Hi David,
> Here is a puzzle (to me if not to you).
>
> In sage 2.10.2 (although the problem occurs in earlier versions)
> on a CoreDuo MacIntosh running under MacOS X.5.2 we have:
>
>
> a = gp.sin(1)
> octave.eval('format long g')
> b = octave.sin(1)
> c = math.sin(1)
> eps = 1. - (4./3.-1.)*3.
> d = a*eps
> a
> 0.8414709848078965066525023216
> b
> 0.841470984807897
> c
> 0.8414709848078965
> (a-b)/d
> -2.640423314436302686
> (a-c)/d
> -553.9021661362176753
> (b-c)/d
> -553.7921192926074518167939202
>
> Notice that a, b, c all seem to agree to about 16 digits, but when
> the 'native' sage value is mixed with the gp and octave values a
> horrendously large error occurs.
>
> The same behavior occurs for cos(1), exp(1), atan(1).
>
> Something very peculiar is happening. What? Why?
>
> Thank you,
>
> David Galant
my guess is that in a-c, c is converted to 'sage.interfaces.gp.GpElement'
with a smaller precision:
sage: a-a.parent()(c)
-1.0349334749767836598 E-13
sage: a-c
-1.0349334749767836598 E-13
sage: c
0.8414709848078965
sage: a.parent()(c)
0.8414709848080000000000000000
Paul Zimmermann
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