%0 Journal Article %A Guillermo Mantilla-Soler %A Carlos Rivera %T The integral trace form as a complete invariant for real $S_n$ number fields %J Documenta mathematica %D 2022 %P 1865-1889 %V 27 %U http://geodesic.mathdoc.fr/articles/10.4171/dm/x20/ %R 10.4171/dm/x20 %F 10_4171_dm_x20