Index

A

a (mathematicskit.special_functions.FilterCoefficients attribute) abelianization() (in module mathematicskit.topology) absorption_probabilities() (mathematicskit.probability.MarkovChain method) acceptance_rate (mathematicskit.probability.MCMCResult attribute) Adam (class in mathematicskit.optimization) adams_bashforth_boundary_locus() (in module mathematicskit.integrators) adams_bashforth_integrate() (in module mathematicskit.integrators) AdaptiveQuadrature (class in mathematicskit.calculus) add() (mathematicskit.abstract_algebra.GF method) (mathematicskit.number_theory.EllipticCurve method) add_edge() (mathematicskit.graph_theory.Graph method) adjusted_p_values (mathematicskit.statistics.MultipleTestingResult attribute) adjusted_r_squared (mathematicskit.numerical_analysis.RegressionResult attribute) (mathematicskit.statistics.RegressionResult attribute) AdvectionEquation1D (class in mathematicskit.pde) ai (mathematicskit.special_functions.AiryResult attribute) ai_prime (mathematicskit.special_functions.AiryResult attribute) aic() (mathematicskit.statistics.MaximumLikelihoodResult method) airy_functions() (in module mathematicskit.special_functions) AiryResult (class in mathematicskit.special_functions) aitken_delta_squared() (in module mathematicskit.numerical_analysis) algebraic_connectivity (mathematicskit.graph_theory.SpectralResult attribute) all_subgroups() (in module mathematicskit.abstract_algebra) alpha (mathematicskit.statistics.MultipleTestingResult attribute)

amplification_factor() (in module mathematicskit.pde) amplitude (mathematicskit.special_functions.JacobiEllipticResult attribute) analyze_homomorphism() (in module mathematicskit.abstract_algebra) apply_filter() (in module mathematicskit.special_functions) approximation (mathematicskit.special_functions.WaveletDecompositionResult attribute) ar_autocorrelation() (in module mathematicskit.statistics) arc_length (mathematicskit.geometry.CurveFrameResult attribute) archimedes_pi_bounds() (in module mathematicskit.calculus) are_orthogonal() (in module mathematicskit.combinatorics) area (mathematicskit.geometry.ConvexHullResult attribute) (mathematicskit.geometry.LatticePolygonResult attribute) area_element (mathematicskit.geometry.SurfaceCurvatureResult attribute) argument_principle() (in module mathematicskit.complex_analysis) arithmetic_decode() (in module mathematicskit.information_theory) arithmetic_encode() (in module mathematicskit.information_theory) arithmetic_geometric_mean() (in module mathematicskit.special_functions) arithmetic_intervals() (in module mathematicskit.information_theory) ARModelResult (class in mathematicskit.statistics) AssignmentResult (class in mathematicskit.graph_theory) astar_shortest_path() (in module mathematicskit.graph_theory) autocorrelation (mathematicskit.statistics.ARModelResult attribute) autocorrelation() (in module mathematicskit.statistics) average_length (mathematicskit.information_theory.PrefixCode property) awgn_capacity() (in module mathematicskit.information_theory)

