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Subject: Re: [geda-user] Apollon
From: John Doty <jpd AT noqsi DOT com>
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Date: Mon, 14 Sep 2015 18:40:31 -0600
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On Sep 14, 2015, at 3:04 PM, Peter Stuge (peter AT stuge DOT se) [via geda-user AT delorie DOT com] <geda-user AT delorie DOT com> wrote:

> John Doty wrote:
>>> I disagree very strongly with floating point, but using a fixed-size
>>> decimal is an important improvement!
>> 
>> The trouble is that common computer numerics do not actually obey the
>> same rules as mathematical numbers.
> 
> Nod.
> 
> 
>> Rational numbers fix these problems.
> ..
>> For rendering on a grid, use fixed or floating point. The rationals
>> that fall on your grid are a set of measure zero, anyway.
> 
> Output (rendering on grid) is one issue, and is easy enough to deal
> with in isolation.
> 
> But input (rotate by 60 degrees) is another issue, and less easy to
> handle, because it's very important for usability that user
> input->output and vice versa is also closed.

Unfortunately, a closed system handling rational rotation angles requires that you go to the field of algebraic numbers for translations. Mathematica has proprietary code that can perform rigorous calculations with algebraics, but I don’t know of any other system that can do this. You wind up manipulating numbers whose printed representation looks like Root[4 + 3 #1 + 2 #1^2 + #1^3 &, 1].

> 
> Fun!

Indeed!

> 
> 
> //Peter
> 

John Doty              Noqsi Aerospace, Ltd.
http://www.noqsi.com/
jpd AT noqsi DOT com