[Cuis-dev] Some un-accurate information on The Cuis Book

[Juan Vuletich]

Hi Nicolas,

On 2/27/2023 7:42 PM, Nicolas Cellier via Cuis-dev wrote:
> Hi Juan,
> I like this POV

Cool.

> Previously, I was more aligned with the pragmatic considerations of 
> Luciano
> You can't have reduction of Complex to Number because that would mean 
> implementing complex extension of functions in Number, and that's 
> maybe not what we want... {[-2 sqrt]. [-2 log]. [-2 arcSin]} 
> shouldAllFail.
>
> With this POV, if we want to use a complex extension of sqrt, then we 
> have to be explicit: -2 asComplex sqrt.
>
> Of course, Float is not Real...
> Most of the reals cannot be represented in our computers, because we 
> don't have any algorithm to compute them...
> There are only a countable infinity of reals that we can compute, 
> that's not that much ;)

Still, a Float is a lot more than a specific rational number with 2^k 
denominator. It is a belief that our unknown real number is 'close' to 
it. Not precise, but good enough to be the basis for all engineering.

> Arithmetic operations with Float operands might be inexact 
> (approximated), and that's the reason why we convert to Float and not 
> the other way around, mixing inexact and exact arithmetic leads to 
> inexact results...
>
> For Complex, this would be more like falling in a 2nd dimension...
>
> Nicolas

Yep.

>
>
> Le lun. 27 févr. 2023 à 22:41, Juan Vuletich via Cuis-dev 
> <cuis-dev at lists.cuis.st <mailto:cuis-dev at lists.cuis.st>> a écrit :
>
>     On 2/26/2023 10:48 AM, ken.dickey--- via Cuis-dev wrote:
>     > On 2023-02-26 05:31, ken.dickey--- via Cuis-dev wrote:
>     >
>     >> BTW, we can do better.  I think -4+0i above should be and print
>     as -4.
>     >
>     > Ah! The code is already there and just needed to be uncommented
>     > (attached).
>     >
>     > As we have Complex>>basicReal:imaginary: why does
>     > Complex>>real:imaginary not do the simplification?  Can we not just
>     > enable this?
>     >
>     > Thanks,
>     > -KenD
>
>     Given that in Math, Complex is an extension of Real (and not of
>     Integer
>     or Rational), I think that consistency with Floats is most important.
>     And Floats don't reduce to Integer (it would be a huge mistake to do
>     that). That's why the commented code in #real:imaginary: would
>     only go
>     back if the imaginary part is not Float: doing it for Complex with
>     Float
>     parts would be the same as converting 0.0 to 0.
>
>     And doing it differently for Complex with Float parts and with
>     Integer
>     parts would not be simpler. It would be more complicated, and need
>     this
>     extra explanation to make sense.
>
>     In the Number hierarchy, Float is like a pit you can't exit once you
>     fall into it. As Complex is an extension of Real, I think Complex
>     should
>     do the same.
>
>     Maybe this rant should be in the comment at #real:imaginary:,
>     after all.
>
>     Thanks,
>
>     -- 
>     Juan Vuletich
>     cuis.st <http://cuis.st>
>     github.com/jvuletich <http://github.com/jvuletich>
>     researchgate.net/profile/Juan-Vuletich
>     <http://researchgate.net/profile/Juan-Vuletich>
>     independent.academia.edu/JuanVuletich
>     <http://independent.academia.edu/JuanVuletich>
>     patents.justia.com/inventor/juan-manuel-vuletich
>     <http://patents.justia.com/inventor/juan-manuel-vuletich>
>     linkedin.com/in/juan-vuletich-75611b3
>     <http://linkedin.com/in/juan-vuletich-75611b3>
>     twitter.com/JuanVuletich <http://twitter.com/JuanVuletich>
>
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>

Cheers,

-- 
Juan Vuletich
cuis.st
github.com/jvuletich
researchgate.net/profile/Juan-Vuletich
independent.academia.edu/JuanVuletich
patents.justia.com/inventor/juan-manuel-vuletich
linkedin.com/in/juan-vuletich-75611b3
twitter.com/JuanVuletich

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