Index _ | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | V | X | Z _ __pow__() (sage.rings.integer.Integer method) A absolute_degree() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) absolute_discriminant() (sage.rings.rational_field.RationalField method) absolute_norm() (sage.rings.rational.Rational method) absolute_polynomial() (sage.rings.rational_field.RationalField method) additive_order() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) algdep() (in module sage.arith.misc) algebraic_closure() (sage.rings.rational_field.RationalField method) algebraic_dependency() (in module sage.arith.misc) arith_int (class in sage.rings.fast_arith) arith_llong (class in sage.rings.fast_arith) as_integer_ratio() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) aurifeuillian() (in module sage.rings.factorint) automorphisms() (sage.rings.rational_field.RationalField method) B balanced_digits() (sage.rings.integer.Integer method) bernmm_bern_modp() (in module sage.rings.bernmm) bernmm_bern_rat() (in module sage.rings.bernmm) bernoulli() (in module sage.arith.misc) bernoulli_mod_p() (in module sage.rings.bernoulli_mod_p) bernoulli_mod_p_single() (in module sage.rings.bernoulli_mod_p) binary() (sage.rings.integer.Integer method) binomial() (in module sage.arith.misc) (sage.rings.integer.Integer method) binomial_coefficients() (in module sage.arith.misc) bit_length() (sage.rings.integer.Integer method) bits() (sage.rings.integer.Integer method) C carmichael_lambda() (in module sage.arith.misc) ceil() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) characteristic() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) charpoly() (sage.rings.rational.Rational method) class_number() (sage.rings.integer.Integer method) (sage.rings.rational_field.RationalField method) completion() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) complex_embedding() (sage.rings.rational_field.RationalField method) conjugate() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) construction() (sage.rings.rational_field.RationalField method) content() (sage.rings.rational.Rational method) continuant() (in module sage.arith.misc) continued_fraction() (sage.rings.rational.Rational method) continued_fraction_list() (sage.rings.rational.Rational method) coprime_integers() (sage.rings.integer.Integer method) CRT() (in module sage.arith.misc) crt() (in module sage.arith.misc) (sage.arith.multi_modular.MultiModularBasis_base method) (sage.rings.integer.Integer method) CRT_basis() (in module sage.arith.misc) crt_basis() (in module sage.rings.integer_ring) CRT_list() (in module sage.arith.misc) CRT_vectors() (in module sage.arith.misc) D dedekind_psi() (in module sage.arith.misc) dedekind_sum() (in module sage.arith.misc) defining_polynomial() (sage.rings.rational_field.RationalField method) degree() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) denom() (sage.rings.rational.Rational method) denominator() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) differences() (in module sage.arith.misc) digits() (sage.rings.integer.Integer method) discriminant() (sage.rings.rational_field.RationalField method) divide_knowing_divisible_by() (sage.rings.integer.Integer method) divides() (sage.rings.integer.Integer method) divisors() (in module sage.arith.misc) (sage.rings.integer.Integer method) E embeddings() (sage.rings.rational_field.RationalField method) eratosthenes() (in module sage.arith.misc) euclidean_degree() (sage.rings.integer.Integer method) Euler_Phi (class in sage.arith.misc) exact_log() (sage.rings.integer.Integer method) exp() (sage.rings.integer.Integer method) extend_with_primes() (sage.arith.multi_modular.MultiModularBasis_base method) extension() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) F factor() (in module sage.arith.misc) (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) factor_aurifeuillian() (in module sage.rings.factorint) factor_cunningham() (in module sage.rings.factorint) factor_trial_division() (in module sage.rings.factorint) factor_using_flint() (in module sage.rings.factorint_flint) factor_using_pari() (in module sage.rings.factorint_pari) factorial() (in module sage.arith.misc) (sage.rings.integer.Integer method) falling_factorial() (in module sage.arith.misc) floor() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) four_squares() (in