B

b (mathematicskit.special_functions.FilterCoefficients attribute) backtracking_coloring() (in module mathematicskit.graph_theory) backward() (mathematicskit.calculus.Variable method) backward_difference() (in module mathematicskit.calculus) BarnsleyFern (class in mathematicskit.fractals_chaos) barycentric_subdivision() (in module mathematicskit.topology) basis (mathematicskit.abstract_algebra.GroebnerResult attribute) (mathematicskit.number_theory.LLLResult attribute) bec_capacity() (in module mathematicskit.information_theory) bell_number() (in module mathematicskit.combinatorics) bellman_ford_shortest_paths() (in module mathematicskit.graph_theory) bendixson_criterion() (in module mathematicskit.ode_dynamics) BendixsonResult (class in mathematicskit.ode_dynamics) benjamini_hochberg() (in module mathematicskit.statistics) bernoulli_numbers() (in module mathematicskit.combinatorics) bernstein_polynomial() (in module mathematicskit.numerical_analysis) bessel_first_kind() (in module mathematicskit.special_functions) bessel_second_kind() (in module mathematicskit.special_functions) best_rational_approximation() (in module mathematicskit.number_theory) Beta (class in mathematicskit.probability) beta_binomial_posterior() (in module mathematicskit.probability) beta_function() (in module mathematicskit.special_functions) betti_a (mathematicskit.topology.MayerVietorisResult attribute) betti_b (mathematicskit.topology.MayerVietorisResult attribute) betti_intersection (mathematicskit.topology.MayerVietorisResult attribute) betti_numbers (mathematicskit.topology.HomologyResult attribute) betti_numbers() (in module mathematicskit.topology) (mathematicskit.topology.PersistenceDiagram method) betti_union (mathematicskit.topology.MayerVietorisResult attribute) bezier_curve() (in module mathematicskit.geometry) BezoutResult (class in mathematicskit.number_theory) BFGS (class in mathematicskit.optimization) bi (mathematicskit.special_functions.AiryResult attribute) bi_prime (mathematicskit.special_functions.AiryResult attribute) bias (mathematicskit.statistics.JackknifeResult attribute) bias_corrected (mathematicskit.statistics.JackknifeResult attribute) bifurcation_diagram() (in module mathematicskit.ode_dynamics) binary_entropy() (in module mathematicskit.information_theory) Binomial (class in mathematicskit.probability)

binormal (mathematicskit.geometry.CurveFrameResult attribute) bipartite_matching() (in module mathematicskit.graph_theory) BipartiteMatchingResult (class in mathematicskit.graph_theory) bipartition (mathematicskit.graph_theory.SpectralResult attribute) Bisection (class in mathematicskit.numerical_analysis) bit_flip_decode() (in module mathematicskit.information_theory) BitFlipResult (class in mathematicskit.information_theory) blahut_arimoto() (in module mathematicskit.information_theory) bonferroni_correction() (in module mathematicskit.statistics) bootstrap_confidence_interval() (in module mathematicskit.statistics) BootstrapResult (class in mathematicskit.statistics) bottleneck_distance() (in module mathematicskit.topology) bound (mathematicskit.probability.TailBoundResult attribute) boundary (mathematicskit.geometry.LatticePolygonResult attribute) boundary_components (mathematicskit.topology.SurfaceClassification attribute) boundary_components() (in module mathematicskit.topology) boundary_matrix() (mathematicskit.topology.SimplicialComplex method) box_counting_dimension() (in module mathematicskit.fractals_chaos) box_counts (mathematicskit.fractals_chaos.BoxCountingResult attribute) box_sizes (mathematicskit.fractals_chaos.BoxCountingResult attribute) BoxCountingResult (class in mathematicskit.fractals_chaos) brackets (mathematicskit.optimization.ScalarSearchResult attribute) BranchingProcessResult (class in mathematicskit.probability) breakpoints (mathematicskit.complex_analysis.Contour attribute) brouwer_fixed_point() (in module mathematicskit.topology) brownian_motion() (in module mathematicskit.probability) BrownianMotionResult (class in mathematicskit.probability) Broyden (class in mathematicskit.numerical_analysis) Brusselator (class in mathematicskit.ode_dynamics) brusselator_hopf_threshold() (in module mathematicskit.ode_dynamics) bsc_capacity() (in module mathematicskit.information_theory) bsc_transmit() (in module mathematicskit.information_theory) buffon_needle() (in module mathematicskit.probability) BuffonNeedleResult (class in mathematicskit.probability) burgers_cole_hopf_solution() (in module mathematicskit.pde) burgers_riemann_solution() (in module mathematicskit.pde) BurgersConservationLaw1D (class in mathematicskit.pde) BurgersEquation1D (class in mathematicskit.pde) butterworth_filter() (in module mathematicskit.special_functions) BVPResult (class in mathematicskit.integrators)

