Claus Fieker, Tommy Hofmann
Published 2024-04-10Version 1
We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we showcase the functionality in two examples related to the investigation of the Cohen-Lenstra heuristic for quadratic fields and the Galois module structure of rings of integers.
Comments: Submitted as chapter for the upcoming book on the computer algebra system OSCAR
Galois module structure of cyclic extensions of local Fields of characteristic zero
Harmonically balanced capitulation over quadratic fields of type (9,9)
Galois scaffolds and Galois module structure in extensions of characteristic $p$ local fields of degree $p^2$
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