William Stein wrote:
>
> This is really no different than:
>
> sage: n = 5; m = Mod(5, 19)
> sage: n == m
> True
> sage: n.additive_order()
> +Infinity
> sage: m.additive_order()
> 19
>
> I don't consider this a bug. The original poster's issues might stem
> from misunderstanding about how floating point numbers are used and
> abused in Sage (or MATLAB or any other math software, for that
> matter).
>
> William
You're going to have a rather hard time convincing me that, upon
encountering a decimal point, any other math software is going to flip
out and silently return incorrect results for basic matrix operations.
Recall:
sage: m = matrix([ [-0.3, 0.2, 0.1],
[0.2, -0.4, 0.4],
[0.1, 0.2, -0.5] ])
sage: m.echelon_form()
[ 1.00000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 1.00000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 1.00000000000000]
And for any other math software:
1. http://michael.orlitzky.com/screenshots/derive-v6.10.png
2. http://michael.orlitzky.com/screenshots/maple-v13.png
3. http://michael.orlitzky.com/screenshots/mathcad-v14.png
4. http://michael.orlitzky.com/screenshots/mathematica-v7.png
5. http://michael.orlitzky.com/screenshots/matlab-v2009b.png
6. http://michael.orlitzky.com/screenshots/minitab-v15.1.1.png
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