Mark Dickinson wrote:

On Mon, Nov 24, 2008 at 8:01 PM, Rocco Orlando Rossi wrote:

...

I appreciate the inclusion of the fractions module in Python 2.6 and therefore in Python 3.0. But I feel there's something missing: no possibility for complex rationals (or arbitrary precision) integers.

This seems like a specialist need to me---one that belongs in a Python extension package or library, but not in core Python.

Call is 'algebra'?, and included quaternions.

Another thought: the field Q(i) is just one of an infinite number of quadratic extensions of the field of rationals. Why implement that one and not the others? Put another way, the field of complex numbers is a fairly natural object, but the choice to represent it as reals adjoin sqrt(-1) is quite arbitrary---one could just as easily adjoin sqrt(-2), or sqrt(-3), or (-1+sqrt(-3))/2 instead.

Have you investigated sage? (www.sagemath.org)

Mark

On 24 Nov 2008, at 20:24, Mark Dickinson wrote:

On Mon, Nov 24, 2008 at 8:01 PM, Rocco Orlando Rossi wrote:

...

I appreciate the inclusion of the fractions module in Python 2.6 and therefore in Python 3.0. But I feel there's something missing: no possibility for complex rationals (or arbitrary precision) integers.

This seems like a specialist need to me---one that belongs in a Python extension package or library, but not in core Python.

Another thought: the field Q(i) is just one of an infinite number of quadratic extensions of the field of rationals. Why implement that one and not the others? Put another way, the field of complex numbers is a fairly natural object, but the choice to represent it as reals adjoin sqrt(-1) is quite arbitrary---one could just as easily adjoin sqrt(-2), or sqrt(-3), or (-1+sqrt(-3))/2 instead.

If we want Q(i), then surely we also want Z[i]. Gaussian integers have plenty of uses. -- Arnaud