On Nov 21, 2:59 am, William Stein <wst...@gmail.com> wrote: > Why are you planning to build a framework for "numeral systems" (I'm > not sure what that means, by the way)? What is the motivation for > _you_ doing this? I think explaining that would be extremely helpful > in evaluating this proposal.
A simple example of a numeral system is the following: take an integer q, digits 0,...,q-1. Then each integer can be represented as finite sum \sum_0^N d_n q^n where die d_n are digits. But there are a lot of other numeral systems (other bases, other digit sets). Some of them have some nice applications: For example, take an imaginary quadratic integer as base, and a suitable digit set, then you can use it to build multiples of a point of an elliptic curve over a finite field efficiently. (base corresponds to a zero of the characteristic polynomial of the Frobenius on the point group; use a Frobenius-and-add method). I'm working with such numeral systems and I need an implementation in some (mathematics) software for my research. But it seems, that there is no such thing in one of the known software packages and everyone who needs implementation does it on his own. At the moment I plan to implement some of the standard numeral systems algorithms (e.g. for calculating the digits) in Sage. I want to do that in a general and flexible way, such that it can be used for a lot of other numeral systems as well. The presented framework is now a result of this generalization process. It should cover more or less all numeral systems used somewhere. When such a framework exists, one can easily implement algorithms for a special numeral system, but can also use all the other general methods provided by the framework. > Also, is there similar functionality in Mathematica or Maple? No, there isn't any (except for calculating the digits in the standard numeral system described above (simple example)). Daniel -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
