Index

A

a_times_b_minus_c() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) a_times_b_plus_c() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) algebraic_closure() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.finite_field_base.FiniteField method) AlgebraicClosureFiniteField() (in module sage.rings.algebraic_closure_finite_field)

AlgebraicClosureFiniteField_generic (class in sage.rings.algebraic_closure_finite_field) AlgebraicClosureFiniteField_pseudo_conway (class in sage.rings.algebraic_closure_finite_field) AlgebraicClosureFiniteFieldElement (class in sage.rings.algebraic_closure_finite_field) as_finite_field_element() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method)

C

c_minus_a_times_b() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) Cache_givaro (class in sage.rings.finite_rings.element_givaro) Cache_ntl_gf2e (class in sage.rings.finite_rings.element_ntl_gf2e) cardinality() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) change_level() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) characteristic() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e method) (sage.rings.finite_rings.finite_field_pari_ffelt.FiniteField_pari_ffelt method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) charpoly() (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method)

check_consistency() (sage.rings.finite_rings.conway_polynomials.PseudoConwayLattice method) construction() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) conway_polynomial() (in module sage.rings.finite_rings.conway_polynomials) create_key_and_extra_args() (sage.rings.finite_rings.integer_mod_ring.IntegerModFactory method) (sage.rings.finite_rings.residue_field.ResidueFieldFactory method) create_object() (sage.rings.finite_rings.integer_mod_ring.IntegerModFactory method) (sage.rings.finite_rings.residue_field.ResidueFieldFactory method) crt() (in module sage.rings.finite_rings.integer_mod_ring)

D

degree() (sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e method) (sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e method) (sage.rings.finite_rings.finite_field_pari_ffelt.FiniteField_pari_ffelt method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

E

Element (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic attribute) (sage.rings.finite_rings.finite_field_pari_ffelt.FiniteField_pari_ffelt attribute) element_from_data() (sage.rings.finite_rings.element_givaro.Cache_givaro method) exists_conway_polynomial() (in module sage.rings.finite_rings.conway_polynomials)

exponent() (sage.rings.finite_rings.element_givaro.Cache_givaro method) extension() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

F

factored_order() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) factored_unit_order() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) fetch_int() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e method) field() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) FiniteField (class in sage.rings.finite_rings.finite_field_base) FiniteField_ext_pari (class in sage.rings.finite_rings.finite_field_ext_pari) FiniteField_givaro (class in sage.rings.finite_rings.finite_field_givaro) FiniteField_givaro_iterator (class in sage.rings.finite_rings.element_givaro) FiniteField_givaroElement (class in sage.rings.finite_rings.element_givaro) FiniteField_ntl_gf2e (class in sage.rings.finite_rings.finite_field_ntl_gf2e) FiniteField_ntl_gf2eElement (class in sage.rings.finite_rings.element_ntl_gf2e) FiniteField_pari_ffelt (class in sage.rings.finite_rings.finite_field_pari_ffelt)

FiniteField_prime_modn (class in sage.rings.finite_rings.finite_field_prime_modn) FiniteFieldElement_pari_ffelt (class in sage.rings.finite_rings.element_pari_ffelt) FiniteFieldHomomorphism_generic (class in sage.rings.finite_rings.hom_finite_field) FiniteFieldHomomorphism_givaro (class in sage.rings.finite_rings.hom_finite_field_givaro) FiniteFieldHomomorphism_prime (class in sage.rings.finite_rings.hom_prime_finite_field) FiniteFieldHomset (class in sage.rings.finite_rings.homset) FiniteFieldIterator (class in sage.rings.finite_rings.finite_field_base) fixed_field() (sage.rings.finite_rings.hom_finite_field.FrobeniusEndomorphism_finite_field method) (sage.rings.finite_rings.hom_finite_field_givaro.FrobeniusEndomorphism_givaro method) (sage.rings.finite_rings.hom_prime_finite_field.FrobeniusEndomorphism_prime method) frobenius_endomorphism() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) FrobeniusEndomorphism_finite_field (class in sage.rings.finite_rings.hom_finite_field) FrobeniusEndomorphism_givaro (class in sage.rings.finite_rings.hom_finite_field_givaro) FrobeniusEndomorphism_prime (class in sage.rings.finite_rings.hom_prime_finite_field)

