create_object ( version, key, ** extra_args ) #Ĭreate the unique cyclotomic field defined by key. 0 sage: cf18 ( z9 ) zeta18^2 sage: cf9 ( z18 ) -zeta9^5 sage: cf18 ( z3 ) zeta18^3 - 1 sage: cf18 ( z6 ) zeta18^3 sage: cf18 ( z6 ) ** 2 zeta18^3 - 1 sage: cf9 ( z3 ) zeta9^3 create_key ( n = 0, names = None, embedding = True ) #Ĭreate the unique key for the cyclotomic field specified by the 0 sage: cf18 = CyclotomicField ( 18 ) z18 = cf18. 0 sage: cf3 ( z6 ) zeta3 + 1 sage: cf6 ( z3 ) zeta6 - 1 sage: cf9 = CyclotomicField ( 9 ) z9 = cf9. 0 sage: cf3 = CyclotomicField ( 3 ) z3 = cf3. Sage: cf30 = CyclotomicField ( 30 ) sage: cf5 = CyclotomicField ( 5 ) sage: cf3 = CyclotomicField ( 3 ) sage: cf30. Michael Daub, Chris Wuthrich (): adding Dirichlet characters for abelian fields John Jones (2017-07): improve check for is_galois(), add is_abelian(), building on work in patch by Chris WuthrichĪnna Haensch (2018-03): added quadratic_defect() Peter Bruin (2016-06): make number fields fully satisfy unique representation Kiran Kedlaya (2016-05): relative number fields hash based on relative polynomials Vincent Delecroix (2015-02): comparisons/floor/ceil using embeddings Julian Rueth (): absolute number fields are unique parents Robert Harron (2012-08): added is_CM(), complex_conjugation(), andĬhristian Stump (2012-11): added conversion to universal cyclotomic field Simon King (2010-05): Improve coercion from GAP Robert Bradshaw (2008-10): specified embeddings into ambient fields William Stein (): major rewrite and documentation Steven Sivek (): added support for relative extensions William Stein (2004, 2005): initial version Toggle table of contents sidebar Number Fields # Enumeration of Totally Real Fields: PHC interface.Enumeration of Totally Real Fields: Relative Extensions.Enumeration of Primitive Totally Real Fields.Unit and S-unit groups of Number Fields.Helper classes for structural embeddings and isomorphisms of number fields.Sets of homomorphisms between number fields.Elements of bounded height in number fields.Splitting fields of polynomials over number fields.Optimized Quadratic Number Field Elements.
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