Index _ | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Z _ _add_() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) _lmul_() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) _mul_() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) _mul_trunc_() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) _rmul_() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) _sub_() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) A A_invariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) a_realization() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing method) abc_pd (class in sage.rings.polynomial.polynomial_compiled) adams_operator() (sage.rings.polynomial.polynomial_element.Polynomial method) adams_operator_on_roots() (sage.rings.polynomial.polynomial_element.Polynomial method) add_as_you_wish() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) add_bigoh() (sage.rings.polynomial.polynomial_element.Polynomial method) add_generator() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) (sage.rings.polynomial.pbori.pbori.ReductionStrategy method) (sage.rings.polynomial.symmetric_reduction.SymmetricReductionStrategy method) add_generator_delayed() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) add_m_mul_q() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) add_pd (class in sage.rings.polynomial.polynomial_compiled) add_up_polynomials() (in module sage.rings.polynomial.pbori.pbori) algebra_generators() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ParentMethods method) algebraic_dependence() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) AlgebraicForm (class in sage.rings.invariants.invariant_theory) all_done() (sage.rings.polynomial.real_roots.ocean method) all_generators() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) all_roots_in_interval() (sage.rings.polynomial.polynomial_element.Polynomial method) all_spolys_in_next_degree() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) alpha_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) ambient() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) any_irreducible_factor() (sage.rings.polynomial.polynomial_element.Polynomial method) any_root() (sage.rings.polynomial.polynomial_element.Polynomial method) append() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialVector method) apply_map() (sage.rings.polynomial.polydict.PolyDict method) approx_bp() (sage.rings.polynomial.real_roots.ocean method) args() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) arithmetic_invariants() (sage.rings.invariants.invariant_theory.BinaryQuintic method) as_float() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_float method) (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) as_QuadraticForm() (sage.rings.invariants.invariant_theory.QuadraticForm method) associated_primes() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) B B (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing attribute) B_invariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) base_extend() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) base_field() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_field method) base_ring() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) basis (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal property) basis_is_groebner() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) bateman_bound() (in module sage.rings.polynomial.cyclotomic) bernstein_down() (in module sage.rings.polynomial.real_roots) bernstein_expand() (in module sage.rings.polynomial.real_roots) bernstein_polynomial() (sage.rings.polynomial.real_roots.bernstein_polynomial_factory_ar method) (sage.rings.polynomial.real_roots.bernstein_polynomial_factory_intlist method) (sage.rings.polynomial.real_roots.bernstein_polynomial_factory_ratlist method) bernstein_polynomial_factory (class in sage.rings.polynomial.real_roots) bernstein_polynomial_factory_ar (class in sage.rings.polynomial.real_roots) bernstein_polynomial_factory_intlist (class in sage.rings.polynomial.real_roots) bernstein_polynomial_factory_ratlist (class in sage.rings.polynomial.real_roots) bernstein_up() (in module sage.rings.polynomial.real_roots) beta_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) binary_cubic_coefficients_from_invariants() (in module sage.rings.invariants.reconstruction) binary_form_from_invariants() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) binary_pd (class in sage.rings.polynomial.polynomial_compiled) binary_quadratic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) binary_quadratic_coefficients_from_invariants() (in module sage.rings.invariants.reconstruction) binary_quartic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) binary_quintic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) binary_quintic_coefficients_from_invariants() (in module sage.rings.invariants.reconstruction) BinaryQuartic (class in sage.rings.invariants.invariant_theory) BinaryQuintic (class in sage.rings.invariants.invariant_theory) bitsize_doctest() (in module sage.rings.polynomial.real_roots) blocks() (sage.rings.polynomial.term_order.TermOrder method) BooleanMonomial (class in sage.rings.polynomial.pbori.pbori) BooleanMonomialIterator (class in sage.rings.polynomial.pbori.pbori) BooleanMonomialMonoid (class in sage.rings.polynomial.pbori.pbori) BooleanMonomialVariableIterator (class in sage.rings.polynomial.pbori.pbori) BooleanMulAction (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomial (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomialEntry (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomialIdeal (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomialIterator (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomialRing (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomialRing_base (class in sage.rings.polynomial.multi_polynomial_ring_base) BooleanPolynomialRing_constructor() (in module sage.rings.polynomial.polynomial_ring_constructor) BooleanPolynomialVector (class in sage.rings.polynomial.pbori.pbori) BooleanPolynomialVectorIterator (class in sage.rings.polynomial.pbori.pbori) BooleConstant (class in sage.rings.polynomial.pbori.pbori) BooleSet (class in sage.rings.polynomial.pbori.pbori) BooleSetIterator (class in sage.rings.polynomial.pbori.pbori) bp_done() (sage.rings.polynomial.real_roots.island method) buchberger() (in module sage.rings.polynomial.toy_buchberger) buchberger_improved() (in module sage.rings.polynomial.toy_buchberger) C C_invariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) can_convert_to_singular() (in module sage.rings.polynomial.polynomial_singular_interface) can_rewrite() (sage.rings.polynomial.pbori.pbori.ReductionStrategy method) canonical_form() (sage.rings.invariants.invariant_theory.BinaryQuintic method) cardinality() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) cartesian_product() (sage.rings.polynomial.pbori.pbori.BooleSet method) CCuddNavigator (class in sage.rings.polynomial.pbori.pbori) change() (sage.rings.polynomial.pbori.pbori.BooleSet method) change_ring() (sage.rings.polynomial.ideal.Ideal_1poly_field method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) change_var() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) change_variable_name() (sage.rings.polynomial.polynomial_element.Polynomial method) characteristic() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) charpoly() (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) cheap_reductions() (sage.rings.polynomial.pbori.pbori.ReductionStrategy method) cl_maximum_root() (in module sage.rings.polynomial.real_roots) cl_maximum_root_first_lambda() (in module sage.rings.polynomial.real_roots) cl_maximum_root_local_max() (in module sage.rings.polynomial.real_roots) class_group() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) class_number() (sage.rings.fraction_field.FractionField_1poly_field method) clean_top_by_chain_criterion() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) clebsch_invariants() (sage.rings.invariants.invariant_theory.BinaryQuintic method) clone() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) coeff_pd (class in sage.rings.polynomial.polynomial_compiled) coefficient() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polydict.PolyDict method) coefficient_matrix() (in module sage.rings.polynomial.toy_variety) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) coefficients() (sage.rings.invariants.invariant_theory.AlgebraicForm method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) coefficients_monomials() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_gf2 method) coeffs() (sage.rings.invariants.invariant_theory.BinaryQuartic method) (sage.rings.invariants.invariant_theory.BinaryQuintic method) (sage.rings.invariants.invariant_theory.QuadraticForm method) (sage.rings.invariants.invariant_theory.TernaryCubic method) (sage.rings.invariants.invariant_theory.TernaryQuadratic method) coeffs_bitsize() (sage.rings.polynomial.real_roots.bernstein_polynomial_factory_ar method) (sage.rings.polynomial.real_roots.bernstein_polynomial_factory_intlist method) (sage.rings.polynomial.real_roots.bernstein_polynomial_factory_ratlist method) coerce_coefficients() (sage.rings.polynomial.polydict.PolyDict method) combine_to_positives() (sage.rings.polynomial.polydict.ETuple method) common_nonzero_positions() (sage.rings.polynomial.polydict.ETuple method) CompiledPolynomialFunction (class in sage.rings.polynomial.polynomial_compiled) complete_primary_decomposition() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) completion() (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) complex_embeddings() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_field method) complex_roots() (in module sage.rings.polynomial.complex_roots) (sage.rings.polynomial.polynomial_element.Polynomial method) compose_power() (sage.rings.polynomial.polynomial_element.Polynomial method) compose_trunc() (sage.rings.polynomial.polynomial_element.Polynomial method) composed_op() (sage.rings.polynomial.polynomial_element.Polynomial method) connected_components() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) connection_graph() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) constant() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.CCuddNavigator method) constant_coefficient() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) ConstantPolynomialSection (class in