C

c (mathematicskit.number_theory.PollardRhoResult attribute) (mathematicskit.special_functions.FresnelResult attribute) cancellation_bits_lost() (in module mathematicskit.numerical_analysis) canonical_code() (in module mathematicskit.information_theory) capacity (mathematicskit.information_theory.ChannelCapacityResult attribute) cartesian (mathematicskit.topology.TriangleGrid property) catalan_number() (in module mathematicskit.combinatorics) category (mathematicskit.numerical_analysis.FloatBits attribute) cauchy_integral_formula() (in module mathematicskit.complex_analysis) cauchy_riemann() (in module mathematicskit.complex_analysis) CauchyRiemannResult (class in mathematicskit.complex_analysis) cayley_table() (mathematicskit.abstract_algebra.FiniteGroup method) cdf() (mathematicskit.probability.ContinuousDistribution method) (mathematicskit.probability.DiscreteDistribution method) cech_complex() (in module mathematicskit.topology) CellularAutomaton (class in mathematicskit.fractals_chaos) center (mathematicskit.complex_analysis.LaurentSeriesResult attribute) (mathematicskit.geometry.CircleResult attribute) centers (mathematicskit.linalg.GershgorinResult attribute) central_difference() (in module mathematicskit.calculus) central_limit_theorem_sample_means() (in module mathematicskit.probability) chain_effective_sample_size() (in module mathematicskit.probability) ChannelCapacityResult (class in mathematicskit.information_theory) chaos_game() (in module mathematicskit.fractals_chaos) character_table() (in module mathematicskit.abstract_algebra) characteristic_polynomial() (in module mathematicskit.linalg) CharacterTableResult (class in mathematicskit.abstract_algebra) chebyshev1_filter() (in module mathematicskit.special_functions) chebyshev_differentiation_matrix() (in module mathematicskit.pde) chebyshev_nodes() (in module mathematicskit.numerical_analysis) chebyshev_poisson_1d() (in module mathematicskit.pde) chebyshev_poisson_2d() (in module mathematicskit.pde) chebyshev_polynomial() (in module mathematicskit.special_functions) chebyshev_tail() (in module mathematicskit.probability) ChebyshevInterpolant (class in mathematicskit.numerical_analysis) check_cfl() (in module mathematicskit.pde) check_diffusion_stability() (in module mathematicskit.pde) chi_square_goodness_of_fit() (in module mathematicskit.statistics) chi_square_independence() (in module mathematicskit.statistics) chinese_remainder_theorem() (in module mathematicskit.number_theory) cholesky_decompose() (in module mathematicskit.linalg) cholesky_solve() (in module mathematicskit.linalg) CholeskyResult (class in mathematicskit.linalg) circle() (in module mathematicskit.geometry) (in module mathematicskit.topology) circle_contour() (in module mathematicskit.complex_analysis) CircleResult (class in mathematicskit.geometry) circular_convolve() (in module mathematicskit.special_functions) class_sizes (mathematicskit.abstract_algebra.CharacterTableResult property) classes (mathematicskit.abstract_algebra.CharacterTableResult attribute) classification (mathematicskit.ode_dynamics.FixedPointResult attribute) classify_fixed_point_2d() (in module mathematicskit.ode_dynamics) classify_mobius() (in module mathematicskit.complex_analysis) classify_surface() (in module mathematicskit.topology) clenshaw_curtis_nodes_and_weights() (in module mathematicskit.calculus) ClenshawCurtisQuadrature (class in mathematicskit.calculus) clique_number() (in module mathematicskit.graph_theory) clique_simplices() (in module mathematicskit.topology) closest_pair() (in module mathematicskit.geometry) ClosestPairResult (class in mathematicskit.geometry) cn (mathematicskit.special_functions.JacobiEllipticResult attribute) codeword (mathematicskit.information_theory.BitFlipResult attribute) codewords (mathematicskit.information_theory.PrefixCode attribute) coefficient (mathematicskit.statistics.CorrelationResult attribute) coefficient() (mathematicskit.complex_analysis.LaurentSeriesResult method) coefficients (mathematicskit.complex_analysis.LaurentSeriesResult attribute) (mathematicskit.linalg.LeastSquaresResult attribute) (mathematicskit.numerical_analysis.MinimaxResult attribute) (mathematicskit.numerical_analysis.NewtonDividedDifference attribute) (mathematicskit.numerical_analysis.RegressionResult attribute) (mathematicskit.special_functions.ScalogramResult attribute) (mathematicskit.statistics.ARModelResult attribute) (mathematicskit.statistics.RegressionResult attribute) cofactor (mathematicskit.number_theory.ECMResult attribute) (mathematicskit.number_theory.PollardRhoResult attribute) cohens_d() (in module mathematicskit.statistics) col_strategy (mathematicskit.optimization.GameResult attribute) collocation_bvp() (in module mathematicskit.integrators) coloring (mathematicskit.graph_theory.ColoringResult attribute) ColoringResult (class in mathematicskit.graph_theory) cols (mathematicskit.graph_theory.AssignmentResult attribute) combinations_count() (in module mathematicskit.combinatorics) commutator_subgroup() (in module mathematicskit.abstract_algebra) compare_convolution_methods() (in module mathematicskit.special_functions)

