On Tue, May 18, 2010 at 8:27 AM, jvkersch <joris.vankerscha...@gmail.com> wrote:
> Dear all,
>
> I would like to follow up on my differential forms class query (http://
> groups.google.be/group/sage-devel/browse_thread/thread/
> 2feef1f0be557585/75173b6c6f52450d) with a question about Sage
> programming/invoking style.
>
> If R^n has coordinates x, y, ... (or whatever), then the algebra of
> differential forms is generated by the differentials dx, dy, ...  (the
> differentials of each of the coordinate functions).  So there's a one-
> to-one correspondence between generators and coordinates on the
> underlying space.  Is it allowable programming practice to implement
> the DifferentialForms class so that the following construction becomes
> possible:
>
> sage:   F.<x, y, z>  = DifferentialForms()
> sage:   F.gens()
>>>>>      (dx, dy, dz)
>
> but also
> sage:  x in F.gens()
>>>>>      False
>
> That is, should the names between <> be exactly the generators
> themselves, rather than something which can be made into a generator
> in a non-canonical way?
>
> I am not entirely comfortable with this approach, but in this way I
> avoid having to check whether the names, number, ... of generators are
> correct, since ParentWithBase.__init__ takes care of that.

I'm definitely not comfortable with this; it seems like a recipe for
confusion.   I have to admit that I don't at all understand your
argument for this.

 -- William

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