sage.rings.polynomial.polynomial_element) construction() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_dense method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_integral_domain method) contained_vars() (in module sage.rings.polynomial.pbori.pbori) contains_one() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) content() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ElementMethods method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.padics.polynomial_padic.Polynomial_padic method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) content_ideal() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) context (class in sage.rings.polynomial.real_roots) convolution() (in module sage.rings.polynomial.convolution) covariant_conic() (sage.rings.invariants.invariant_theory.TernaryQuadratic method) cover_ring() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) create_key() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRingFactory method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRingFactory method) create_object() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRingFactory method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRingFactory method) cyclotomic_coeffs() (in module sage.rings.polynomial.cyclotomic) cyclotomic_part() (sage.rings.polynomial.polynomial_element.Polynomial method) cyclotomic_polynomial() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) cyclotomic_value() (in module sage.rings.polynomial.cyclotomic) D d_basis() (in module sage.rings.polynomial.toy_d_basis) de_casteljau() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_float method) (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) de_casteljau_doublevec() (in module sage.rings.polynomial.real_roots) de_casteljau_intvec() (in module sage.rings.polynomial.real_roots) defining_ideal() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) deg() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleConstant method) degree() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense_inexact method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) degree_lowest_rational_function() (in module sage.rings.polynomial.multi_polynomial_element) degree_of_semi_regularity() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) degree_on_basis() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ParentMethods method) degree_reduction_next_size() (in module sage.rings.polynomial.real_roots) degrees() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) delta() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) delta_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) Delta_invariant() (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) Delta_prime_invariant() (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) denom() (sage.rings.fraction_field_FpT.FpTElement method) denominator() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) derivative() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) derivative_at_minus_one() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) derivative_i() (sage.rings.polynomial.polydict.PolyDict method) dict() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) diff() (sage.rings.polynomial.pbori.pbori.BooleSet method) (sage.rings.polynomial.polynomial_element.Polynomial method) differentiate() (sage.rings.polynomial.polynomial_element.Polynomial method) dimension() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialIdeal method) disc() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) discriminant() (sage.rings.invariants.invariant_theory.QuadraticForm method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_p method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) dispersion() (sage.rings.polynomial.polynomial_element.Polynomial method) dispersion_set() (sage.rings.polynomial.polynomial_element.Polynomial method) divide() (sage.rings.polynomial.pbori.pbori.BooleSet method) divide_by_gcd() (sage.rings.polynomial.polydict.ETuple method) divide_by_var() (sage.rings.polynomial.polydict.ETuple method) divided_difference() (sage.rings.polynomial.polynomial_ring.PolynomialRing_field method) divides() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polydict.ETuple method) (sage.rings.polynomial.polynomial_element.Polynomial method) divisors() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) divisors_of() (sage.rings.polynomial.pbori.pbori.BooleSet method) done() (sage.rings.polynomial.real_roots.island method) dotprod() (sage.rings.polynomial.polydict.ETuple method) down_degree() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) down_degree_iter() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) downscale() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) dprod_imatrow_vec() (in module sage.rings.polynomial.real_roots) dual() (sage.rings.invariants.invariant_theory.QuadraticForm method) dummy_pd (class in sage.rings.polynomial.polynomial_compiled) E eadd() (sage.rings.polynomial.polydict.ETuple method) eadd_p() (sage.rings.polynomial.polydict.ETuple method) eadd_scaled() (sage.rings.polynomial.polydict.ETuple method) easy_linear_factors() (in module sage.rings.polynomial.pbori.pbori) EisensteinD() (sage.rings.invariants.invariant_theory.BinaryQuartic method) EisensteinE() (sage.rings.invariants.invariant_theory.BinaryQuartic method) Element (sage.rings.polynomial.laurent_polynomial_ring.LaurentPolynomialRing_mpair attribute) (sage.rings.polynomial.laurent_polynomial_ring.LaurentPolynomialRing_univariate attribute) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular attribute) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic attribute) element() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_element method) Element_hidden (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict attribute) elength() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) elim_pol() (in module sage.rings.polynomial.toy_variety) eliminate_linear_variables() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_gf2 method) elimination_ideal() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.multi_polynomial_ideal.NCPolynomialIdeal method) else_branch() (sage.rings.polynomial.pbori.pbori.CCuddNavigator method) emax() (sage.rings.polynomial.polydict.ETuple method) emin() (sage.rings.polynomial.polydict.ETuple method) empty() (sage.rings.polynomial.pbori.pbori.BooleSet method) emul() (sage.rings.polynomial.polydict.ETuple method) escalar_div() (sage.rings.polynomial.polydict.ETuple method) esub() (sage.rings.polynomial.polydict.ETuple method) ETuple (class in sage.rings.polynomial.polydict) euclidean_degree() (sage.rings.polynomial.polynomial_element.Polynomial method) exponents() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) extend_variables() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) F F_covariant() (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) factor() (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.padics.polynomial_padic.Polynomial_padic method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) factor_mod() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) factor_of_slope() (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_cdv method) factor_padic() (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) faugere_step_dense() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) fcp() (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) FGLMStrategy (class in sage.rings.polynomial.pbori.pbori) field_extension() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_domain method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) find_roots() (sage.rings.polynomial.real_roots.ocean method) first() (sage.rings.invariants.invariant_theory.TwoAlgebraicForms method) first_hilbert_series() (in module sage.rings.polynomial.hilbert) first_term() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) flattening_morphism() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) FlatteningMorphism (class in sage.rings.polynomial.flatten) footprint() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) form() (sage.rings.invariants.invariant_theory.AlgebraicForm method) FormsBase (class in sage.rings.invariants.invariant_theory) Fp_FpT_coerce (class in sage.rings.fraction_field_FpT) FpT (class in sage.rings.fraction_field_FpT) FpT_Fp_section (class in sage.rings.fraction_field_FpT) FpT_iter (class in sage.rings.fraction_field_FpT) FpT_Polyring_section (class in sage.rings.fraction_field_FpT) FpTElement (class in sage.rings.fraction_field_FpT) fraction() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) fraction_field() (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_field method) FractionField() (in module sage.rings.fraction_field) FractionField_1poly_field (class in sage.rings.fraction_field) FractionField_generic (class in sage.rings.fraction_field) FractionFieldElement (class in sage.rings.fraction_field_element) FractionFieldElement_1poly_field (class in sage.rings.fraction_field_element) FractionFieldEmbedding (class in sage.rings.fraction_field) FractionFieldEmbeddingSection (class in sage.rings.fraction_field) FractionSpecializationMorphism (class in sage.rings.polynomial.flatten) free_resolution() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) from_fraction_field() (in module sage.rings.polynomial.laurent_polynomial_ring) from_h_vector() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted method) from_invariants() (sage.rings.invariants.invariant_theory.BinaryQuintic class method) (sage.rings.invariants.invariant_theory.QuadraticForm class method) from_ocean() (sage.rings.polynomial.real_roots.linear_map method) (sage.rings.polynomial.real_roots.warp_map method) from_polynomial() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ParentMethods method) function_field() (sage.rings.fraction_field.FractionField_1poly_field method) G g_covariant() (sage.rings.invariants.invariant_theory.BinaryQuartic method) galois_group() (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) galois_group_davenport_smith_test() (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) gamma_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) gauss_on_polys() (in module sage.rings.polynomial.pbori.pbori) gcd() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_p method) (sage.rings.polynomial.polynomial_number_field.Polynomial_absolute_number_field_dense method) (sage.rings.polynomial.polynomial_number_field.Polynomial_relative_number_field_dense