module sage.arith.misc) four_squares_pyx() (in module sage.rings.sum_of_squares) frac() (in module sage.rings.rational_field) fraction_field() (sage.rings.integer_ring.IntegerRing_class method) free_integer_pool() (in module sage.rings.integer) fundamental_discriminant() (in module sage.arith.misc) G gamma() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) gauss_sum() (in module sage.arith.misc) GCD() (in module sage.arith.misc) gcd() (in module sage.arith.misc) gcd_int() (sage.rings.fast_arith.arith_int method) GCD_list() (in module sage.rings.integer) gcd_longlong() (sage.rings.fast_arith.arith_llong method) gen() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) generic_power() (in module sage.arith.power) gens() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) get_gcd() (in module sage.arith.misc) get_inverse_mod() (in module sage.arith.misc) global_height() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) global_height_arch() (sage.rings.rational.Rational method) global_height_non_arch() (sage.rings.rational.Rational method) H height() (sage.rings.rational.Rational method) hex() (sage.rings.integer.Integer method) hilbert_conductor() (in module sage.arith.misc) hilbert_conductor_inverse() (in module sage.arith.misc) hilbert_symbol() (in module sage.arith.misc) hilbert_symbol_negative_at_S() (sage.rings.rational_field.RationalField method) I imag() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) int_to_Q (class in sage.rings.rational) int_to_Z (class in sage.rings.integer) Integer (class in sage.rings.integer) integer_ceil() (in module sage.arith.misc) integer_floor() (in module sage.arith.misc) integer_rational_power() (in module sage.rings.rational) integer_trunc() (in module sage.arith.misc) IntegerRing() (in module sage.rings.integer_ring) IntegerRing_class (class in sage.rings.integer_ring) IntegerWrapper (class in sage.rings.integer) inverse_mod() (in module sage.arith.misc) (sage.rings.integer.Integer method) inverse_mod_int() (sage.rings.fast_arith.arith_int method) inverse_mod_longlong() (sage.rings.fast_arith.arith_llong method) inverse_of_unit() (sage.rings.integer.Integer method) is_absolute() (sage.rings.rational_field.RationalField method) is_discriminant() (sage.rings.integer.Integer method) is_field() (sage.rings.integer_ring.IntegerRing_class method) is_fundamental_discriminant() (sage.rings.integer.Integer method) is_Integer() (in module sage.rings.integer) is_integer() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_IntegerRing() (in module sage.rings.integer_ring) is_integral() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_integrally_closed() (sage.rings.integer_ring.IntegerRing_class method) is_irreducible() (sage.rings.integer.Integer method) is_noetherian() (sage.rings.integer_ring.IntegerRing_class method) is_norm() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_nth_power() (sage.rings.rational.Rational method) is_one() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_padic_square() (sage.rings.rational.Rational method) is_perfect_power() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_power_of() (sage.rings.integer.Integer method) is_power_of_two() (in module sage.arith.misc) is_prime() (in module sage.arith.misc) (sage.rings.integer.Integer method) is_prime_field() (sage.rings.rational_field.RationalField method) is_prime_power() (in module sage.arith.misc) (sage.rings.integer.Integer method) is_pseudoprime() (in module sage.arith.misc) (sage.rings.integer.Integer method) is_pseudoprime_power() (in module sage.arith.misc) (sage.rings.integer.Integer method) is_Rational() (in module sage.rings.rational) is_rational() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_RationalField() (in module sage.rings.rational_field) is_S_integral() (sage.rings.rational.Rational method) is_S_unit() (sage.rings.rational.Rational method) is_square() (in module sage.arith.misc) (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) is_squarefree() (in module sage.arith.misc) (sage.rings.integer.Integer method) is_sum_of_two_squares_pyx() (in module sage.rings.sum_of_squares) is_surjective() (sage.rings.rational.Z_to_Q method) is_unit() (sage.rings.integer.Integer method) isqrt() (sage.rings.integer.Integer method) J jacobi() (sage.rings.integer.Integer method) jacobi_symbol() (in module