On Sun, Jul 25, 2010 at 8:10 PM, Carl Witty <[email protected]> wrote:
> You seem to want to make the vertex dictionary respect the equivalence
> relation defined by Sage equality. If so, you're going to be in
> trouble, since Sage equality actually is not an equivalence relation:
Is it really too much to ask?
It sounds like the proper thing to do here, then, is to adjust the
circulant graph constructor to use Mod(i) instead of i in the edge
additions, and then profusely document this issue -- perhaps a whole
chapter in the reference manual about graph gotchas... This is just
really unsatisfying. I like the idea of having graphs be free enough
that you can make anything you want a vertex.
A mathematician would not usually say that the integer is equal to the
coset. I can see why we might want
> sage: 3 == Mod(7, 4)
> True
But this highlights yet another place where mathematics and computer
science are less than perfect bedfellows. Just a day or two ago this
sort of thing was discovered in another thread. In short, Python sets
do not implement a total ordering (since < means inclusion), and so
are not sortable...
What to do, what to do?
Definition: Mod(n, m, parent=None)
Docstring:
Return the equivalence class of n modulo m as an element of
ZZ/mZZ.
According to this definition, I would expect
sage: Integer(7) == Mod(7,12)
False
Following the Python set notation, which I think is equally silly but
much harder to change, we would have
sage: Integer(7) < Mod(7,12)
True
..........
--
Robert L. Miller
http://www.rlmiller.org/
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