Anonymous user
Talk:Cipolla's algorithm: Difference between revisions
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::: Do you understand what I am saying here? If not, can you describe your disagreement with the issue I have raised? If I am wrong, it certainly would not be the first time -- everybody makes mistakes, you know this. However, '''if''' I am wrong, I also want to know '''specifically''' where I am wrong. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 14:17, 28 March 2016 (UTC)
:::: For sure I read what you wrote. I assume that you have read the parallel with complex numbers : i is a member of C (complex numbers) , the value of i² in R (real numbers) is -1, and nobody wants to know the 'value' of i in R, because this has no meaning, because i is not a square in R. In the same way ω is a member of Fp2 , the value of ω² in Fp is well defined (say -6, 7, or whatever not a square). When you compute in C (9 + i) * (9 - i) you find 81 - i² = 82 in R . You do'nt care about the value of i . i vanishes. The only thing you need is i² . This is the same, and the beauty of Cipolla's algorithm : ω vanishes. You do not need its 'value' in Fp .
:::: Similarily , with p = 13 and ω² = 7 , (1 + ω) * (1 - ω) = -6 (mod 13). No need to 'know' ω. So, what is the value of -1 -3ω in Fp2 ? It is -1 -3ω, the same as -1 -3i is -1 -3i in the field of complex numbers. No further computation to do.
:::: <math>\sqrt{-6}</math> is only a symbol, just like <math>\sqrt{-1}</math> = i is just a symbol.
:::: So, my disagreement is the following : ω is only a symbol of Fp2, and you cannot assign a value to it in Fp. You '''cannot''' compute -1 -3ω in Fp. This has meaning only in Fp2. And this is not needed by the algorithm, evidently.
:::: 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)
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