# whats happening ?

**Jason Moxham
**
J.L.Moxham@maths.soton.ac.uk

*Sat, 2 Nov 2002 02:52:30 +0000*

On Wednesday 23 Oct 2002 1:08 am, Kevin Ryde wrote:
>* Jason Moxham <J.L.Moxham@maths.soton.ac.uk> writes:
*>* > mpz_rootexact (like mpz_divexact but for roots) using varible precis=
*ion
>* > , division free p-adic newton method
*>*
*>* Not sure if there'd be much direct use for that. When would one know
*>* a number is an exact power?
*>*
*
I have come across it a few times , but nothing springs to mind . If the=20
p-adics are faster (than real newton iterations)(and they should be) for=20
perfect_power testing then we can get the mpz_rootexact for free.
>* > mpz_perfect_power_p using parts of the above fn's
*>*
*>* If it finds a use there then it'd be fine.
*>*
*>* > mpz_invert_2exp (like mpz_invert but 2^n modulas) again using above
*>* > p-adics
*>*
*
again this fn would come for free from a p-adic perfect power testing fn =
,=20
although I don't know of any uses besides redc-init
>* I looked at that as part of the redc, since it wants such an inverse.
*>* The function would match mpz_invert nicely, but again I'm not sure
*>* quite how much use it would get.
*>*
*>* Paul Z had some ideas about efficiency which I've (still) yet to look
*>* at properly. Efficiency isn't a big deal for the prospective mpm
*>* since the inverse is calculated just once at the start.
*>*
*
interesting , they could be usefull for the p-adic perfect power test