On Jun 25, 3:39 am, Dima Pasechnik <dimp...@gmail.com> wrote:
> Do you mean "real algebraic numbers" ?
> So the code in question actually computes these numbers to a high
> precision, no?

The ones I have seen giving me trouble appear to be mostly from QQbar,
and not in AA, so are complex.  The one case I isolated and tracked
carefully was complex.

Some sample code on the ticket (#11543) aims to show some of the work
done to create a hash.  There is a long discussion in sage/rings/
qqbar.py at the second __hash__ method, at line 2356.  It seems to be
a matter of using enough precision to distinguish numbers that are
very close to one another, but the exact problem looks beyond me.
Though John's comment about equality does not surprise me.

It sure would be nice if somebody knowledgeable wanted to improve this
situation, but perhaps it is just an unavoidable fact of life.

In the meantime, workaround for matrix printing is up at

http://trac.sagemath.org/sage_trac/ticket/11544

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