I wouldn't worry about the fact that things don't expand automatically. This sort of thing is intentional. If users want things to expand, they will call expand(), or simplify() (which will probably end up calling expand()), and things will simplify then thanks to the _eval_power routine.
Aaron Meurer On Mon, Dec 1, 2014 at 11:29 AM, Chris Swierczewski <[email protected]> wrote: > I have a preliminary implementation below that I can write up as a pull > request if people would prefer to take a look that way. I have not performed > any of the sympy tests yet but will do so later this afternoon. > > class MyRootOf(RootOf): > __doc__ = RootOf.__doc__ > > def __init__(self, *args, **kwds): > RootOf.__init__(self, *args, **kwds) > > def _eval_power(self, exponent): > if exponent >= self.poly.degree(): > exponent = int(exponent) > result = 1 > base = self.poly.gen > modulus = self.poly > while exponent > 0: > if (exponent % 2): > result = reduced(result*base, [modulus])[1] > exponent >>= 1 > base = reduced(base*base, [modulus])[1] > return result.subs(self.poly.gen,self).as_expr() > return RootOf._eval_power(self, exponent) > > This is a basic implementation of a modular exponentiation algorithm. The > basic idea is that since a root $b$ satisfies $p(b) = c*b**n = q(b)$ then > $b**n = - (1/c) * q(b)$. Here is a simple test: > > f = 3*y**5 + 2*y - 1 > root = MyRootOf(f,0) > print root**5 > -2*RootOf(3*y**5 + 2*y - 1, 0)/3 + 1/3 > > > From what I gathered the method _eval_power() is called every time a Sympy > Expr subtype is exponentiated. This makes it so that p.eval(b) or p.subs(b) > uses the above modular exponentiation algorithm. Just overloading __pow__() > doesn't cut it. > > I have some preliminary timings as well demonstrating that expansions of > polynomial expressions in this new RootOf is about x1.5 - x2 faster than the > original behavior which keeps track of all the higher powers. > > I tried finding a way to make expressions like > > root**4 * (1 + root) > > symplify appropriately. But after diving into how Sympy handle's Mul's I see > that the default behavior of expressions like x*(1+x) is to not > automatically expand. I doubt that this behavior should be changed since > it'll impact so many other computations. However, if somebody know of how I > can default expand expressions involving RootOf / MyRootOf objects I would > greatly appreciate the feedback and suggestions. > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/bf63ac31-569a-4bcb-b9fd-ae6662d8c6e2%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2Bm-EwFDzbnfrVh-q2_ndvCFggE6n41PPfmY4rYSKcF1g%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