method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) gen() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ParentMethods method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.pbori.pbori.BooleanMonomialMonoid method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) gen_index() (in module sage.rings.polynomial.polydict) GenDictWithBasering (class in sage.rings.polynomial.infinite_polynomial_ring) generic_pd (class in sage.rings.polynomial.polynomial_compiled) generic_power_trunc() (in module sage.rings.polynomial.polynomial_element) gens() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ParentMethods method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.pbori.pbori.BooleanMonomialMonoid method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.symmetric_reduction.SymmetricReductionStrategy method) gens_dict() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) genus() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) get() (sage.rings.polynomial.polydict.PolyDict method) get_base_order_code() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) get_be_log() (sage.rings.polynomial.real_roots.context method) get_cparent() (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) get_dc_log() (sage.rings.polynomial.real_roots.context method) get_form() (sage.rings.invariants.invariant_theory.SeveralAlgebraicForms method) get_msb_bit() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_float method) (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) get_order_code() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) get_realfield_rndu() (in module sage.rings.polynomial.real_roots) get_var_mapping() (in module sage.rings.polynomial.pbori.pbori) GF2X_BuildIrred_list() (in module sage.rings.polynomial.polynomial_gf2x) GF2X_BuildRandomIrred_list() (in module sage.rings.polynomial.polynomial_gf2x) GF2X_BuildSparseIrred_list() (in module sage.rings.polynomial.polynomial_gf2x) global_height() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) gpol() (in module sage.rings.polynomial.toy_d_basis) graded_free_resolution() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) graded_part() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) gradient() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) greater_tuple (sage.rings.polynomial.term_order.TermOrder property) greater_tuple_block() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_deglex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_degneglex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_degrevlex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_invlex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_lex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_matrix() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_negdeglex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_negdegrevlex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_neglex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_negwdeglex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_negwdegrevlex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_wdeglex() (sage.rings.polynomial.term_order.TermOrder method) greater_tuple_wdegrevlex() (sage.rings.polynomial.term_order.TermOrder method) groebner_basis() (sage.rings.polynomial.ideal.Ideal_1poly_field method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialIdeal method) (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) groebner_basis_degrevlex() (in module sage.rings.polynomial.msolve) groebner_cover() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) groebner_fan() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) GroebnerStrategy (class in sage.rings.polynomial.pbori.pbori) H h_covariant() (sage.rings.invariants.invariant_theory.BinaryQuartic method) H_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) h_polynomial() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) h_vector() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) hamming_weight() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_element method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) has_constant_part() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleConstant method) has_cyclotomic_factor() (sage.rings.polynomial.polynomial_element.Polynomial method) has_degree_order() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) has_root() (sage.rings.polynomial.real_roots.island method) head_normal_form() (sage.rings.polynomial.pbori.pbori.ReductionStrategy method) hensel_lift() (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_cdv method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) Hessian() (sage.rings.invariants.invariant_theory.TernaryCubic method) hilbert_numerator() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) hilbert_poincare_series() (in module sage.rings.polynomial.hilbert) hilbert_polynomial() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) hilbert_series() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) homogeneous_components() (sage.rings.polynomial.multi_polynomial.MPolynomial method) homogeneous_symmetric_function() (in module sage.rings.polynomial.omega) homogenize() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) homogenized() (sage.rings.invariants.invariant_theory.AlgebraicForm method) (sage.rings.invariants.invariant_theory.SeveralAlgebraicForms method) I i_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) id() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) ideal() (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) Ideal_1poly_field (class in sage.rings.polynomial.ideal) if_then_else() (in module sage.rings.polynomial.pbori.pbori) implications() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) in_subalgebra() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) include_divisors() (sage.rings.polynomial.pbori.pbori.BooleSet method) increase_precision() (sage.rings.polynomial.real_roots.ocean method) index() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) InfiniteGenDict (class in sage.rings.polynomial.infinite_polynomial_ring) InfinitePolynomial (class in sage.rings.polynomial.infinite_polynomial_element) InfinitePolynomial_dense (class in sage.rings.polynomial.infinite_polynomial_element) InfinitePolynomial_sparse (class in sage.rings.polynomial.infinite_polynomial_element) InfinitePolynomialGen (class in sage.rings.polynomial.infinite_polynomial_ring) InfinitePolynomialRing_dense (class in sage.rings.polynomial.infinite_polynomial_ring) InfinitePolynomialRing_sparse (class in sage.rings.polynomial.infinite_polynomial_ring) InfinitePolynomialRingFactory (class in sage.rings.polynomial.infinite_polynomial_ring) inhomogeneous_quadratic_form() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) int_list() (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) INTEGER_LIMIT (sage.rings.fraction_field_FpT.FpT attribute) IntegerValuedPolynomialRing (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Bases (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Bases.ElementMethods (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Bases.ParentMethods (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Binomial (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Binomial.Element (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Shifted (class in sage.rings.polynomial.integer_valued_polynomials) IntegerValuedPolynomialRing.Shifted.Element (class in sage.rings.polynomial.integer_valued_polynomials) integral() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) integral_closure() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) integral_i() (sage.rings.polynomial.polydict.PolyDict method) inter_reduction() (in module sage.rings.polynomial.toy_buchberger) interpolate() (in module sage.rings.polynomial.pbori.pbori) interpolate_smallest_lex() (in module sage.rings.polynomial.pbori.pbori) interpolation() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) interpolation_polynomial() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) interred_libsingular() (in module sage.rings.polynomial.multi_polynomial_ideal_libsingular) interreduced_basis() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialIdeal method) (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) interreduction() (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) intersect() (sage.rings.polynomial.pbori.pbori.BooleSet method) intersection() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) interval_bernstein_polynomial (class in sage.rings.polynomial.real_roots) interval_bernstein_polynomial_float (class in sage.rings.polynomial.real_roots) interval_bernstein_polynomial_integer (class in sage.rings.polynomial.real_roots) interval_roots() (in module sage.rings.polynomial.complex_roots) intervals_disjoint() (in module sage.rings.polynomial.complex_roots) intvec_to_doublevec() (in module sage.rings.polynomial.real_roots) invariants() (sage.rings.invariants.invariant_theory.BinaryQuintic method) (sage.rings.invariants.invariant_theory.QuadraticForm method) InvariantTheoryFactory (class in sage.rings.invariants.invariant_theory) inverse() (sage.rings.polynomial.flatten.FlatteningMorphism method) inverse_mod() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) inverse_of_unit() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) inverse_series_trunc() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) irreducible_element() (sage.rings.polynomial.polynomial_ring.PolynomialRing_dense_finite_field method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_dense_mod_p method) irrelevant_ideal() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) is_block_order() (sage.rings.polynomial.term_order.TermOrder method) is_constant() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleConstant method) (sage.rings.polynomial.polydict.ETuple method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_cyclotomic() (sage.rings.polynomial.polynomial_element.Polynomial method) is_cyclotomic_product() (sage.rings.polynomial.polynomial_element.Polynomial method) is_eisenstein() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) is_equal() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) is_exact() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) is_field() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) is_finite() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) is_FractionField() (in module sage.rings.fraction_field) is_FractionFieldElement() (in