On Tue, Mar 27, 2018 at 9:57 PM, Michael Orlitzky <mich...@orlitzky.com> wrote:
> On 03/27/2018 03:11 PM, William Stein wrote:
>>
>> Sorry -- I'm not trying to flamebait you, but in order to have any
>> further discussion,  what exactly do you think a floating point number
>> in a computer is?
>> What is the mathematical meaning of
>>
>>>>> float(1)
>>
>
> The thread was about casual users, who shouldn't have to care about the
> implementation details behind what "0.5" means. To a casual user, 0.5 is
> one-half. I didn't bring this up to fight about by pet bug again, but
> because of the similarity between this and the fact that 12/4 is not
> three. Casual users don't want to hear about the coercion framework,
> categories, maps and what-not -- they just want to be able to put in
> trivial homework problems and get out the right answers.
>
>
>>> Can two equal matrices have different ranks?
>>
>> Yes, e.g.,
>>
>> X = matrix(GF(3),[0])
>> Y = matrix(ZZ,[3])
>> [X == Y, X.rank(), Y.rank()]
>>
>> --> [True, 0, 1]
>>
>
> But will MATLAB tell you that two equal matrices have different ranks? I
> know sage will do it.

I think what we really need is more diversity of equivalence
operators, e.g. "~="   ;)

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