compare_fft_methods() (in module mathematicskit.special_functions) compare_optimizers() (in module mathematicskit.optimization) complementary_error_function() (in module mathematicskit.special_functions) complementary_slackness (mathematicskit.optimization.KKTResult attribute) complete_bipartite_graph() (in module mathematicskit.graph_theory) complete_elliptic_integral_first_kind() (in module mathematicskit.special_functions) complete_elliptic_integral_second_kind() (in module mathematicskit.special_functions) complete_graph() (in module mathematicskit.graph_theory) complex_at() (mathematicskit.topology.Filtration method) complex_derivative() (in module mathematicskit.complex_analysis) complex_grid() (in module mathematicskit.complex_analysis) complex_step_derivative() (in module mathematicskit.calculus) components (mathematicskit.statistics.PCAResult attribute) ComponentsResult (class in mathematicskit.graph_theory) composition_series() (in module mathematicskit.abstract_algebra) CompositionSeriesResult (class in mathematicskit.abstract_algebra) condition_number (mathematicskit.linalg.LeastSquaresResult attribute) (mathematicskit.numerical_analysis.RegressionResult attribute) condition_number() (in module mathematicskit.numerical_analysis) condition_number_2norm() (in module mathematicskit.linalg) conditional_entropy() (in module mathematicskit.information_theory) confidence_level (mathematicskit.statistics.BootstrapResult attribute) (mathematicskit.statistics.ConfidenceIntervalResult attribute) ConfidenceIntervalResult (class in mathematicskit.statistics) confluent_hypergeometric_1f1() (in module mathematicskit.special_functions) conjugacy_classes() (in module mathematicskit.abstract_algebra) conjugate() (mathematicskit.combinatorics.YoungDiagram method) ConjugateGradient (class in mathematicskit.linalg) connected_components() (in module mathematicskit.graph_theory) contains() (mathematicskit.linalg.GershgorinResult method) continued_fraction_expansion() (in module mathematicskit.number_theory) ContinuedFractionResult (class in mathematicskit.number_theory) ContinuousDistribution (class in mathematicskit.probability) Contour (class in mathematicskit.complex_analysis) contour_integral() (in module mathematicskit.complex_analysis) control_variates_integrate() (in module mathematicskit.probability) converged (mathematicskit.information_theory.BitFlipResult attribute) (mathematicskit.information_theory.ChannelCapacityResult attribute) (mathematicskit.linalg.EigenResult attribute) (mathematicskit.linalg.IterativeSolveResult attribute) (mathematicskit.numerical_analysis.MinimaxResult attribute) (mathematicskit.numerical_analysis.RootResult attribute) (mathematicskit.numerical_analysis.SystemRootResult attribute) (mathematicskit.optimization.LagrangeResult attribute) (mathematicskit.optimization.OptimizeResult attribute) (mathematicskit.optimization.ScalarSearchResult attribute) convergents (mathematicskit.number_theory.ContinuedFractionResult attribute) convex_hull() (in module mathematicskit.geometry) ConvexHullResult (class in mathematicskit.geometry) convolutional_encode() (in module mathematicskit.information_theory) ConvolutionComparisonResult (class in mathematicskit.special_functions) convolve_direct() (in module mathematicskit.special_functions) convolve_fft() (in module mathematicskit.special_functions) coordinates (mathematicskit.topology.SimplicialComplex property) CorrelationResult (class in mathematicskit.statistics) cos() (mathematicskit.calculus.Dual method) (mathematicskit.calculus.Variable method) coset_of() (mathematicskit.abstract_algebra.QuotientGroup method) cost (mathematicskit.optimization.LeastSquaresResult attribute) count (mathematicskit.abstract_algebra.SylowResult property) count_bracelets() (in module mathematicskit.combinatorics) count_labeled_trees() (in module mathematicskit.combinatorics) count_necklaces() (in module mathematicskit.combinatorics) count_orbits() (in module mathematicskit.abstract_algebra) count_spanning_trees() (in module mathematicskit.graph_theory) count_triangle_free_colorings() (in module mathematicskit.combinatorics) courant_number() (in module mathematicskit.pde) cramer_solve() (in module mathematicskit.linalg) critical_points() (in module mathematicskit.topology) CriticalPointsResult (class in mathematicskit.topology) cross_correlate() (in module mathematicskit.special_functions) crossing_fraction (mathematicskit.probability.BuffonNeedleResult attribute) CRTResult (class in mathematicskit.number_theory) ctmc_stationary_distribution() (in module mathematicskit.probability) ctmc_transition_matrix() (in module mathematicskit.probability) CubicSpline (class in mathematicskit.numerical_analysis) curvature (mathematicskit.geometry.CurveFrameResult attribute) curve (mathematicskit.number_theory.ECMResult attribute) CurveFrameResult (class in mathematicskit.geometry) curves (mathematicskit.number_theory.ECMResult attribute) cycle_graph() (in module mathematicskit.graph_theory) cyclic_latin_square() (in module mathematicskit.combinatorics) cyclic_subgroup() (in module mathematicskit.abstract_algebra) CyclicGroup (class in mathematicskit.abstract_algebra) cylinder_surface() (in module mathematicskit.geometry)