module sage.rings.fraction_field_element) is_gen() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) is_generator() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) is_global() (sage.rings.polynomial.term_order.TermOrder method) is_groebner() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) is_homogeneous() (sage.rings.invariants.invariant_theory.FormsBase method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_injective() (sage.rings.fraction_field.FractionFieldEmbedding method) (sage.rings.polynomial.polynomial_element.PolynomialBaseringInjection method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_coercion method) (sage.rings.polynomial.polynomial_ring_homomorphism.PolynomialRingHomomorphism_from_base method) is_integral() (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method) is_integral_domain() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) is_irreducible() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_GF2X method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) is_LaurentPolynomialRing() (in module sage.rings.polynomial.laurent_polynomial_ring) is_linearly_dependent() (in module sage.rings.polynomial.toy_variety) is_local() (sage.rings.polynomial.term_order.TermOrder method) is_lorentzian() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_maximal() (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) is_monic() (sage.rings.polynomial.polynomial_element.Polynomial method) is_monomial() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_MPolynomial() (in module sage.rings.polynomial.multi_polynomial) is_MPolynomialIdeal() (in module sage.rings.polynomial.multi_polynomial_ideal) is_MPolynomialRing() (in module sage.rings.polynomial.multi_polynomial_ring_base) is_multiple_of() (sage.rings.polynomial.polydict.ETuple method) is_nilpotent() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_noetherian() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) is_one() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleConstant method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) is_pair() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) is_Polynomial() (in module sage.rings.polynomial.polynomial_element) is_PolynomialQuotientRing() (in module sage.rings.polynomial.polynomial_quotient_ring) is_PolynomialRing() (in module sage.rings.polynomial.polynomial_ring) is_PolynomialSequence() (in module sage.rings.polynomial.multi_polynomial_sequence) is_prime() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) is_primitive() (sage.rings.polynomial.polynomial_element.Polynomial method) is_real_rooted() (sage.rings.polynomial.polynomial_element.Polynomial method) is_singleton() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) is_singleton_or_pair() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) is_sparse() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) is_square() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_squarefree() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) is_surjective() (sage.rings.fraction_field.FractionFieldEmbedding method) (sage.rings.polynomial.polynomial_element.PolynomialBaseringInjection method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_coercion method) (sage.rings.polynomial.polynomial_ring_homomorphism.PolynomialRingHomomorphism_from_base method) is_symmetric() (sage.rings.polynomial.multi_polynomial.MPolynomial method) is_term() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) is_triangular() (in module sage.rings.polynomial.toy_variety) is_unique_factorization_domain() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) is_unit() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_domain method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) is_univariate() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) is_weighted_degree_order() (sage.rings.polynomial.term_order.TermOrder method) is_weil_polynomial() (sage.rings.polynomial.polynomial_element.Polynomial method) is_zero() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleConstant method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) island (class in sage.rings.polynomial.real_roots) iter() (sage.rings.fraction_field_FpT.FpT method) iterator_exp_coeff() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) iterindex() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) J j_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) J_covariant() (sage.rings.invariants.invariant_theory.TernaryCubic method) (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) jacobian_ideal() (sage.rings.polynomial.multi_polynomial.MPolynomial method) K karatsuba_threshold() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) kbase_libsingular() (in module sage.rings.polynomial.multi_polynomial_ideal_libsingular) key_basis() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) krull_dimension() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) L lagrange_polynomial() (sage.rings.polynomial.polynomial_ring.PolynomialRing_field method) latex() (sage.rings.polynomial.polydict.PolyDict method) LaurentPolynomial (class in sage.rings.polynomial.laurent_polynomial) LaurentPolynomial_univariate (class in sage.rings.polynomial.laurent_polynomial) LaurentPolynomialRing() (in module sage.rings.polynomial.laurent_polynomial_ring) LaurentPolynomialRing_generic (class in sage.rings.polynomial.laurent_polynomial_ring_base) LaurentPolynomialRing_mpair (class in sage.rings.polynomial.laurent_polynomial_ring) LaurentPolynomialRing_univariate (class in sage.rings.polynomial.laurent_polynomial_ring) LC() (in module sage.rings.polynomial.toy_d_basis) lc() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) LCM() (in module sage.rings.polynomial.toy_buchberger) lcm() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) lcmt() (sage.rings.polynomial.polydict.PolyDict method) lead() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.PolynomialConstruct method) (sage.rings.polynomial.pbori.pbori.PolynomialFactory method) lead_deg() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) lead_divisors() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) leading_coefficient() (sage.rings.polynomial.polynomial_element.Polynomial method) less_bits() (sage.rings.polynomial.real_roots.island method) lex_lead() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) lex_lead_deg() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) lift() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) linear_map (class in sage.rings.polynomial.real_roots) linear_representation() (in module sage.rings.polynomial.toy_variety) list() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) ll_red_nf_noredsb() (in module sage.rings.polynomial.pbori.pbori) ll_red_nf_noredsb_single_recursive_call() (in module sage.rings.polynomial.pbori.pbori) ll_red_nf_redsb() (in module sage.rings.polynomial.pbori.pbori) ll_reduce_all() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) LM() (in module sage.rings.polynomial.toy_buchberger) (in module sage.rings.polynomial.toy_d_basis) lm() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) local_height() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) local_height_arch() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) lshift_coeffs() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) lsign() (sage.rings.polynomial.real_roots.bernstein_polynomial_factory method) LT() (in module sage.rings.polynomial.toy_buchberger) lt() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) M macaulay2_str() (sage.rings.polynomial.term_order.TermOrder method) macaulay_resultant() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) MacMahonOmega() (in module sage.rings.polynomial.omega) magma_str() (sage.rings.polynomial.term_order.TermOrder method) main() (sage.rings.polynomial.pbori.pbori.FGLMStrategy method) make_element() (in module sage.rings.fraction_field_element) (in module sage.rings.polynomial.polynomial_gf2x) (in module sage.rings.polynomial.polynomial_modn_dense_ntl) (in module sage.rings.polynomial.polynomial_zmod_flint) (in module sage.rings.polynomial.polynomial_zz_pex) make_element_old() (in module sage.rings.fraction_field_element) make_ETuple() (in module sage.rings.polynomial.polydict) make_generic_polynomial() (in module sage.rings.polynomial.polynomial_element) make_padic_poly() (in module sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense) make_PolyDict() (in module sage.rings.polynomial.polydict) make_PolynomialRealDense() (in module sage.rings.polynomial.polynomial_real_mpfr_dense) map_coefficients() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) map_every_x_to_x_plus_one() (in module sage.rings.polynomial.pbori.pbori) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) matrix() (sage.rings.invariants.invariant_theory.QuadraticForm method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) (sage.rings.polynomial.term_order.TermOrder method) max_abs_doublevec() (in module sage.rings.polynomial.real_roots) max_bitsize_intvec_doctest() (in module sage.rings.polynomial.real_roots) max_exp() (sage.rings.polynomial.polydict.PolyDict method) max_index() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) maximal_degree() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) maximal_order() (sage.rings.fraction_field.FractionField_1poly_field method) maximum_root_first_lambda() (in module sage.rings.polynomial.real_roots) maximum_root_local_max() (in module sage.rings.polynomial.real_roots) min_exp() (sage.rings.polynomial.polydict.PolyDict method) min_max_delta_intvec() (in module sage.rings.polynomial.real_roots) min_max_diff_doublevec() (in module sage.rings.polynomial.real_roots) min_max_diff_intvec() (in module sage.rings.polynomial.real_roots) minimal_associated_primes() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) minimal_elements() (sage.rings.polynomial.pbori.pbori.BooleSet method) minimalize() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) minimalize_and_tail_reduce() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) minpoly() (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) minpoly_mod() (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) mk_context() (in module sage.rings.polynomial.real_roots) mk_ibpf() (in module sage.rings.polynomial.real_roots) mk_ibpi() (in module sage.rings.polynomial.real_roots) mod() (sage.rings.polynomial.polynomial_element.Polynomial method) mod_mon_set() (in module