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How do you build your intuition in algebraic number theory?

Generally my intuition in elementary number theory came from just numerically fiddling with python (and also elementary number theory is pretty easy so you can build intuition without much effort anyway).

But for ANT I don't know any software package to help me fiddle with algebraic number theory -- and on top that ANT is hard, so for example how does people even find results like Dirichlet's unit theorem (for an easier example, say $\mathbb{Z}[\zeta_{23}]$ is not an UFD) to be "intuitive" ?

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    $\begingroup$ Posted also on Mathematics: Building intuition in algebraic number theory. $\endgroup$
    – Martin Sleziak
    Commented Sep 28, 2019 at 15:10
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    $\begingroup$ Just learn the subject. Intuition comes later. $\endgroup$
    – GH from MO
    Commented Sep 28, 2019 at 15:14
  • $\begingroup$ Please avoid cross-posting to different sites within as little as an hour. You should only consider postiong on MO if your question doesn't get an answer within a few days of posting. $\endgroup$
    – Wojowu
    Commented Sep 28, 2019 at 15:28

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I read the question as a request for software packages in the field of algebraic number theory. A free option is PARI/GP, see these lecture notes for some examples, and also this overview of the relevant commands. A more extensive overview is given in Topics in computational algebraic number theory.

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  • $\begingroup$ Thanks a lot ! That kinda answers my question, so do you recommend some beginner-friendly introduction re: how to use PARI/GP for ANT ? $\endgroup$
    – Lelouch
    Commented Sep 28, 2019 at 15:53
  • $\begingroup$ well, the linked resources give some intro to this specific application, but probably you will first want to try a more general intro to PARI/GP, which could be www-fourier.ujf-grenoble.fr/~panchish/pariCRY/tutorial.pdf $\endgroup$
    – Carlo Beenakker
    Commented Sep 28, 2019 at 17:01

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