D

d (mathematicskit.number_theory.PellResult attribute) D (mathematicskit.topology.SmithNormalFormResult attribute) dalembert_solution() (in module mathematicskit.pde) daubechies_filter() (in module mathematicskit.special_functions) de_casteljau() (in module mathematicskit.geometry) decode() (mathematicskit.information_theory.PrefixCode method) degree (mathematicskit.abstract_algebra.Polynomial property) degrees (mathematicskit.abstract_algebra.CharacterTableResult property) delaunay_triangulation() (in module mathematicskit.geometry) derangement_count() (in module mathematicskit.combinatorics) derivative (mathematicskit.numerical_analysis.HornerResult attribute) derivative() (in module mathematicskit.calculus) (mathematicskit.numerical_analysis.HermiteInterpolant method) DerivativeResult (class in mathematicskit.calculus) derived_series() (in module mathematicskit.abstract_algebra) descriptive_stats() (in module mathematicskit.statistics) DescriptiveStatsResult (class in mathematicskit.statistics) details (mathematicskit.special_functions.WaveletDecompositionResult attribute) df (mathematicskit.statistics.HypothesisTestResult attribute) dft_naive() (in module mathematicskit.special_functions) dgamma (mathematicskit.complex_analysis.Contour attribute) diagram() (mathematicskit.topology.PersistenceDiagram method) diffusion_number() (in module mathematicskit.pde) DihedralGroup (class in mathematicskit.abstract_algebra) dijkstra_shortest_paths() (in module mathematicskit.graph_theory) dimension (mathematicskit.fractals_chaos.BoxCountingResult attribute) (mathematicskit.topology.SimplicialComplex property)

direct_result (mathematicskit.special_functions.ConvolutionComparisonResult attribute) direct_time (mathematicskit.special_functions.ConvolutionComparisonResult attribute) discrete_wavelet_transform() (in module mathematicskit.special_functions) DiscreteDistribution (class in mathematicskit.probability) distance (mathematicskit.geometry.ClosestPairResult attribute) (mathematicskit.graph_theory.SearchResult attribute) distance_matrix() (in module mathematicskit.optimization) distances (mathematicskit.graph_theory.ShortestPathResult attribute) distribution (mathematicskit.statistics.MaximumLikelihoodResult attribute) divergence (mathematicskit.ode_dynamics.BendixsonResult attribute) divided_difference_table (mathematicskit.numerical_analysis.NewtonDividedDifference property) divider_length() (in module mathematicskit.fractals_chaos) divisor_sum() (in module mathematicskit.number_theory) dla_cluster() (in module mathematicskit.fractals_chaos) dn (mathematicskit.special_functions.JacobiEllipticResult attribute) dodecahedron_graph() (in module mathematicskit.graph_theory) domain_coloring() (in module mathematicskit.complex_analysis) DomainColoringResult (class in mathematicskit.complex_analysis) domino_tilings() (in module mathematicskit.combinatorics) dopri5_integrate() (in module mathematicskit.integrators) dopri5_step() (in module mathematicskit.integrators) douglas_peucker() (in module mathematicskit.geometry) Dual (class in mathematicskit.calculus) dual (mathematicskit.calculus.Dual attribute) dual_feasible (mathematicskit.optimization.KKTResult attribute) DuffingOscillator (class in mathematicskit.ode_dynamics)