sage.rings.polynomial.pbori.pbori) mod_var_set() (in module sage.rings.polynomial.pbori.pbori) modular_composition() (sage.rings.polynomial.polynomial_gf2x.Polynomial_GF2X method) module sage.rings.fraction_field sage.rings.fraction_field_element sage.rings.fraction_field_FpT sage.rings.invariants.invariant_theory sage.rings.invariants.reconstruction sage.rings.monomials sage.rings.polynomial.complex_roots sage.rings.polynomial.convolution sage.rings.polynomial.cyclotomic sage.rings.polynomial.flatten sage.rings.polynomial.hilbert sage.rings.polynomial.ideal sage.rings.polynomial.infinite_polynomial_element sage.rings.polynomial.infinite_polynomial_ring sage.rings.polynomial.integer_valued_polynomials sage.rings.polynomial.laurent_polynomial sage.rings.polynomial.laurent_polynomial_ring sage.rings.polynomial.laurent_polynomial_ring_base sage.rings.polynomial.msolve sage.rings.polynomial.multi_polynomial sage.rings.polynomial.multi_polynomial_element sage.rings.polynomial.multi_polynomial_ideal sage.rings.polynomial.multi_polynomial_ideal_libsingular sage.rings.polynomial.multi_polynomial_libsingular sage.rings.polynomial.multi_polynomial_ring sage.rings.polynomial.multi_polynomial_ring_base sage.rings.polynomial.multi_polynomial_sequence sage.rings.polynomial.omega sage.rings.polynomial.padics.polynomial_padic sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense sage.rings.polynomial.padics.polynomial_padic_flat sage.rings.polynomial.pbori.pbori sage.rings.polynomial.polydict sage.rings.polynomial.polynomial_compiled sage.rings.polynomial.polynomial_element sage.rings.polynomial.polynomial_element_generic sage.rings.polynomial.polynomial_fateman sage.rings.polynomial.polynomial_gf2x sage.rings.polynomial.polynomial_integer_dense_flint sage.rings.polynomial.polynomial_integer_dense_ntl sage.rings.polynomial.polynomial_modn_dense_ntl sage.rings.polynomial.polynomial_number_field sage.rings.polynomial.polynomial_quotient_ring sage.rings.polynomial.polynomial_quotient_ring_element sage.rings.polynomial.polynomial_rational_flint sage.rings.polynomial.polynomial_real_mpfr_dense sage.rings.polynomial.polynomial_ring sage.rings.polynomial.polynomial_ring_constructor sage.rings.polynomial.polynomial_ring_homomorphism sage.rings.polynomial.polynomial_singular_interface sage.rings.polynomial.polynomial_zmod_flint sage.rings.polynomial.polynomial_zz_pex sage.rings.polynomial.real_roots sage.rings.polynomial.refine_root sage.rings.polynomial.symmetric_ideal sage.rings.polynomial.symmetric_reduction sage.rings.polynomial.term_order sage.rings.polynomial.toy_buchberger sage.rings.polynomial.toy_d_basis sage.rings.polynomial.toy_variety modulus() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_dense_mod_n method) monic() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) monics() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) monomial() (sage.rings.polynomial.laurent_polynomial_ring.LaurentPolynomialRing_mpair method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) monomial_all_divisors() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) monomial_coefficient() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polydict.PolyDict method) (sage.rings.polynomial.polynomial_element.Polynomial method) monomial_divides() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) monomial_exponent() (in module sage.rings.polynomial.polydict) monomial_lcm() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) monomial_pairwise_prime() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) monomial_quotient() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) monomial_reduce() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) monomial_reduction() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) MonomialConstruct (class in sage.rings.polynomial.pbori.pbori) MonomialFactory (class in sage.rings.polynomial.pbori.pbori) monomials() (in module sage.rings.monomials) (sage.rings.invariants.invariant_theory.BinaryQuartic method) (sage.rings.invariants.invariant_theory.BinaryQuintic method) (sage.rings.invariants.invariant_theory.QuadraticForm method) (sage.rings.invariants.invariant_theory.TernaryCubic method) (sage.rings.invariants.invariant_theory.TernaryQuadratic method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) monomials_of_degree() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) more_bits() (sage.rings.polynomial.real_roots.island method) MPolynomial (class in sage.rings.polynomial.multi_polynomial) MPolynomial_element (class in sage.rings.polynomial.multi_polynomial_element) MPolynomial_libsingular (class in sage.rings.polynomial.multi_polynomial) (class in sage.rings.polynomial.multi_polynomial_libsingular) MPolynomial_polydict (class in sage.rings.polynomial.multi_polynomial_element) MPolynomialIdeal (class in sage.rings.polynomial.multi_polynomial_ideal) MPolynomialIdeal_macaulay2_repr (class in sage.rings.polynomial.multi_polynomial_ideal) MPolynomialIdeal_magma_repr (class in sage.rings.polynomial.multi_polynomial_ideal) MPolynomialIdeal_quotient (class in sage.rings.polynomial.multi_polynomial_ideal) MPolynomialIdeal_singular_base_repr (class in sage.rings.polynomial.multi_polynomial_ideal) MPolynomialIdeal_singular_repr (class in sage.rings.polynomial.multi_polynomial_ideal) MPolynomialRing_base (class in sage.rings.polynomial.multi_polynomial_ring_base) MPolynomialRing_libsingular (class in sage.rings.polynomial.multi_polynomial_libsingular) MPolynomialRing_macaulay2_repr (class in sage.rings.polynomial.multi_polynomial_ring) MPolynomialRing_polydict (class in sage.rings.polynomial.multi_polynomial_ring) MPolynomialRing_polydict_domain (class in sage.rings.polynomial.multi_polynomial_ring) mul_pd (class in sage.rings.polynomial.polynomial_compiled) mult_fact_sim_C() (in module sage.rings.polynomial.pbori.pbori) multiples() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) multiples_of() (sage.rings.polynomial.pbori.pbori.BooleSet method) multiplication_trunc() (sage.rings.polynomial.polynomial_element.Polynomial method) N n_forms() (sage.rings.invariants.invariant_theory.SeveralAlgebraicForms method) n_nodes() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleSet method) n_variables() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) n_vars() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) name() (sage.rings.polynomial.term_order.TermOrder method) navigation() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleSet method) NCPolynomialIdeal (class in sage.rings.polynomial.multi_polynomial_ideal) newton_polygon() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_cdv method) newton_polytope() (sage.rings.polynomial.multi_polynomial.MPolynomial method) newton_raphson() (sage.rings.polynomial.polynomial_element.Polynomial method) newton_slopes() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_cdv method) next() (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.infinite_polynomial_ring.GenDictWithBasering method) next_spoly() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) nf() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) (sage.rings.polynomial.pbori.pbori.ReductionStrategy method) nf3() (in module sage.rings.polynomial.pbori.pbori) ngens() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.pbori.pbori.BooleanMonomialMonoid method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) nmonomials() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) Node (class in sage.rings.polynomial.hilbert) nonzero_positions() (sage.rings.polynomial.polydict.ETuple method) nonzero_values() (sage.rings.polynomial.polydict.ETuple method) norm() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) normal_basis() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) normalisation() (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) npairs() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) nparts() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) nth_root() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) ntl_set_directly() (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) ntl_ZZ_pX() (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) number_field() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) number_of_real_roots() (sage.rings.polynomial.polynomial_element.Polynomial method) number_of_roots_in_interval() (sage.rings.polynomial.polynomial_element.Polynomial method) number_of_terms() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_element method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) numer() (sage.rings.fraction_field_FpT.FpTElement method) numerator() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) nvariables() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) O ocean (class in sage.rings.polynomial.real_roots) Omega_ge() (in module sage.rings.polynomial.omega) one() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) one_basis() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ParentMethods method) ord() (sage.rings.polynomial.polynomial_element.Polynomial method) order() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) P p (sage.rings.polynomial.pbori.pbori.BooleanPolynomialEntry attribute) padded_list() (sage.rings.polynomial.polynomial_element.Polynomial method) parallel_reduce() (in module sage.rings.polynomial.pbori.pbori) parameter() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) part() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) partition() (in module sage.rings.polynomial.omega) parts() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) Phi_invariant() (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) plot() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.polynomial_element.Polynomial method) polar_conic() (sage.rings.invariants.invariant_theory.TernaryCubic method) poly_repr() (sage.rings.polynomial.polydict.PolyDict method) PolyDict (class in sage.rings.polynomial.polydict) polygen() (in module sage.rings.polynomial.polynomial_ring) polygens() (in module sage.rings.polynomial.polynomial_ring) Polynomial (class in sage.rings.polynomial.polynomial_element) polynomial() (sage.rings.invariants.invariant_theory.AlgebraicForm method) (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ElementMethods method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) Polynomial_absolute_number_field_dense (class in sage.rings.polynomial.polynomial_number_field) polynomial_coefficient() (sage.rings.polynomial.polydict.PolyDict