nth root

[Mensanator]

On Feb 1, 8:20�pm, casevh <cas... at gmail.com> wrote:
> On Feb 1, 1:04�pm, Mensanator <mensana... at aol.com> wrote:
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>
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> > On Feb 1, 2:27�am, casevh <cas... at gmail.com> wrote:
>
> > > On Jan 31, 9:36�pm, "Tim Roberts" <t.robe... at cqu.edu.au> wrote:
>
> > > > Actually, all I'm interested in is whether the 100 digit numbers have an exact integral root, or not. �At the moment, because of accuracy concerns, I'm doing something like
>
> > > > � � � � � � � � � � for root in powersp:
> > > > � � � � � � � � � � � � � � nroot = round(bignum**(1.0/root))
> > > > � � � � � � � � � � � � � � if bignum==long(nroot)**root:
> > > > � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �.........
> > > > which is probably very inefficient, but I can't see anything better.....
>
> > > > Tim
>
> > > Take a look at gmpy and the is_power function. I think it will do
> > > exactly what you want.
>
> > And the root function will give you the root AND tell you whether
> > it was an integral root:
>
> > >>> gmpy.root(a,13)
>
> > (mpz(3221), 0)
>
> > In this case, it wasn't.
>
> I think the original poster wants to know if a large number has an
> exact integral root for any exponent. is_power will give you an answer
> to that question but won't tell you what the root or exponent is. Once
> you know that the number is a perfect power, you can root to find the
> root.

But how do you know what exponent to use?

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> > >http://code.google.com/p/gmpy/
>
> > > casevh