Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Division of two complex numbers
Date: Mon, 20 Jan 2025 14:40:42 -0800
Organization: A noiseless patient Spider
Lines: 177
Message-ID: <vmmjda$3fp83$1@dont-email.me>
References: <zMjaMvWZUkHX6SOb195JTQnVpSA@jntp> <vmmcjk$3dtpt$1@dont-email.me>
 <XmWkVwNVTy8QHqeS0TsrPZNuk_c@jntp> <vmmden$3e97a$1@dont-email.me>
 <GKkg17e0FiGdEqKCQvNrtvN0OLY@jntp> <vmmdso$3e97a$2@dont-email.me>
 <q-ufmQf4sCFn4XF8BtUedW5gSA8@jntp> <vmmf64$3e97a$3@dont-email.me>
 <S2Hn3AKfn1Y3YxkyXKTCa1i4D4Q@jntp> <vmmg5v$3e97a$4@dont-email.me>
 <51Tdfq24D44V9MS0l646QQuIrfo@jntp>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 20 Jan 2025 23:40:43 +0100 (CET)
Injection-Info: dont-email.me; posting-host="f83ba5790de8b51aa60b613f63b035eb";
	logging-data="3663107"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/gH/gJypVXBkiFhtTGry6oTcxvaN8FDzk="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:YGM5p/b9XB3imb9QwxGN7P1Lb6A=
In-Reply-To: <51Tdfq24D44V9MS0l646QQuIrfo@jntp>
Content-Language: en-US
Bytes: 7990

On 1/20/2025 1:50 PM, Python wrote:
> Le 20/01/2025 à 22:45, "Chris M. Thomasson" a écrit :
>> On 1/20/2025 1:35 PM, Python wrote:
>>> Le 20/01/2025 à 22:28, "Chris M. Thomasson" a écrit :
>>>> On 1/20/2025 1:09 PM, Python wrote:
>>>>> Le 20/01/2025 à 22:06, "Chris M. Thomasson" a écrit :
>>>>>> On 1/20/2025 1:04 PM, Python wrote:
>>>>>>> Le 20/01/2025 à 21:59, "Chris M. Thomasson" a écrit :
>>>>>>>> On 1/20/2025 12:51 PM, Python wrote:
>>>>>>>>> Le 20/01/2025 à 21:44, "Chris M. Thomasson" a écrit :
>>>>>>>>>> On 1/20/2025 12:20 PM, Python wrote:
>>>>>>>>>>> Le 20/01/2025 à 21:09, Tom Bola a écrit :
>>>>>>>>>>>> Am 20.01.2025 20:33:12 Moebius schrieb:
>>>>>>>>>>>>
>>>>>>>>>>>>> Am 20.01.2025 um 19:27 schrieb Python:
>>>>>>>>>>>>>> Le 20/01/2025 à 19:23, Richard Hachel  a écrit :
>>>>>>>>>>>>>>> Le 20/01/2025 à 19:10, Python a écrit :
>>>>>>>>>>>>>>>> Le 20/01/2025 à 18:58, Richard Hachel  a écrit :
>>>>>>>>>>>>>>>>>>> Mathematicians give:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> z1/z2=[(aa'+bb')/(a'²+b'²)]+i[(ba'-ab')/(a'²+b'²)]
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> It was necessary to write:
>>>>>>>>>>>>>>>>>>> z1/z2=[(aa'-bb')/(a'²-b'²)]+i[(ba'-ab')/(a'²-b'²)]
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I've explained how i is defined in a positive way in 
>>>>>>>>>>>>>>>> modern algebra. i^2 = -1 is not a definition. It is a 
>>>>>>>>>>>>>>>> *property* that can be deduced from a definition of i.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>  That is what I saw.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>  Is not a definition.
>>>>>>>>>>>>>>>  It doesn't explain why.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> We have the same thing with Einstein and relativity.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> [snip unrelated nonsense about your idiotic views on 
>>>>>>>>>>>>>>> Relativity]
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is clear that i²=-1, but we don't say WHY. It is clear 
>>>>>>>>>>>>>>> however that if i is both 1 and -1 (which gives two 
>>>>>>>>>>>>>>> possible solutions) we can consider its square as the 
>>>>>>>>>>>>>>> product of itself by its opposite, and vice versa.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I've posted a definition of i (which is NOT i^2 = -1) 
>>>>>>>>>>>>>> numerous times. A "positive" definition as you asked for.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I've already told this idiot:
>>>>>>>>>>>>>
>>>>>>>>>>>>> Complex numbers can be defined as (ordered) pairs of real 
>>>>>>>>>>>>> numbers.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Then we may define (in this context):
>>>>>>>>>>>>>
>>>>>>>>>>>>>           i := (0, 1) .
>>>>>>>>>>>>>
>>>>>>>>>>>>>  From this we get: i^2 = -1.
>>>>>>>>>>>>
>>>>>>>>>>>> For R.H.
>>>>>>>>>>>>   By the binominal formulas we have: (a, b)^2 = a^2 + 2ab + b^2
>>>>>>>>>>>
>>>>>>>>>>> Huh? This is not the binomial formula which is (a + b)^2 = 
>>>>>>>>>>> a^2 + 2ab + b^2
>>>>>>>>>>>
>>>>>>>>>>> (a, b)^2 does not mean anything without any additional 
>>>>>>>>>>> definition/ context.
>>>>>>>>>>>
>>>>>>>>>>>>   So we get: (0, 1)^2 ) 0^2 + 2*(0 - 1) + 1 = 0 + (-2) + 1 = -1 
>>>>>>>>>>>
>>>>>>>>>>> you meant  (0, 1)^2 = 0^2 + 2*(0 - 1) + 1 = 0 + (-2) + 1 = -1 ?
>>>>>>>>>>>
>>>>>>>>>>> This does not make sense without additional context.
>>>>>>>>>>>
>>>>>>>>>>> In R(epsilon) = R[X]/X^2 (dual numbers a + b*epsilon where 
>>>>>>>>>>> epsilon is such as
>>>>>>>>>>> epsilon =/= 0 and epsilon^2 0) we do have :
>>>>>>>>>>>
>>>>>>>>>>> (0, 1) ^ 2 = 0
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> vec2 ct_cmul(in vec2 p0, in vec2 p1)
>>>>>>>>>> {
>>>>>>>>>>      return vec2(p0.x * p1.x - p0.y * p1.y, p0.x * p1.y + p0.y 
>>>>>>>>>> * p1.x);
>>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> So what? This is not an application of the binomial formula...
>>>>>>>>>
>>>>>>>>> What's you point?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> It's a way I multiply two vectors together as if they are 
>>>>>>>> complex numbers.
>>>>>>>>
>>>>>>>> Another one:
>>>>>>>>
>>>>>>>> #define cx_mul(a, b) vec2(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x)
>>>>>>>>
>>>>>>>> I can pass in normal vectors to this in GLSL. vec2's
>>>>>>>
>>>>>>> Good! You know how to write a C program. :-) (pun intended)
>>>>>>
>>>>>> Fwiw, that is not is C, it's from one of my GLSL shaders. ;^)
>>>>>
>>>>> It is also C.
>>>>
>>>> No. GLSL is not C at all, it has a similar style, but is different 
>>>> for sure.
>>>
>>> It is exactly the same syntax. *facepalm*.
>>> Ok, let's say so, if you wish, so you can implement complex 
>>> multiplication in a GLSL shader.
>>
>> No. C and GLSL are completely different languages. Have you ever even 
>> used GLSL? You can do fun things in GLSL that C cannot do at all.
> 
> This is ridiculous nitpicking.
> #define cx_mul(a, b) vec2(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x)
> 
> may compile in C, also can your function ct_cmul above.
> I didn't wrote that GLSL was C, I wrote that the code you wrote was C.

