#4544: comparison of CDF (or any inexact) elements needs work
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Reporter: craigcitro | Owner: jkantor
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.1
Component: numerical | Keywords:
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So currently, we compare elements of inexact rings like `CDF` by just
comparing their components as `double`s. We use this for sorting, and
expect the results to be consistent between runs, architectures, etc.
However, this is wildly untrue. Here's a good example:
{{{
sage: z1, z2 = [ x[0] for x in f.roots()[-2:] ]
sage: R = CDF['x']
sage: f = R([17,1,0,0,0,1]) ; f
1.0*x^5 + 1.0*x + 17.0
sage: f.roots()
[(-1.72502775061, 1),
(1.4372759883 + 1.06991737978*I, 1),
(1.4372759883 - 1.06991737978*I, 1),
(-0.574762112991 + 1.65506825348*I, 1),
(-0.574762112991 - 1.65506825348*I, 1)]
sage: z1, z2 = [ x[0] for x in f.roots()[-2:] ]
sage: z1
-0.574762112991 + 1.65506825348*I
sage: z2
-0.574762112991 - 1.65506825348*I
sage: z1.real() == z2.real()
False
}}}
Notice that the `+`/`-` ordering is different for the two pairs of complex
conjugate roots. What we '''should''' do is pass a parameter to `__cmp__`
that describes a threshold such that if the difference is smaller than
this threshold in absolute value, things compare equal. This could even be
a parameter to the ring.
There are a ton of questions this brings up, such as, "how is this done in
other systems?" Notice this also underlies the following confusing result:
{{{
sage: [ f(x[0]).is_zero() for x in f.roots() ]
[False, False, False, False, False]
}}}
Someone should do some research and start a sage-devel conversation,
probably.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4544>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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