nth root
Mensanator
mensanator at aol.com
Mon Feb 2 12:49:48 EST 2009
On Feb 2, 1:01 am, casevh <cas... at gmail.com> wrote:
> On Feb 1, 10:02 pm, Mensanator <mensana... at aol.com> wrote:
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> > On Feb 1, 8:20 pm, casevh <cas... at gmail.com> wrote:
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> > > On Feb 1, 1:04 pm, Mensanator <mensana... at aol.com> wrote:
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> > > > On Feb 1, 2:27 am, casevh <cas... at gmail.com> wrote:
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> > > > > 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)
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> > > > (mpz(3221), 0)
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> > > > 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?
>
> That's the gotcha. :) You still need to test all prime exponents until
> you find the correct one. But it is much faster to use is_power to
> check whether or not a number has representation as a**b and then try
> all the possible exponents than to just try all the possible exponents
> on all the numbers.
Ok. I was under the impression that the OP was only interested
in the 13th root, so that is_power wouldn't necessarily be of any
use to him. If is_power returned true, you would still have to do
root(a,13) to see if it's actually a 13th power. That's executing
two gmpy functions and takes twice as much time as doing root(a,13)
alone.
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> > > > >http://code.google.com/p/gmpy/
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> > > > > casevh
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