G

gen() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e method) (sage.rings.finite_rings.finite_field_pari_ffelt.FiniteField_pari_ffelt method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) gens() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method)

get_object() (sage.rings.finite_rings.integer_mod_ring.IntegerModFactory method)

I

ideal() (sage.rings.finite_rings.residue_field.ResidueField_generic method) import_data() (sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e method) inclusion() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) index() (sage.rings.finite_rings.homset.FiniteFieldHomset method) int_repr() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) int_to_log() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) integer_representation() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) IntegerModFactory (class in sage.rings.finite_rings.integer_mod_ring) IntegerModRing_generic (class in sage.rings.finite_rings.integer_mod_ring) is_aut() (sage.rings.finite_rings.homset.FiniteFieldHomset method) is_conway() (sage.rings.finite_rings.finite_field_base.FiniteField method) is_field() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) is_finite() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) is_FiniteField() (in module sage.rings.finite_rings.finite_field_base)

is_identity() (sage.rings.finite_rings.hom_finite_field.FrobeniusEndomorphism_finite_field method) is_injective() (sage.rings.finite_rings.hom_finite_field.FiniteFieldHomomorphism_generic method) (sage.rings.finite_rings.hom_finite_field.FrobeniusEndomorphism_finite_field method) is_IntegerModRing() (in module sage.rings.finite_rings.integer_mod_ring) is_integral_domain() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) is_noetherian() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) is_one() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) is_perfect() (sage.rings.finite_rings.finite_field_base.FiniteField method) is_prime_field() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) is_square() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) is_surjective() (sage.rings.finite_rings.hom_finite_field.FiniteFieldHomomorphism_generic method) (sage.rings.finite_rings.hom_finite_field.FrobeniusEndomorphism_finite_field method) is_unique_factorization_domain() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) is_unit() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) is_zero() (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method)

K

krull_dimension() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

L

late_import() (in module sage.rings.finite_rings.finite_field_ntl_gf2e) lift() (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) (sage.rings.finite_rings.residue_field.ResidueFieldHomomorphism_global method) (sage.rings.finite_rings.residue_field.ResidueField_generic method) lift_map() (sage.rings.finite_rings.residue_field.ResidueField_generic method) LiftingMap (class in sage.rings.finite_rings.residue_field) list() (sage.rings.finite_rings.homset.FiniteFieldHomset method)

list_of_elements_of_multiplicative_group() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) log() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) log_repr() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) log_to_int() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method)

M

minimal_polynomial() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) minpoly() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) modulus() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) multiplicative_generator() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

multiplicative_group_is_cyclic() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) multiplicative_order() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) multiplicative_subgroups() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

N

next() (sage.rings.finite_rings.element_givaro.FiniteField_givaro_iterator method) (sage.rings.finite_rings.finite_field_base.FiniteFieldIterator method) ngens() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.finite_field_base.FiniteField method)

nth_root() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method)

O

order() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e method) (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) (sage.rings.finite_rings.hom_finite_field.FrobeniusEndomorphism_finite_field method) (sage.rings.finite_rings.homset.FiniteFieldHomset method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

order_c() (sage.rings.finite_rings.element_givaro.Cache_givaro method)

P

poly_repr() (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) polynomial() (sage.rings.finite_rings.conway_polynomials.PseudoConwayLattice method) (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_prime_modn.FiniteField_prime_modn method) polynomial_ring() (sage.rings.finite_rings.finite_field_base.FiniteField method) power() (sage.rings.finite_rings.hom_finite_field.FrobeniusEndomorphism_finite_field method) prime_subfield() (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.finite_field_ntl_gf2e.FiniteField_ntl_gf2e method)

primitive_element() (sage.rings.finite_rings.finite_field_base.FiniteField method) PseudoConwayLattice (class in sage.rings.finite_rings.conway_polynomials) pth_power() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) pth_root() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method)