method) polynomial_construction() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) polynomial_default_category() (in module sage.rings.polynomial.polynomial_ring_constructor) Polynomial_dense_mod_n (class in sage.rings.polynomial.polynomial_modn_dense_ntl) Polynomial_dense_mod_p (class in sage.rings.polynomial.polynomial_modn_dense_ntl) Polynomial_dense_modn_ntl_ZZ (class in sage.rings.polynomial.polynomial_modn_dense_ntl) Polynomial_dense_modn_ntl_zz (class in sage.rings.polynomial.polynomial_modn_dense_ntl) Polynomial_generic_cdv (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_cdvf (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_cdvr (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_dense (class in sage.rings.polynomial.polynomial_element) Polynomial_generic_dense_cdv (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_dense_cdvf (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_dense_cdvr (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_dense_field (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_dense_inexact (class in sage.rings.polynomial.polynomial_element) Polynomial_generic_domain (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_field (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_sparse (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_sparse_cdv (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_sparse_cdvf (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_sparse_cdvr (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_generic_sparse_field (class in sage.rings.polynomial.polynomial_element_generic) Polynomial_GF2X (class in sage.rings.polynomial.polynomial_gf2x) Polynomial_integer_dense_flint (class in sage.rings.polynomial.polynomial_integer_dense_flint) Polynomial_integer_dense_ntl (class in sage.rings.polynomial.polynomial_integer_dense_ntl) polynomial_is_variable() (in module sage.rings.polynomial.polynomial_element) Polynomial_padic (class in sage.rings.polynomial.padics.polynomial_padic) Polynomial_padic_capped_relative_dense (class in sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense) Polynomial_padic_flat (class in sage.rings.polynomial.padics.polynomial_padic_flat) Polynomial_rational_flint (class in sage.rings.polynomial.polynomial_rational_flint) Polynomial_relative_number_field_dense (class in sage.rings.polynomial.polynomial_number_field) polynomial_ring() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_dense method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) Polynomial_singular_repr (class in sage.rings.polynomial.polynomial_singular_interface) Polynomial_template (class in sage.rings.polynomial.polynomial_gf2x) (class in sage.rings.polynomial.polynomial_zmod_flint) (class in sage.rings.polynomial.polynomial_zz_pex) Polynomial_zmod_flint (class in sage.rings.polynomial.polynomial_zmod_flint) Polynomial_ZZ_pEX (class in sage.rings.polynomial.polynomial_zz_pex) PolynomialBaseringInjection (class in sage.rings.polynomial.polynomial_element) PolynomialConstruct (class in sage.rings.polynomial.pbori.pbori) PolynomialFactory (class in sage.rings.polynomial.pbori.pbori) PolynomialQuotientRing_coercion (class in sage.rings.polynomial.polynomial_quotient_ring) PolynomialQuotientRing_domain (class in sage.rings.polynomial.polynomial_quotient_ring) PolynomialQuotientRing_field (class in sage.rings.polynomial.polynomial_quotient_ring) PolynomialQuotientRing_generic (class in sage.rings.polynomial.polynomial_quotient_ring) PolynomialQuotientRingElement (class in sage.rings.polynomial.polynomial_quotient_ring_element) PolynomialQuotientRingFactory (class in sage.rings.polynomial.polynomial_quotient_ring) PolynomialRealDense (class in sage.rings.polynomial.polynomial_real_mpfr_dense) PolynomialRing() (in module sage.rings.polynomial.polynomial_ring_constructor) PolynomialRing_cdvf (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_cdvr (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_commutative (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_finite_field (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_mod_n (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_mod_p (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_padic_field_capped_relative (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_padic_field_generic (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_padic_ring_capped_absolute (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_padic_ring_capped_relative (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_padic_ring_fixed_mod (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_dense_padic_ring_generic (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_field (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_general (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_integral_domain (class in sage.rings.polynomial.polynomial_ring) PolynomialRing_singular_repr (class in sage.rings.polynomial.polynomial_singular_interface) PolynomialRingHomomorphism_from_base (class in sage.rings.polynomial.polynomial_ring_homomorphism) polynomials() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) PolynomialSequence() (in module sage.rings.polynomial.multi_polynomial_sequence) PolynomialSequence_generic (class in sage.rings.polynomial.multi_polynomial_sequence) PolynomialSequence_gf2 (class in sage.rings.polynomial.multi_polynomial_sequence) PolynomialSequence_gf2e (class in sage.rings.polynomial.multi_polynomial_sequence) Polyring_FpT_coerce (class in sage.rings.fraction_field_FpT) pow_pd (class in sage.rings.polynomial.polynomial_compiled) power_trunc() (sage.rings.polynomial.polynomial_element.Polynomial method) prec() (sage.rings.polynomial.polynomial_element.Polynomial method) prec_degree() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense_inexact method) precision_absolute() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) precision_relative() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) PrecisionError precompute_degree_reduction_cache() (in module sage.rings.polynomial.real_roots) primary_decomposition() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) primary_decomposition_complete() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) product_on_basis() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Binomial method) (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted method) pseudo_divrem() (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) pseudo_quo_rem() (sage.rings.polynomial.polynomial_element.Polynomial method) pseudoinverse() (in module sage.rings.polynomial.real_roots) Q quadratic_form() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) QuadraticForm (class in sage.rings.invariants.invariant_theory) quaternary_biquadratic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) quaternary_quadratic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) quo_rem() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_field method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) quotient() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) quotient_by_principal_ideal() (sage.rings.polynomial.polynomial_ring.PolynomialRing_commutative method) R R_invariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) radical() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.polynomial_element.Polynomial method) random_element() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) random_set() (in module sage.rings.polynomial.pbori.pbori) rational_reconstruct() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) rational_reconstruction() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) rational_root_bounds() (in module sage.rings.polynomial.real_roots) real_root_intervals() (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) real_roots() (in module sage.rings.polynomial.real_roots) (sage.rings.polynomial.polynomial_element.Polynomial method) reciprocal_transform() (sage.rings.polynomial.polynomial_element.Polynomial method) recursively_insert() (in module sage.rings.polynomial.pbori.pbori) red_tail() (in module sage.rings.polynomial.pbori.pbori) reduce() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method) (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_quotient method) (sage.rings.polynomial.multi_polynomial_ideal.NCPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialIdeal method) (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) (sage.rings.polynomial.symmetric_reduction.SymmetricReductionStrategy method) reduced() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_gf2 method) reduced_form() (sage.rings.polynomial.multi_polynomial.MPolynomial method) reduced_normal_form() (sage.rings.polynomial.pbori.pbori.ReductionStrategy method) reducible_by() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) reduction_strategy (sage.rings.polynomial.pbori.pbori.GroebnerStrategy attribute) ReductionStrategy (class in sage.rings.polynomial.pbori.pbori) refine() (sage.rings.polynomial.real_roots.island method) refine_all() (sage.rings.polynomial.real_roots.ocean method) refine_recurse() (sage.rings.polynomial.real_roots.island method) refine_root() (in module sage.rings.polynomial.refine_root) region() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial method) (sage.rings.polynomial.real_roots.rr_gap method) region_width() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial method) relative_bounds() (in module sage.rings.polynomial.real_roots) remove_var() (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) remove_zeros() (sage.rings.polynomial.polydict.PolyDict method) repr_long() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) require_field (in module sage.rings.polynomial.multi_polynomial_ideal) RequireField (class in sage.rings.polynomial.multi_polynomial_ideal) res() (sage.rings.polynomial.multi_polynomial_ideal.NCPolynomialIdeal method) rescale() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) reset() (sage.rings.polynomial.symmetric_reduction.SymmetricReductionStrategy method) reset_root_width() (sage.rings.polynomial.real_roots.island method) (sage.rings.polynomial.real_roots.ocean method) residue() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) residue_class_degree() (sage.rings.polynomial.ideal.Ideal_1poly_field method) residue_field() (sage.rings.polynomial.ideal.Ideal_1poly_field method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_dense_mod_n method) resultant() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_p