Talk:Square form factorization: Difference between revisions

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Now look under the hood; m is the multiplier,
Now look under the hood; m is the multiplier,
forms P# are in the principal and A# in an ambiguous cycle.<br/>
forms P# are on the principal and A# on an ambiguous cycle.<br/>
Each time, after just a few steps, the multiplier or some
Each time, after just a few steps, the multiplier or some
trivial factor is returned and the principal cycle exited:
trivial factor is returned and the principal cycle exited:
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A9 = ( 22, 14146,-5455)</nowiki>
A9 = ( 22, 14146,-5455)</nowiki>


The pattern repeats. Not showing m = 15 through 385,
The pattern continues. Not showing m = 15 through 385,
the last multiplier gives:
the last multiplier gives:


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augmenting the list with primes 13 through 37 all of the above
augmenting the list with primes 13 through 37 all of the above
numbers eventually yield. But this is just a patch: there are many
numbers eventually yield. But this is just a patch: there are many
more N beyond 50,000,000... At least it's clear that a larger set of
more N beyond 50,000,000... At least it's clear that a larger set
multipliers should be used, although I would prefer a search method
of multipliers should be used, although I prefer a search method
where the problem doesn't exist.
where the problem doesn't exist.


This is what happens if the last square form is saved
This is what happens if the last square form is saved and we
and we continue searching the principal cycle:
[[Square_Form_Factorization#Classical heuristic|continue searching the principal cycle]]:


<nowiki>N = 4558849
<nowiki>N = 4558849
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and back on the principal cycle where a proper square is
and back on the principal cycle where a proper square is
only two steps away:
but two steps away:


<nowiki>P14 = (-1898, 7334, 11^2)
<nowiki>P14 = (-1898, 7334, 11^2)
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turns out to be improper &mdash; a roundabout but dependable route.
turns out to be improper &mdash; a roundabout but dependable route.


To complete the picture, this is the same factorization applying a queue:
To complete the picture, this is the same factorization
[[Square_Form_Factorization#FreeBASIC|applying a queue]]:


<nowiki>N = 4558849
<nowiki>N = 4558849
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A6 = (-766, 6894, 2343)
A6 = (-766, 6894, 2343)
f = 383 N/f = 11903</nowiki>
f = 383 N/f = 11903</nowiki>
&mdash;[[User_talk:Udo_e._pops|Udo e.]]



Can't say I really followed that, nevermind, a translation of the 2nd C entry fixed my problems. --[[User:Petelomax|Pete Lomax]] ([[User talk:Petelomax|talk]]) 19:23, 20 March 2021 (UTC)
Can't say I really followed that, nevermind, a translation of the 2nd C entry fixed my problems. --[[User:Petelomax|Pete Lomax]] ([[User talk:Petelomax|talk]]) 19:23, 20 March 2021 (UTC)
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