sage.arith.misc) K kronecker() (in module sage.arith.misc) (sage.rings.integer.Integer method) kronecker_symbol() (in module sage.arith.misc) krull_dimension() (sage.rings.integer_ring.IntegerRing_class method) L lcm() (in module sage.arith.functions) LCM_list() (in module sage.arith.functions) legendre_symbol() (in module sage.arith.misc) list() (sage.arith.multi_modular.MultiModularBasis_base method) (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) local_height() (sage.rings.rational.Rational method) local_height_arch() (sage.rings.rational.Rational method) log() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) long_to_Z (class in sage.rings.integer) M make_integer() (in module sage.rings.integer) make_rational() (in module sage.rings.rational) maximal_order() (sage.rings.rational_field.RationalField method) minpoly() (sage.rings.rational.Rational method) mod_ui() (sage.rings.rational.Rational method) module sage.arith.functions sage.arith.misc sage.arith.multi_modular sage.arith.power sage.rings.bernmm sage.rings.bernoulli_mod_p sage.rings.factorint sage.rings.factorint_flint sage.rings.factorint_pari sage.rings.fast_arith sage.rings.integer sage.rings.integer_ring sage.rings.rational sage.rings.rational_field sage.rings.sum_of_squares Moebius (class in sage.arith.misc) mqrr_rational_reconstruction() (in module sage.arith.misc) multifactorial() (sage.rings.integer.Integer method) MultiModularBasis (class in sage.arith.multi_modular) MultiModularBasis_base (class in sage.arith.multi_modular) multinomial() (in module sage.arith.misc) multinomial_coefficients() (in module sage.arith.misc) multiplicative_order() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) MutableMultiModularBasis (class in sage.arith.multi_modular) N nbits() (sage.rings.integer.Integer method) ndigits() (sage.rings.integer.Integer method) next_prime() (in module sage.arith.misc) (sage.arith.multi_modular.MutableMultiModularBasis method) (sage.rings.integer.Integer method) next_prime_power() (in module sage.arith.misc) (sage.rings.integer.Integer method) next_probable_prime() (in module sage.arith.misc) (sage.rings.integer.Integer method) ngens() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) norm() (sage.rings.rational.Rational method) nth_prime() (in module sage.arith.misc) nth_root() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) number_field() (sage.rings.rational_field.RationalField method) number_of_divisors() (in module sage.arith.misc) numer() (sage.rings.rational.Rational method) numerator() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) O oct() (sage.rings.integer.Integer method) odd_part() (in module sage.arith.misc) (sage.rings.integer.Integer method) ord() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) order() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) ordinal_str() (sage.rings.integer.Integer method) P p_primary_part() (sage.rings.integer.Integer method) parameter() (sage.rings.integer_ring.IntegerRing_class method) partial_product() (sage.arith.multi_modular.MultiModularBasis_base method) perfect_power() (sage.rings.integer.Integer method) period() (sage.rings.rational.Rational method) places() (sage.rings.rational_field.RationalField method) plot() (sage.arith.misc.Euler_Phi method) (sage.arith.misc.Moebius method) (sage.arith.misc.Sigma method) polynomial() (sage.rings.rational_field.RationalField method) popcount() (sage.rings.integer.Integer method) power_basis() (sage.rings.rational_field.RationalField method) power_mod() (in module sage.arith.misc) powermod() (sage.rings.integer.Integer method) precomputation_list() (sage.arith.multi_modular.MultiModularBasis_base method) previous_prime() (in module sage.arith.misc) (sage.rings.integer.Integer method) previous_prime_power() (in module sage.arith.misc) (sage.rings.integer.Integer method) prime_divisors() (in module sage.arith.misc) (sage.rings.integer.Integer method) prime_factors() (in module sage.arith.misc) (sage.rings.integer.Integer method) prime_powers() (in module sage.arith.misc) prime_range() (in module sage.rings.fast_arith) prime_to_m_part() (in module sage.arith.misc) (sage.rings.integer.Integer method) prime_to_S_part() (sage.rings.rational.Rational method) primes() (in module sage.arith.misc) primes_first_n() (in module