method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) retract() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) reverse() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) reverse_intvec() (in module sage.rings.polynomial.real_roots) reversed() (sage.rings.polynomial.polydict.ETuple method) revert_series() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) rich_compare() (sage.rings.polynomial.polydict.PolyDict method) ring() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.invariants.invariant_theory.FormsBase method) (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleSet method) ring_of_integers() (sage.rings.fraction_field.FractionField_1poly_field method) root_bounds() (in module sage.rings.polynomial.real_roots) root_field() (sage.rings.polynomial.padics.polynomial_padic.Polynomial_padic method) (sage.rings.polynomial.polynomial_element.Polynomial method) roots() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.real_roots.ocean method) rr_gap (class in sage.rings.polynomial.real_roots) rshift_coeffs() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) S S (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing attribute) S_class_group() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) S_invariant() (sage.rings.invariants.invariant_theory.TernaryCubic method) S_units() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) sage.rings.fraction_field module sage.rings.fraction_field_element module sage.rings.fraction_field_FpT module sage.rings.invariants.invariant_theory module sage.rings.invariants.reconstruction module sage.rings.monomials module sage.rings.polynomial.complex_roots module sage.rings.polynomial.convolution module sage.rings.polynomial.cyclotomic module sage.rings.polynomial.flatten module sage.rings.polynomial.hilbert module sage.rings.polynomial.ideal module sage.rings.polynomial.infinite_polynomial_element module sage.rings.polynomial.infinite_polynomial_ring module sage.rings.polynomial.integer_valued_polynomials module sage.rings.polynomial.laurent_polynomial module sage.rings.polynomial.laurent_polynomial_ring module sage.rings.polynomial.laurent_polynomial_ring_base module sage.rings.polynomial.msolve module sage.rings.polynomial.multi_polynomial module sage.rings.polynomial.multi_polynomial_element module sage.rings.polynomial.multi_polynomial_ideal module sage.rings.polynomial.multi_polynomial_ideal_libsingular module sage.rings.polynomial.multi_polynomial_libsingular module sage.rings.polynomial.multi_polynomial_ring module sage.rings.polynomial.multi_polynomial_ring_base module sage.rings.polynomial.multi_polynomial_sequence module sage.rings.polynomial.omega module sage.rings.polynomial.padics.polynomial_padic module sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense module sage.rings.polynomial.padics.polynomial_padic_flat module sage.rings.polynomial.pbori.pbori module sage.rings.polynomial.polydict module sage.rings.polynomial.polynomial_compiled module sage.rings.polynomial.polynomial_element module sage.rings.polynomial.polynomial_element_generic module sage.rings.polynomial.polynomial_fateman module sage.rings.polynomial.polynomial_gf2x module sage.rings.polynomial.polynomial_integer_dense_flint module sage.rings.polynomial.polynomial_integer_dense_ntl module sage.rings.polynomial.polynomial_modn_dense_ntl module sage.rings.polynomial.polynomial_number_field module sage.rings.polynomial.polynomial_quotient_ring module sage.rings.polynomial.polynomial_quotient_ring_element module sage.rings.polynomial.polynomial_rational_flint module sage.rings.polynomial.polynomial_real_mpfr_dense module sage.rings.polynomial.polynomial_ring module sage.rings.polynomial.polynomial_ring_constructor module sage.rings.polynomial.polynomial_ring_homomorphism module sage.rings.polynomial.polynomial_singular_interface module sage.rings.polynomial.polynomial_zmod_flint module sage.rings.polynomial.polynomial_zz_pex module sage.rings.polynomial.real_roots module sage.rings.polynomial.refine_root module sage.rings.polynomial.symmetric_ideal module sage.rings.polynomial.symmetric_reduction module sage.rings.polynomial.term_order module sage.rings.polynomial.toy_buchberger module sage.rings.polynomial.toy_d_basis module sage.rings.polynomial.toy_variety module saturation() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) scalar_lmult() (sage.rings.polynomial.polydict.PolyDict method) scalar_rmult() (sage.rings.polynomial.polydict.PolyDict method) scale_intvec_var() (in module sage.rings.polynomial.real_roots) scaled_coeffs() (sage.rings.invariants.invariant_theory.BinaryQuartic method) (sage.rings.invariants.invariant_theory.BinaryQuintic method) (sage.rings.invariants.invariant_theory.QuadraticForm method) (sage.rings.invariants.invariant_theory.TernaryCubic method) (sage.rings.invariants.invariant_theory.TernaryQuadratic method) second() (sage.rings.invariants.invariant_theory.TwoAlgebraicForms method) section() (sage.rings.fraction_field.FractionFieldEmbedding method) (sage.rings.fraction_field_FpT.Fp_FpT_coerce method) (sage.rings.fraction_field_FpT.Polyring_FpT_coerce method) (sage.rings.fraction_field_FpT.ZZ_FpT_coerce method) (sage.rings.polynomial.flatten.FlatteningMorphism method) (sage.rings.polynomial.polynomial_element.PolynomialBaseringInjection method) select() (in module sage.rings.polynomial.toy_buchberger) (in module sage.rings.polynomial.toy_d_basis) (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) selmer_generators() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) selmer_group() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) set() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleSet method) set_karatsuba_threshold() (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) set_random_seed() (in module sage.rings.polynomial.pbori.pbori) setgens() (sage.rings.polynomial.symmetric_reduction.SymmetricReductionStrategy method) SeveralAlgebraicForms (class in sage.rings.invariants.invariant_theory) shift() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ElementMethods method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX method) shrink_bp() (sage.rings.polynomial.real_roots.island method) singular_moreblocks() (sage.rings.polynomial.term_order.TermOrder method) singular_str() (sage.rings.polynomial.term_order.TermOrder method) size_double() (sage.rings.polynomial.pbori.pbori.BooleSet method) slimgb_libsingular() (in module sage.rings.polynomial.multi_polynomial_ideal_libsingular) slope_factorization() (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_cdv method) slope_range() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_float method) (sage.rings.polynomial.real_roots.interval_bernstein_polynomial_integer method) small_roots() (in module sage.rings.polynomial.polynomial_modn_dense_ntl) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_n method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) small_spolys_in_next_degree() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) solve() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_gf2 method) some_elements() (sage.rings.fraction_field.FractionField_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) some_spolys_in_next_degree() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) sortkey (sage.rings.polynomial.term_order.TermOrder property) sortkey_block() (sage.rings.polynomial.term_order.TermOrder method) sortkey_deglex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_degneglex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_degrevlex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_invlex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_lex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_matrix() (sage.rings.polynomial.term_order.TermOrder method) sortkey_negdeglex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_negdegrevlex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_neglex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_negwdeglex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_negwdegrevlex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_wdeglex() (sage.rings.polynomial.term_order.TermOrder method) sortkey_wdegrevlex() (sage.rings.polynomial.term_order.TermOrder method) sparse_iter() (sage.rings.polynomial.polydict.ETuple method) specialization() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) SpecializationMorphism (class in sage.rings.polynomial.flatten) split_for_targets() (in module sage.rings.polynomial.real_roots) splitting_field() (sage.rings.polynomial.polynomial_element.Polynomial method) spol() (in module sage.rings.polynomial.toy_buchberger) (in module sage.rings.polynomial.toy_d_basis) spoly() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) sqr_pd (class in sage.rings.polynomial.polynomial_compiled) sqrt() (sage.rings.fraction_field_FpT.FpTElement method) square() (sage.rings.polynomial.polynomial_element.Polynomial method) squarefree_decomposition() (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint method) squeezed() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) stable_hash() (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleSet method) std() (sage.rings.polynomial.multi_polynomial_ideal.NCPolynomialIdeal method) std_libsingular() (in module sage.rings.polynomial.multi_polynomial_ideal_libsingular) stretch() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) sub_m_mul_q() (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) subresultants() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.polynomial_element.Polynomial method) subs() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) subsample_vec_doctest() (in module sage.rings.polynomial.real_roots) subset0() (sage.rings.polynomial.pbori.pbori.BooleSet method) subset1() (sage.rings.polynomial.pbori.pbori.BooleSet method) substitute_variables() (in module sage.rings.polynomial.pbori.pbori) suggest_plugin_variable() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) sum() (sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict method) sum_of_coefficients() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases.ElementMethods method) super_categories() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Bases method) support() (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method) sylvester_matrix() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) symmetric_basis() (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) symmetric_cancellation_order() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) symmetric_power() (sage.rings.polynomial.polynomial_element.Polynomial