I missed your main point. Fair enough. Fwiw, a fun part of GLSL is doing 
stuff like:

vec3 a = vec3(.25, 1, .75);
vec2 b = a.xz;
vec2 c = b + vec2(.75, .25);

c now equals (1, 1)

;^)


> 
> Anyway, this is not the point. Either in C or GLSL the fact that you can 
> implement complex multiplication (or in ANY language) is NOT THE POINT 
> it is IRRELEVANT!
> 
>>> Again: SO WHAT? ? ? This is NOT THE POINT of the discussion.
>>
>> I thought it might help the OP.
> 
> In what manner? ?  Nobody, not even the OP pretended that it cannot be 
> implemented.
> 
> Seriously Chris, what's wrong with you?
> 
>>>>> Again what's *your* point? Your posts makes absolutely no sense in 
>>>>> the context of this thread!
>>>>
>>>> Just a way to multiply two 2-ary vectors as if they were complex 
>>>> numbers. Now, here is a little C99 program I just typed in the 
>>>> newsreader. It should compile.
>>>> _____________________________
>>>> [snip irrelevant triviality]
>>>
>>> So what? ? ?
>>>> I thought it might help out the OP.
>>>
>>> In which way? ? ? Hachel didn't write that it cannot be done (he's 
>>> not that silly), he claimed (wrongly) that it is the wrong way to 
>>> define multiplication between complex numbers.
>>>
>>>>>>>
>>>>>>> This is quite off-topic to point out that multiplication of 
>>>>>>> complex numbers in C/C++ can be done.
>>>>>>>
>>>>>>> The discussion is not about that it can be done, even crank 
>>>>>>> Hachel would admit this. It is *why* it makes sense to define 
>>>>>>> multiplication *that way*.
> 
========== REMAINDER OF ARTICLE TRUNCATED ==========