Le jeudi 02 juin 2011 à 21:28 -0600, Aaron S. Meurer a écrit : > On Jun 2, 2011, at 9:21 PM, Ronan Lamy wrote: > > > Le jeudi 02 juin 2011 à 17:07 -0600, Aaron S. Meurer a écrit : > >> On May 31, 2011, at 11:11 AM, Ronan Lamy wrote: > >> > >>> Le mardi 31 mai 2011 à 09:43 -0700, Vinzent Steinberg a écrit : > >>>> On May 30, 9:52 pm, Mateusz Paprocki <matt...@gmail.com> wrote: > >>>>> That could work: > >>>>> > >>>>> ZZ.sum([1, 2, 3]) -> sum([1, 2, 3]) > >>>>> RR.sum([1.0, 2.0]) -> mpmath.fsum([1.0, 2.0]) > >>>>> EX.sum([x, y, z]) -> Add(*[x, y, z]) > >>>>> > >>>>> etc. > >>>> > >>>> This is exactly what I have been thinking of. > >>> > >>> But do we really need lots of different sum() functions? Is there a > >>> difference between ZZ.sum([1, 2, 3]) and EX.sum([1, 2, 3])? > >> > >> Yes. You can sum integers perfectly efficiently just by passing them > >> to the built-in sum() (also remember that ZZ(1) != S(1) in general > >> because of the ground types, but EX(1) == S(1) always). > > > > ZZ(1) != S(1), but only some times, is rather counter-intuitive. I don't > > understand what ZZ is really supposed to mean anyway. If it's the ring > > of integers, why can its value change? And why is it instantiable? > > ZZ(1) means 1 in the current ground type. If the ground type is Python, > it returns int(1). If it's gmpy, it returns mpz(1). Actually, ZZ(1) > == S(1) only if you manually choose the sympy ground types. Note that > I am using "==" here to mean actually something more like "is". I > should really have said "type(ZZ(1)) != type(S(1))". __eq__ itself > works as expected regardless of the underlying type. > OK. So "ZZ" means "integer type". That's what I find counter-intuitive then.
> In general, ZZ stands for the domain of integers, and you can pass it > to Poly under the domain option (you can also do stuff like ZZ[x] to > create the domain of polynomials in x with integer coefficients). > ZZ(1) is just syntactic sugar that makes it easy to coerce elements to > that domain. OK. By domain, you mean type, right? (That 'ZZ[x]' is a rather confusing bit of syntactic sugar that seems to suggest a mathematical meaning it doesn't really have and looks weird when you replace ZZ with any of its possible values) > > > >> But something > >> like Add(*(x, -x, x, x, -x)) is almost two times faster than sum((x, > >> -x, x, x, -x)): > > > > That's rather an implementation detail, and using Add(*[...]) is wrong > > anyway, if we want to allow extensions of sympy. Besides, it doesn't > > explain why EX.sum([n, -n, n, n]) should be different from ZZ.sum([n, > > -n, n, n]). > > Do you mean that n is symbolic? If so, then ZZ.sum([n, -n, n, n]) > doesn't make sense. > It would make sense if 'ZZ' meant 'the ring of integers'. Actually, even though that's not the case, it works anyway because ZZ.sum is always just sum. > Aaron Meurer > > > > >> > >> In [1]: Add(*(x, -x, x, x, -x)) > >> Out[1]: x > >> > >> In [2]: %timeit Add(*(x, -x, x, x, -x)) > >> 1000 loops, best of 3: 170 us per loop > >> > >> In [3]: sum((x, -x, x, x, -x)) > >> Out[3]: x > >> > >> In [4]: %timeit sum((x, -x, x, x, -x)) > >> 1000 loops, best of 3: 313 us per loop > >> > >> In [16]: b = map(S, range(100)) > >> > >> In [24]: %timeit Add(*b) > >> 1000 loops, best of 3: 546 us per loop > >> > >> In [25]: %timeit sum(b) > >> 1000 loops, best of 3: 268 us per loop > >> > >> (all run without the cache, as suggested above). Note that [16] > >> ensures that sum(b) goes through Add. Otherwise, you get > >> > >> In [26]: %timeit Add(*range(100)) > >> 1000 loops, best of 3: 1.45 ms per loop > >> > >> In [27]: %timeit sum(range(100)) > >> 100000 loops, best of 3: 2.7 us per loop > >> > >> which just proves what we already know, which is that Python ints are > >> (apparently 10x) faster than SymPy Integers. > >> > >> Aaron Meurer > >> > > > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To post to this group, send email to sympy@googlegroups.com. > > To unsubscribe from this group, send email to > > sympy+unsubscr...@googlegroups.com. > > For more options, visit this group at > > http://groups.google.com/group/sympy?hl=en. > > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
