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Over a number field, given the norm of an principal ideal, is there a way to find the principal ideal?

Also, Given ideals is there an algorithm to find principal ideals?

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  • $\begingroup$ What do you mean by 'sort' principal ideals? Do you mean to sort them by norm? $\endgroup$
    – Stanley Yao Xiao
    Dec 6, 2017 at 10:51
  • $\begingroup$ no, just to separate principal ideals. Sorry for the confusion. $\endgroup$
    – student
    Dec 6, 2017 at 10:58
  • $\begingroup$ There may be several principal ideals with the same norm. $\endgroup$
    – Gerry Myerson
    Dec 6, 2017 at 11:47
  • $\begingroup$ no problem, but is there a way to find all possible principal ideals having the given norm? $\endgroup$
    – student
    Dec 6, 2017 at 12:30
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    $\begingroup$ To determine if an ideal is principal you may use algorithm 6.5.10 in Cohen's "A course on computational albegraic number theory". To find all ideals of a given norm it is good to know how to factor prime numbers; that is section 4.8 in the same book. $\endgroup$
    – Chris Wuthrich
    Dec 6, 2017 at 13:44

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