Tom, I think I understand your points, but I'd still like to ask you
whether you find it acceptable to have the classes I have suggested in
SymPy?
Also, I think we got a little carried away by the whole Ring.mul vs
__mul__ business. I think it has been established now that the
approaches are interchangeable. Regarding other aspects of your proposal:
- "class Ring which will contain two instances of Operation and will
have only the basic functions, such as storing a set of generators."
This is *more* concrete than the current Ring class. In particular, what
do you mean by storing a set of generators? What are generators of QQ?
What of ZZ(x)?
- deriving RingIdeal from ring, treating it as a subring:
I don't think that makes sense. Ideals have no natural multiplicative
unit, whereas a type of ring I tend to think of has (admittedly, this
may sometimes be relaxed). But I do agree there should be an Ideal
class, which somehow relates to a particular ring. [I'm from a
commutative algebra background. To me an ideal is a particular kind of
module. However, I think it is helpful to have a separate class, since
there are a couple of operations that make sense on ideals that don't on
modules.]
- PolynomialRingIdeal will store a reference to the field
What for? It stores a reference to the ring, which already has a
reference to the field.
I think I should make it clear that I agree that the kinds of classes
you sketch are desirable and needed. As I have said a couple of times I
am somewhat reluctant to designing large, boiler-plate class hierarchies
(as you say, most of your classes will not really *do* anything), mainly
because I don't feel confident I can anticipate the needs of *actual*
code correctly. However, this should not discourage you. If you feel it
helps your project, by all means implement these classes (imho).
As I have also said before, I have some interest in implementing
commutative algebra / algebraic geometry code for sympy myself. But as I
said, I feel like I work in a "lower level" of the class hierarchy. I
may create classes called e.g. "Ideal", but please feel free to
understand them as "ParticularIdeal", i.e. so that you can add more
suitable, general base classes above.
Best,
Tom
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