half a second on this laptop: >> >> In [1]: import flint >> >> In [3]: p1 = flint.fmpz_poly([-6, 1]) >> >> In [4]: p1 >> >> Out[4]: x + (-6) >> >> In [5]: p2 = flint.fmpz_poly([2, -1]) >> >> In [6]: p2 >> >> Out[6]: (-1)*x + 2 >> >> In [7]: %time _ = p1**100*p2**9000 >> CPU times: user 597 ms, sys: 58.9 ms, total: 656 ms >> Wall time: 665 ms >> >> I won't show the output but it's a 9100 degree polynomial with >> coefficients that are 4000 (decimal) digit integers. Note that >> although flint can do this example reasonably quickly it's still not >> hard to push it a bit further and get something that takes too long or >> consumes all the memory in your computer etc. Fundamentally if you >> manipulate arbitrarily large non-sparse polynomials in explicit >> representations then some things are going to hit up against the >> limits of your computer. >> >> I would like to make it so that flint can be used to speed up internal >> calculations in SymPy. Otherwise for raw low-level things like this >> the fact that SymPy is a pure Python library will typically mean that >> even with the best algorithms it will still be about 100x slower than >> something like flint which is implemented in a mix of C and assembly >> language. >> >> Broadly for two polynomials of degree d1 and d2 the algorithmic >> complexity of the basic multiplication algorithm is O(d1 * d2) so >> computing (x-6)**100*(2-x)**9000 should be expected to take about 100x >> longer than (2-x)**9000. Faster algorithms are based on Karatsuba or >> Schönhage–Strassen etc but SymPy doesn't have those. It looks like >> flint has a whole bunch implemented: >> >> http://flintlib.org/sphinx/fmpz_poly.html#multiplication >> https://fredrikj.net/python-flint/ >> >> -- >> Oscar > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/540b2242-930e-43c4-854d-6e1442fc6cf7n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6Lwy3%3Dv%2B9tqB6xXXWVRM3Nq2atGNFF8DF5%3DykusbC-bUQ%40mail.gmail.com.
