# [SciPy-dev] Generic polynomials class (was Re: Volunteer for Scipy Project)

Charles R Harris charlesr.harris@gmail....
Fri Oct 9 13:24:56 CDT 2009

```On Fri, Oct 9, 2009 at 11:08 AM, Anne Archibald
<peridot.faceted@gmail.com>wrote:

> 2009/10/9 Charles R Harris <charlesr.harris@gmail.com>:
> >
> > I'm thinking that instead of a wrapper class what we want is essentially
> a
> > class template replicated with different values for, i.e.,
> multiplication,
> > division, etc. One way to do that in python is with a class factory. For
> > example
> >
>
> I see that this is possible, but I'm not sure I see why it's a good idea.
>
> We need basis objects, since even apart from any code, bases can
> contain substantial amounts of information. For example, if someone
> wants to work with the Lagrange interpolating polynomial on a set of
> points, the natural basis is the Lagrange basis on those points, so
> the polynomial must remember the list of points. Storing that in every
> polynomial is inefficient, not just in terms of space but also because
> basis comparisons - necessary for type-safety on every operation -
> would have to actually go out and compare all the points.
>
> So every polynomial needs to contain (a reference to) the basis it's
> defined on, and there must be a type hierarchy of bases. But if that
> type hierarchy exists, why have a hierarchy of polynomials? After all,
> the algorithms defined depend on the basis, rather than any feature of
> the individual polynomial, and a polynomial is completely defined by
> its coefficients and the basis.
>
> If you're concerned that the polynomial class exists without any real
> code inside it, well, that's a bit awkward, I agree. But if we have
> basis objects and polynomial objects, the code has to go in one or the
> other, and it seems more natural to put it in the basis objects. In a
> way this is similar to the design of your Chebyshev class - you have a
> collection of functions that act on bare coefficient arrays (in my
> design they're in a class, in yours they're module functions) and a
> wrapper class whose code is only there to provide an easy-to-use
> object-oriented interface. And the wrapper class is not completely
> trivial - it handles checking basis equality (in principle it could
> check compatibility, if that turns out to be useful), scalar
> multiplication, and an operator-friendly interface.
>
> In object-oriented buzzword-speak, rather than using (possibly
> multiple) inheritance to provide features using an is-a relationship,
> I'm using inclusion to provide a has-a relationship. Code reuse
> through inheritance will apply at the level of bases, rather than at
> the level of individual polynomials.
> brcuase
>

It's not inheritence, it's a class templaate.  Because classes are objects
in python you can return them from functions.with a defined enviroment.
Another way to look at it is completions. A basis would just be another
passed parameter. and the class code would still only heed to be written
once for all the different types of polynnomial basis.. I think it is a
cleaner way to go.

Chuck
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