Q

quadratic_nonresidue() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method)

R

random_element() (sage.rings.finite_rings.element_givaro.Cache_givaro method) (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) reduction_map() (sage.rings.finite_rings.residue_field.ResidueField_generic method) ReductionMap (class in sage.rings.finite_rings.residue_field) repr (sage.rings.finite_rings.element_givaro.Cache_givaro attribute) ResidueField_generic (class in sage.rings.finite_rings.residue_field) ResidueFieldFactory (class in sage.rings.finite_rings.residue_field)

ResidueFieldHomomorphism_global (class in sage.rings.finite_rings.residue_field) ResidueFiniteField_givaro (class in sage.rings.finite_rings.residue_field) ResidueFiniteField_ntl_gf2e (class in sage.rings.finite_rings.residue_field) ResidueFiniteField_pari_ffelt (class in sage.rings.finite_rings.residue_field) ResidueFiniteField_prime_modn (class in sage.rings.finite_rings.residue_field)

S

sage.rings.algebraic_closure_finite_field (module) sage.rings.finite_rings.conway_polynomials (module) sage.rings.finite_rings.element_givaro (module) sage.rings.finite_rings.element_ntl_gf2e (module) sage.rings.finite_rings.element_pari_ffelt (module) sage.rings.finite_rings.finite_field_base (module) sage.rings.finite_rings.finite_field_ext_pari (module) sage.rings.finite_rings.finite_field_givaro (module) sage.rings.finite_rings.finite_field_ntl_gf2e (module) sage.rings.finite_rings.finite_field_pari_ffelt (module) sage.rings.finite_rings.finite_field_prime_modn (module) sage.rings.finite_rings.hom_finite_field (module) sage.rings.finite_rings.hom_finite_field_givaro (module)

sage.rings.finite_rings.hom_prime_finite_field (module) sage.rings.finite_rings.homset (module) sage.rings.finite_rings.integer_mod_ring (module) sage.rings.finite_rings.residue_field (module) section() (sage.rings.finite_rings.hom_finite_field.FiniteFieldHomomorphism_generic method) (sage.rings.finite_rings.residue_field.ReductionMap method) (sage.rings.finite_rings.residue_field.ResidueFieldHomomorphism_global method) SectionFiniteFieldHomomorphism_generic (class in sage.rings.finite_rings.hom_finite_field) SectionFiniteFieldHomomorphism_givaro (class in sage.rings.finite_rings.hom_finite_field_givaro) SectionFiniteFieldHomomorphism_prime (class in sage.rings.finite_rings.hom_prime_finite_field) some_elements() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) (sage.rings.finite_rings.finite_field_base.FiniteField method) sqrt() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement method) (sage.rings.finite_rings.element_givaro.FiniteField_givaroElement method) (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method) (sage.rings.finite_rings.element_pari_ffelt.FiniteFieldElement_pari_ffelt method) square_roots_of_one() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) subfield() (sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic method) subfields() (sage.rings.finite_rings.finite_field_base.FiniteField method)

T

trace() (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method)

U

unit_gens() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) unit_group() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) unit_group_exponent() (sage.rings.finite_rings.finite_field_base.FiniteField method) (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) unit_group_order() (sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic method) unpickle_Cache_givaro() (in module sage.rings.finite_rings.element_givaro)

unpickle_FiniteField_ext() (in module sage.rings.finite_rings.finite_field_base) unpickle_FiniteField_givaroElement() (in module sage.rings.finite_rings.element_givaro) unpickle_FiniteField_prm() (in module sage.rings.finite_rings.finite_field_base) unpickle_FiniteFieldElement_pari_ffelt() (in module sage.rings.finite_rings.element_pari_ffelt) unpickleFiniteField_ntl_gf2eElement() (in module sage.rings.finite_rings.element_ntl_gf2e)

V

vector_space() (sage.rings.finite_rings.finite_field_base.FiniteField method)

W

weight() (sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement method)

Z

zeta() (sage.rings.finite_rings.finite_field_base.FiniteField method)

zeta_order() (sage.rings.finite_rings.finite_field_base.FiniteField method)