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Make RationalField behave more like a general number field #23245

Open koffie opened 7 years ago

koffie commented 7 years ago

Currently RationalField has significantly less functionality then NumberField_relative and NumberField_absolute . This is annoying since this means that if you want to write code that works for all numberfields you sometimes need to special case QQ.

Here is the list of functions that is currently available for NumberField_absolute, but not for QQ.

'Minkowski_embedding', 'S_class_group', 'S_unit_group', 'S_units', 'absolute_different', 'absolute_field', 'absolute_generator', 'absolute_polynomial', 'absolute_polynomial_ntl', 'absolute_vector_space', 'base_field', 'change_generator', 'change_names', 'complex_conjugation', 'complex_embeddings', 'composite_fields', 'defining_polynomial', 'different', 'disc', 'elements_of_bounded_height', 'elements_of_norm', 'factor', 'fractional_ideal', 'galois_closure', 'galois_group', 'gen_embedding', 'hilbert_conductor', 'hilbert_symbol', 'ideals_of_bdd_norm', 'integral_basis', 'is_CM', 'is_galois', 'is_isomorphic', 'is_relative', 'is_totally_imaginary', 'is_totally_real', 'latex_variable_name', 'maximal_totally_real_subfield', 'narrow_class_group', 'number_of_roots_of_unity', 'optimized_representation', 'optimized_subfields', 'pari_bnf', 'pari_nf', 'pari_polynomial', 'pari_rnfnorm_data', 'pari_zk', 'polynomial', 'polynomial_ntl', 'polynomial_quotient_ring', 'polynomial_ring', 'prime_above', 'prime_factors', 'primes_above', 'primes_of_bounded_norm', 'primes_of_degree_one_iter', 'primes_of_degree_one_list', 'primitive_element', 'primitive_root_of_unity', 'real_embeddings', 'real_places', 'reduced_basis', 'reduced_gram_matrix', 'regulator', 'relative_degree', 'relative_different', 'relative_polynomial', 'relative_vector_space', 'relativize', 'roots_of_unity', 'solve_CRT', 'specified_complex_embedding', 'structure', 'subfield', 'subfields', 'trace_dual_basis', 'trace_pairing', 'uniformizer', 'unit_group', 'units', 'vector_space', 'zeta_coefficients', 'zeta_function'

CC: @koffie @edgarcosta

Component: number fields

Issue created by migration from https://trac.sagemath.org/ticket/23245

fchapoton commented 7 years ago
comment:1

See #7596

edgarcosta commented 7 years ago

Description changed:

--- 
+++ 
@@ -4,8 +4,11 @@
 Here is the list of functions that is currently available for NumberField_absolute, but not for QQ.

 'Minkowski_embedding',
+
  'S_class_group',
+
  'S_unit_group',
+
  'S_units',
  'absolute_different',
  'absolute_field',
edgarcosta commented 7 years ago
comment:3

ups, I didn't mean to change the description.

edgarcosta commented 7 years ago

Description changed:

--- 
+++ 
@@ -4,11 +4,8 @@
 Here is the list of functions that is currently available for NumberField_absolute, but not for QQ.

 'Minkowski_embedding',
-
  'S_class_group',
-
  'S_unit_group',
-
  'S_units',
  'absolute_different',
  'absolute_field',
mkoeppe commented 4 years ago
comment:5

For subfield, see #30171

mkoeppe commented 3 years ago
comment:7

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.