On Mon, 3 Nov 2014, Vincent Delecroix wrote:
The main recurrent problem is that there is no support in Sage for a
ring included in the mathematical RR (= the set of reals) that would
contains QQbar and most constants (e, pi, cos(p/q), ...) and which would
have exact comparisons. The main problem is that it is tricky to get a
ring large enough to be useful and small enough for equality to be
decidable.
Isn't that in principle impossible? IIRC it is not possible to say from
given expressions if they have actually same value. At least it is
impossible for user-defined functions.
Or have I misunderstood something?
I think so, in the symbolic ring (the parent of log(10)) the
comparison is *very* special.
sage: cmp(cos(1), log(5))
1
sage: cmp(cos(1).n(20), log(5).n(20))
-1
OK. But Sage can compute both eigenvalues and logarithm to given
precision? So I can just try with 32 bits, return result of comparison if
there is difference on some bit 0..30, and if not, try with 64 bits to see
if bits 0..62 differs and so on until some maximum length.
--
Jori Mäntysalo
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