Hi Simon,

On 2018-06-01, Simon Brandhorst <sbrandho...@web.de> wrote:
> (1) Use unique representation for "ambient" objects ( GL(n,k), O(n,k,e), 
> QQ^n).

+1, unless you say that each set (including a subset of something)
is an ambient object.

> (2) Do not use unique representation for subobjects.

+1, except for subobjects that can be considered "ambient" themselves
(such as: The set of prime numbers in the set of integers; or GL(n,k) in
MatrixSpace(k,n))

> (3) Give the .subobject(self, gens) method a (weak?) cache.

+1, provided that it doesn't add memory leaks.

> (4) Modify == to test equality as subobjects/subsets.

-1, as I tend to think of "==" as a QUICK test.

If testing equality has a potential to hit decision problems (which
certainly is the case for subgroups), then "==" should give a swift
"True" if the two objects are easily seen to be equal (by equality of
the set of generators, say), and should return "False" otherwise.

In these cases, there ought to be a special method that the user will only
call if s/he really is prepared to wait for the answer for a couple of hours.

Note that in a way it would be nice if "==" had a ternary logic
"True/False/Unknown". But Python isn't there yet (although I do recall
that there used to be a PEP for it).

Best regards,
Simon


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