On Wed, Jul 24, 2013 at 11:53 AM, Matthew Rocklin <[email protected]> wrote:
>
> On Wed, Jul 24, 2013 at 11:39 AM, Aaron Meurer <[email protected]> wrote:
>>
>> To me, it's just an element of the cartesian product
>
>
> Note that not all domains will be Cartesian products.  Consider the triangle
> 0 < x < 1 and 0 < y < 1 and x + y < 1 .

It is a subset of the product. All I meant is that the elements are
tuples. How you actually construct these sets for various shapes is
another question.

>
>>
>> , which just contains tuples, so yeah, Contains((x, y), ProductSet(A, B)).
>
>
> This syntax passes the buck to sets.  I think that this is reasonable.
>
>>
>> Or you
>> could write x*y > 0. I guess what we also need are some functions to
>> convert back and forth from set notation to relational notation.
>
>
> This already exists to a certain extent for some (but not all) sets.
>
> In [1]: Interval(0, 1).as_relational(x)
> Out[1]: 0 ≤ x ∧ x ≤ 1

Oh great. That really should be Contains.as_relational.

Aaron Meurer

>
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