sage.arith.misc) primes_of_bounded_norm_iter() (sage.rings.rational_field.RationalField method) primitive_root() (in module sage.arith.misc) prod() (sage.arith.multi_modular.MultiModularBasis_base method) Python Enhancement Proposals PEP 3127 Q Q_to_Z (class in sage.rings.rational) quadratic_defect() (sage.rings.rational_field.RationalField method) quadratic_residues() (in module sage.arith.misc) quo_rem() (sage.rings.integer.Integer method) quotient() (sage.rings.integer_ring.IntegerRing_class method) R radical() (in module sage.arith.misc) random_element() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) random_prime() (in module sage.arith.misc) range() (sage.arith.misc.Moebius method) (sage.rings.integer_ring.IntegerRing_class method) range_by_height() (sage.rings.rational_field.RationalField method) Rational (class in sage.rings.rational) rational_power_parts() (in module sage.rings.rational) rational_recon_int() (sage.rings.fast_arith.arith_int method) rational_recon_longlong() (sage.rings.fast_arith.arith_llong method) rational_reconstruction() (in module sage.arith.misc) (sage.rings.integer.Integer method) RationalField (class in sage.rings.rational_field) real() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) relative_discriminant() (sage.rings.rational_field.RationalField method) relative_norm() (sage.rings.rational.Rational method) replace_prime() (sage.arith.multi_modular.MutableMultiModularBasis method) residue_field() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method) rising_factorial() (in module sage.arith.misc) round() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) S sage.arith.functions module sage.arith.misc module sage.arith.multi_modular module sage.arith.power module sage.rings.bernmm module sage.rings.bernoulli_mod_p module sage.rings.factorint module sage.rings.factorint_flint module sage.rings.factorint_pari module sage.rings.fast_arith module sage.rings.integer module sage.rings.integer_ring module sage.rings.rational module sage.rings.rational_field module sage.rings.sum_of_squares module section() (sage.rings.rational.Q_to_Z method) (sage.rings.rational.Z_to_Q method) selmer_generators() (sage.rings.rational_field.RationalField method) selmer_group() (sage.rings.rational_field.RationalField method) selmer_group_iterator() (sage.rings.rational_field.RationalField method) selmer_space() (sage.rings.rational_field.RationalField method) Sigma (class in sage.arith.misc) sign() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) signature() (sage.rings.rational_field.RationalField method) some_elements() (sage.rings.rational_field.RationalField method) sort_complex_numbers_for_display() (in module sage.arith.misc) sqrt() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) sqrtrem() (sage.rings.integer.Integer method) squarefree_divisors() (in module sage.arith.misc) squarefree_part() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) str() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) subfactorial() (in module sage.arith.misc) sum_of_k_squares() (in module sage.arith.misc) support() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) T test_bit() (sage.rings.integer.Integer method) three_squares() (in module sage.arith.misc) three_squares_pyx() (in module sage.rings.sum_of_squares) trace() (sage.rings.rational.Rational method) trailing_zero_bits() (sage.rings.integer.Integer method) trial_division() (in module sage.arith.misc) (sage.rings.integer.Integer method) trunc() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) two_squares() (in module sage.arith.misc) two_squares_pyx() (in module sage.rings.sum_of_squares) V val_unit() (sage.rings.integer.Integer method) (sage.rings.rational.Rational method) valuation() (in module sage.arith.misc) (sage.rings.integer.Integer method) (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational.Rational method) (sage.rings.rational_field.RationalField method) verify_bernoulli_mod_p() (in module sage.rings.bernoulli_mod_p) X XGCD() (in module sage.arith.misc) xgcd() (in module sage.arith.misc) (sage.rings.integer.Integer method) xgcd_int() (sage.rings.fast_arith.arith_int method) xkcd() (in module sage.arith.misc) xlcm() (in module sage.arith.misc) Z Z_to_Q (class in sage.rings.rational) zeta() (sage.rings.integer_ring.IntegerRing_class method) (sage.rings.rational_field.RationalField method)