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From: efji <efji@efi.efji>
Newsgroups: sci.math
Subject: Re: The splendor of true
Date: Mon, 10 Mar 2025 10:06:33 +0100
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Le 10/03/2025 à 10:04, Chris M. Thomasson a écrit :
> On 3/10/2025 1:33 AM, efji wrote:
>> Le 10/03/2025 à 03:03, Chris M. Thomasson a écrit :
>>
>>>
>>> Indeed. Sorry for the stupid question, but the following parts of 
>>> RH's description:
>>>
>>> Z=aa'+bb'+i(ab'+a'b) and not Z=aa'-bb'+i(ab'+a'b).
>>>
>>> Means a = x component, b = y component, right? ;^o
>>
>> Well...
>> In his disturbed mind, (a,b) = a-b on the x axis :)
>>
>> But forget the pathetic egotic and just try a+jb=(a,b) un R^2 with the 
>> rule (a+ib)*(a'+jb') = aa'+bb'+j(ab'+a'b) which is the rule on the 
>> split-complex set, (thus j^2=1).
>>
> 
> Humm... I am not all that familiar with the split complex numbers. 
> Something like this?
> 
> glm::vec2
> ct_complex_split_mul(
>      const glm::vec2& z1,
>      const glm::vec2& z2
> ) {
>      return {
>          z1.x * z2.x + z1.y * z2.y,
>          z1.x * z2.y + z1.y * z2.x
>      };
> }
> 
> 
> Where:
> 
> glm::vec2 s0 = { 0, 1 };
> 
> std::cout << "s0 * s0 = " << ct_complex_split_mul(s0, s0) << "\n";
> 
> outputs:
> 
> s0 * s0 = (1, 0)
> 
> ?

Yes !

-- 
F.J.