Hi, I found some strange behaviour of the Hilbert class field of a quadratic number field when the class number is 1, so the Hilbert class field is equal to the ground field: sage: K.<w> = QuadraticField(-5); KX.<X> = K[]; H.<h> = K.hilbert_class_field() sage: (X + w + 1).base_extend(H) X + w + 1 No problem: the Hilbert class field is a proper extension, and the polynomial remains the same.
sage: K.<w> = QuadraticField(-1); KX.<X> = K[]; H.<h> = K.hilbert_class_field() sage: (X + w + 1).base_extend(H) X + 1 In this case the Hilbert class field is equal to K, and the part of the polynomial that is not in QQ disappears. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