E

ECMResult (class in mathematicskit.number_theory) edges (mathematicskit.geometry.PolyhedronResult attribute) (mathematicskit.graph_theory.MSTResult attribute) (mathematicskit.topology.MapperResult attribute) edges() (mathematicskit.graph_theory.Graph method) effective_sample_size() (in module mathematicskit.probability) efficiency (mathematicskit.information_theory.PrefixCode property) eigen_general() (in module mathematicskit.linalg) eigen_symmetric() (in module mathematicskit.linalg) EigenResult (class in mathematicskit.linalg) eigenvalues (mathematicskit.graph_theory.SpectralResult attribute) (mathematicskit.linalg.EigenResult attribute) (mathematicskit.linalg.SchurResult property) (mathematicskit.ode_dynamics.FixedPointResult attribute) eigenvectors (mathematicskit.graph_theory.SpectralResult attribute) (mathematicskit.linalg.EigenResult attribute) element_order() (mathematicskit.abstract_algebra.FiniteGroup method) element_orders (mathematicskit.abstract_algebra.GroupPropertiesResult attribute) ElementaryCA (class in mathematicskit.fractals_chaos) elements (mathematicskit.abstract_algebra.CyclicGroup property) (mathematicskit.abstract_algebra.FiniteGroup property) (mathematicskit.abstract_algebra.PermutationGroup property) (mathematicskit.abstract_algebra.QuaternionGroup property) (mathematicskit.abstract_algebra.QuotientGroup property) (mathematicskit.abstract_algebra.Subgroup property) elements() (mathematicskit.abstract_algebra.GF method) elements_of_order() (in module mathematicskit.abstract_algebra) elias_gamma_decode() (in module mathematicskit.information_theory) elias_gamma_encode() (in module mathematicskit.information_theory) ellipse() (in module mathematicskit.geometry) EllipticCurve (class in mathematicskit.number_theory) EllipticSolution (class in mathematicskit.pde) encode() (mathematicskit.information_theory.PrefixCode method) energy() (mathematicskit.pde.WaveEquation1D method) entropy (mathematicskit.information_theory.PrefixCode property) (mathematicskit.information_theory.TypicalSetResult attribute) entropy() (in module mathematicskit.information_theory) epsilon (mathematicskit.information_theory.TypicalSetResult attribute) erlang_b() (in module mathematicskit.probability) error_estimate (mathematicskit.calculus.DerivativeResult attribute) (mathematicskit.calculus.QuadratureResult attribute) error_function() (in module mathematicskit.special_functions) EscapeTimeResult (class in mathematicskit.fractals_chaos) estimate (mathematicskit.probability.MonteCarloResult attribute) (mathematicskit.statistics.BootstrapResult attribute) (mathematicskit.statistics.ConfidenceIntervalResult attribute) (mathematicskit.statistics.JackknifeResult attribute) estimate_convergence_order() (in module mathematicskit.numerical_analysis) estimate_feigenbaum_delta() (in module mathematicskit.ode_dynamics) estimate_limit_cycle_amplitude() (in module mathematicskit.ode_dynamics) estimate_period() (in module mathematicskit.ode_dynamics)

