On Fri, Sep 13, 2024 at 1:10 PM Duncan Murdoch wrote:

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> On 2024-09-13 8:53 a.m., Jonathan Dushoff wrote:
> >> Message: 4
> >> Date: Thu, 12 Sep 2024 11:21:02 -0400
> >> From: Duncan Murdoch
> >> That's not the correct formula, is it? I think the result should be x *
> >> Conj(y) / Mod(y)^2 .

> > Correct, sorry. And thanks.

> >> So that would involve * and
> >> / , not just real arithmetic.

> > Not an expert, but I don't see it. Conj and Mod seem to be numerically
> > straightforward real-like operations. We do those, and then multiply
> > one complex number by one real quotient.

> Are you sure? We aren't dealing with real numbers and complex numbers
> here, we're dealing with those sets extended with infinities and other
> weird things.

Definitely not sure, just thought I would suggest it as a possibility.

> So for example if y is some kind of infinite complex number, then 1/y
> should come out to zero, and if x is finite, the final result of x/y
> should be zero.

> But if we evaluate x/y as (x / Mod(y)^2) * Conj(y), won't we get a NaN
> from zero times infinity?

Yes, and it's not trivial to work around, so probably not worth it.

Thanks,

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