Talk:Cipolla's algorithm: Difference between revisions
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==Is this task ready for promotion to non draft task status?==
--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 21:26, 16 June 2019 (UTC)
== Something seems to be missing here... ==
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::::::::::: No working implementation ... I agree :-) --[[User:G.Brougnard|G.Brougnard]] ([[User talk:G.Brougnard|talk]]) 17:20, 27 March 2016 (UTC)
== Delete this task? (edit: looks like no, just need to better describe the algorithm) ==
Since this is a bogus algorithm, should we delete this task?
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:::: My supporting evidences for proposing this as a task are : it works (and not only with bogus examples), there is a proof it works, it's interesting (our discussion) , and its implementation is relatively easy.--[[User:G.Brougnard|G.Brougnard]] ([[User talk:G.Brougnard|talk]]) 15:51, 28 March 2016 (UTC)
::::: It's not the same. For one thing, the square root of -6 is a different value from the square root of 7. So, if you are going to be drawing analogies, you should consider something more general than complex numbers. And if you consider quaternions, octonions, sedenion, ... you will notice that as you generalize you lose fundamental arithmetic identities.
::::: Anyways, back to Fp, it's only valid for an integer domain. And by making ω² a non-square you have guaranteed that ω violates the rules of Fp.
::::: In other words, ω cannot be a symbol in Fp, nor in Fp² (though ω² remains a valid value in both).
::::: That said, I see that you now have an echolisp implementation - I'll see if I can extract the actual algorithm from that. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 16:09, 28 March 2016 (UTC)
:::::: For sure ω , which is '''not''' in Fp, violates the rules on Fp, this is the aim of the game . How ω , which defines Fp2 , constructs Fp2 , is the soul of Fp2 cannot be in Fp2 ? Remember , Fp2 is the set { x + y ω } . Make x =0, y=1 and you will find ω in Fp2. And , I agree with you, ω² remains a valid value in both, which is quite useful.
::::::: Looking at your algorithm, you do not use ω in Fp2. You only use ω². In other words, while the math may be bogus, that just means that it does not adequately describe the algorithm. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 18:08, 28 March 2016 (UTC)
::::::: In our p=13 Fp world, the square roots of -6, or 7 simply do not exist. And - I never said it is the same - it is an analogy i feel useful to try to understand things , the square root of -1 do not exists either (in R) . --[[User:G.Brougnard|G.Brougnard]] ([[User talk:G.Brougnard|talk]]) 16:43, 28 March 2016 (UTC)
::::::::: Analogies are fine. And they can be useful for describing algorithms. But that does not mean that they are always adequate descriptions. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 19:18, 28 March 2016 (UTC)
:::::::::: Cipolla must be happy to see at least two implementations of his algorithm. He had serious doubts about its validity. :-) --[[User:G.Brougnard|G.Brougnard]] ([[User talk:G.Brougnard|talk]]) 15:22, 29 March 2016 (UTC)
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