Re: [Scheme-reports] Numerical example (real? -2.5+0.0i)

[John Cowan <cowan@x>]

Aubrey Jaffer scripsit:

> Algebraically, the complex numbers are the field of reals extended by
> a solution of x^2+1=0.  All reals are complex; there is no difference
> between real 2.0 and 2.0+0.0i.

I used the term "general complex number" in the same sense it is used
in R5RS, to mean a number whose imaginary part is nonzero.

> FreeSnell <http://people.csail.mit.edu/jaffer/FreeSnell> is a Scheme
> application for computing the optical properties of thin-films.  It
> uses complex numbers intensively in its computations.  The only
> effects of distinguishing real real from complex real numbers would be
> to increase its storage and reduce its performance.

I don't understand this.  How can either storage or performance depend
on the result returned by the real? procedure?

> So no, SCM won't be distinguishing "real reals" from "complex reals".
> 
>  | The rationale here is that a number with imaginary part 0.0 isn't
>  | necessarily on the real line, since 0.0 just means a number x such
>  | that 0 < x < the smallest representable inexact number.
> 
> Is that the official r7rs model of inexact numbers?

Nothing about rationales is official, and this one isn't even in the
report, so that question is self-answering.

> It isn't SCM's model; <http://srfi.schemers.org/srfi-70/srfi-70.html>
> is.  SRFI-70 specifies the result of numerical procedures applied to
> infinities and zeros.

There will eventually be a specification in R7RS-small as well, probably
similar to R5RS and IEEE 754:2008.

> I don't see this information in r7rs-draft-3.pdf, leaving a huge hole
> in the specification.  

I agree.  It would be helpful to provide suitable text.

-- 
Verbogeny is one of the pleasurettes    John Cowan <cowan@x>
of a creatific thinkerizer.             http://www.ccil.org/~cowan
   --Peter da Silva

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