method) SymmetricIdeal (class in sage.rings.polynomial.symmetric_ideal) SymmetricReductionStrategy (class in sage.rings.polynomial.symmetric_reduction) symmetrisation() (sage.rings.polynomial.symmetric_ideal.SymmetricIdeal method) symmGB_F2() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) syzygy() (sage.rings.invariants.invariant_theory.TernaryCubic method) (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) syzygy_module() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_base_repr method) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.multi_polynomial_ideal.NCPolynomialIdeal method) T T_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) T_invariant() (sage.rings.invariants.invariant_theory.TernaryCubic method) T_prime_covariant() (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) tail() (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) tailreduce() (sage.rings.polynomial.symmetric_reduction.SymmetricReductionStrategy method) tau_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) taylor_shift1_intvec() (in module sage.rings.polynomial.real_roots) tensor_with_ring() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_dense method) (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) term_lmult() (sage.rings.polynomial.polydict.PolyDict method) term_order() (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) term_rmult() (sage.rings.polynomial.polydict.PolyDict method) terminal_one() (sage.rings.polynomial.pbori.pbori.CCuddNavigator method) TermOrder (class in sage.rings.polynomial.term_order) TermOrder_from_pb_order() (in module sage.rings.polynomial.pbori.pbori) termorder_from_singular() (in module sage.rings.polynomial.term_order) terms() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) ternary_biquadratic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) ternary_cubic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) ternary_quadratic() (sage.rings.invariants.invariant_theory.InvariantTheoryFactory method) TernaryCubic (class in sage.rings.invariants.invariant_theory) TernaryQuadratic (class in sage.rings.invariants.invariant_theory) then_branch() (sage.rings.polynomial.pbori.pbori.CCuddNavigator method) theta_covariant() (sage.rings.invariants.invariant_theory.BinaryQuintic method) Theta_covariant() (sage.rings.invariants.invariant_theory.TernaryCubic method) Theta_invariant() (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) Theta_prime_invariant() (sage.rings.invariants.invariant_theory.TwoQuaternaryQuadratics method) (sage.rings.invariants.invariant_theory.TwoTernaryQuadratics method) to_bernstein() (in module sage.rings.polynomial.real_roots) to_bernstein_warp() (in module sage.rings.polynomial.real_roots) to_ocean() (sage.rings.polynomial.real_roots.linear_map method) (sage.rings.polynomial.real_roots.warp_map method) top_index() (in module sage.rings.polynomial.pbori.pbori) top_sugar() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) total_degree() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.polydict.PolyDict method) trace() (sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement method) trace_polynomial() (sage.rings.polynomial.polynomial_element.Polynomial method) transformed() (sage.rings.invariants.invariant_theory.AlgebraicForm method) transformed_basis() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) transvectant() (in module sage.rings.invariants.invariant_theory) triangular_decomposition() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) triangular_factorization() (in module sage.rings.polynomial.toy_variety) truncate() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element.Polynomial_generic_dense method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) truncate_abs() (sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense method) try_rand_split() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial method) try_split() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial method) tuple_weight() (sage.rings.polynomial.term_order.TermOrder method) TwoAlgebraicForms (class in sage.rings.invariants.invariant_theory) TwoQuaternaryQuadratics (class in sage.rings.invariants.invariant_theory) twostd() (sage.rings.polynomial.multi_polynomial_ideal.NCPolynomialIdeal method) TwoTernaryQuadratics (class in sage.rings.invariants.invariant_theory) U umbra() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) unary_pd (class in sage.rings.polynomial.polynomial_compiled) UnflatteningMorphism (class in sage.rings.polynomial.flatten) union() (sage.rings.polynomial.pbori.pbori.BooleSet method) units() (sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic method) univar_pd (class in sage.rings.polynomial.polynomial_compiled) univariate_polynomial() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) univariate_ring() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) universal_discriminant() (in module sage.rings.polynomial.polynomial_element) universe() (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) unpickle_BooleanPolynomial() (in module sage.rings.polynomial.pbori.pbori) unpickle_BooleanPolynomial0() (in module sage.rings.polynomial.pbori.pbori) unpickle_BooleanPolynomialRing() (in module sage.rings.polynomial.pbori.pbori) unpickle_FpT_element() (in module sage.rings.fraction_field_FpT) unpickle_MPolynomial_libsingular() (in module sage.rings.polynomial.multi_polynomial_libsingular) unpickle_MPolynomialRing_generic() (in module sage.rings.polynomial.multi_polynomial_ring_base) unpickle_MPolynomialRing_generic_v1() (in module sage.rings.polynomial.multi_polynomial_ring_base) unpickle_MPolynomialRing_libsingular() (in module sage.rings.polynomial.multi_polynomial_libsingular) unpickle_PolynomialRing() (in module sage.rings.polynomial.polynomial_ring_constructor) unweighted_degree() (sage.rings.polynomial.polydict.ETuple method) unweighted_quotient_degree() (sage.rings.polynomial.polydict.ETuple method) update() (in module sage.rings.polynomial.toy_buchberger) (in module sage.rings.polynomial.toy_d_basis) usign() (sage.rings.polynomial.real_roots.bernstein_polynomial_factory method) V valuation() (sage.rings.fraction_field_element.FractionFieldElement method) (sage.rings.fraction_field_FpT.FpTElement method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_sparse method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_ZZ method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_modn_ntl_zz method) valuation_of_coefficient() (sage.rings.polynomial.padics.polynomial_padic_capped_relative_dense.Polynomial_padic_capped_relative_dense method) value() (sage.rings.polynomial.pbori.pbori.CCuddNavigator method) var_pd (class in sage.rings.polynomial.polynomial_compiled) variable() (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) variable_has_value() (sage.rings.polynomial.pbori.pbori.GroebnerStrategy method) variable_name() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.polynomial_element.Polynomial method) variable_names_recursive() (sage.rings.polynomial.laurent_polynomial_ring_base.LaurentPolynomialRing_generic method) (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_general method) variable_shift() (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Binomial.Element method) (sage.rings.polynomial.integer_valued_polynomials.IntegerValuedPolynomialRing.Shifted.Element method) VariableBlock (class in sage.rings.polynomial.pbori.pbori) VariableConstruct (class in sage.rings.polynomial.pbori.pbori) VariableFactory (class in sage.rings.polynomial.pbori.pbori) variables() (sage.rings.invariants.invariant_theory.FormsBase method) (sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial method) (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict method) (sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic method) (sage.rings.polynomial.pbori.pbori.BooleanMonomial method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) (sage.rings.polynomial.pbori.pbori.BooleConstant method) (sage.rings.polynomial.polynomial_element.Polynomial method) variations() (sage.rings.polynomial.real_roots.interval_bernstein_polynomial method) variety() (in module sage.rings.polynomial.msolve) (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) (sage.rings.polynomial.pbori.pbori.BooleanPolynomialIdeal method) varname_key() (sage.rings.polynomial.infinite_polynomial_ring.InfinitePolynomialRing_sparse method) vars() (sage.rings.polynomial.pbori.pbori.BooleSet method) vars_as_monomial() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) vector_space_dimension() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr method) W warp_map (class in sage.rings.polynomial.real_roots) weighted_degree() (sage.rings.polynomial.multi_polynomial.MPolynomial method) (sage.rings.polynomial.polydict.ETuple method) weighted_quotient_degree() (sage.rings.polynomial.polydict.ETuple method) weights() (sage.rings.polynomial.term_order.TermOrder method) weil_polynomials() (sage.rings.polynomial.polynomial_ring.PolynomialRing_integral_domain method) weil_restriction() (sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal method) (sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_gf2e method) weyl_algebra() (sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base method) (sage.rings.polynomial.polynomial_ring.PolynomialRing_commutative method) wordsize_rational() (in module sage.rings.polynomial.real_roots) X xgcd() (sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_univariate method) (sage.rings.polynomial.polynomial_element.Polynomial method) (sage.rings.polynomial.polynomial_gf2x.Polynomial_template method) (sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint method) (sage.rings.polynomial.polynomial_integer_dense_ntl.Polynomial_integer_dense_ntl method) (sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_p method) (sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint method) (sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template method) (sage.rings.polynomial.polynomial_zz_pex.Polynomial_template method) Z zero() (sage.rings.polynomial.pbori.pbori.BooleanPolynomialRing method) zeros() (in module sage.rings.polynomial.pbori.pbori) zeros_in() (sage.rings.polynomial.pbori.pbori.BooleanPolynomial method) ZZ_FpT_coerce (class in sage.rings.fraction_field_FpT)