estimate_radius_of_convergence() (in module mathematicskit.calculus) euler_characteristic (mathematicskit.geometry.PolyhedronResult property) (mathematicskit.topology.CriticalPointsResult property) (mathematicskit.topology.HomologyResult property) (mathematicskit.topology.SimplicialComplex property) (mathematicskit.topology.SurfaceClassification attribute) euler_integrate() (in module mathematicskit.integrators) euler_maclaurin_trapezoid() (in module mathematicskit.calculus) euler_maruyama() (in module mathematicskit.probability) euler_product() (in module mathematicskit.number_theory) (in module mathematicskit.special_functions) euler_step() (in module mathematicskit.integrators) euler_totient() (in module mathematicskit.number_theory) eulerian_circuit() (in module mathematicskit.graph_theory) eulerian_trail() (in module mathematicskit.graph_theory) evaluate() (mathematicskit.abstract_algebra.MultivariatePolynomial method) (mathematicskit.abstract_algebra.Polynomial method) (mathematicskit.numerical_analysis.ChebyshevInterpolant method) (mathematicskit.numerical_analysis.CubicSpline method) (mathematicskit.numerical_analysis.HermiteInterpolant method) (mathematicskit.numerical_analysis.Interpolant method) (mathematicskit.numerical_analysis.LagrangeInterpolant method) (mathematicskit.numerical_analysis.MinimaxResult method) (mathematicskit.numerical_analysis.NewtonDividedDifference method) (mathematicskit.numerical_analysis.PadeApproximant method) evaluate_series() (in module mathematicskit.calculus) exact (mathematicskit.probability.TailBoundResult attribute) exact() (mathematicskit.pde.AdvectionEquation1D method) exact_crossing_probability (mathematicskit.probability.BuffonNeedleResult attribute) ExhaustionResult (class in mathematicskit.calculus) exp() (mathematicskit.calculus.Dual method) (mathematicskit.calculus.Variable method) expected_steps_to_absorption() (mathematicskit.probability.MarkovChain method) explained_variance (mathematicskit.statistics.PCAResult attribute) explained_variance_ratio (mathematicskit.statistics.PCAResult attribute) exponent (mathematicskit.numerical_analysis.FloatBits attribute) exponent_bits (mathematicskit.numerical_analysis.FloatBits attribute) Exponential (class in mathematicskit.probability) extended_gcd() (in module mathematicskit.number_theory) extent (mathematicskit.fractals_chaos.EscapeTimeResult attribute) extinct_fraction (mathematicskit.probability.BranchingProcessResult attribute) extra (mathematicskit.calculus.QuadratureResult attribute) (mathematicskit.fractals_chaos.BoxCountingResult attribute) (mathematicskit.linalg.EigenResult attribute) (mathematicskit.number_theory.PellResult attribute) (mathematicskit.numerical_analysis.RootResult attribute) (mathematicskit.numerical_analysis.SystemRootResult attribute) (mathematicskit.ode_dynamics.OdeTrajectory attribute) (mathematicskit.optimization.OptimizeResult attribute) (mathematicskit.pde.PDESolution attribute) (mathematicskit.statistics.HypothesisTestResult attribute)

F

f_vector (mathematicskit.topology.SimplicialComplex property) faces (mathematicskit.geometry.PolyhedronResult attribute) factor (mathematicskit.number_theory.ECMResult attribute) (mathematicskit.number_theory.PollardRhoResult attribute) factor_orders (mathematicskit.abstract_algebra.CompositionSeriesResult attribute) fast_mod_pow() (in module mathematicskit.number_theory) fem_poisson_1d() (in module mathematicskit.pde) ferrers_diagram() (mathematicskit.combinatorics.YoungDiagram method) fft_numpy() (in module mathematicskit.special_functions) fft_radix2() (in module mathematicskit.special_functions) fft_result (mathematicskit.special_functions.ConvolutionComparisonResult attribute) fft_time (mathematicskit.special_functions.ConvolutionComparisonResult attribute) FFTComparisonResult (class in mathematicskit.special_functions) fibonacci() (in module mathematicskit.combinatorics) FilterCoefficients (class in mathematicskit.special_functions) Filtration (class in mathematicskit.topology) final (mathematicskit.pde.PDESolution property) find_fixed_point_newton() (in module mathematicskit.ode_dynamics) find_irreducible_polynomial() (in module mathematicskit.abstract_algebra) FiniteGroup (class in mathematicskit.abstract_algebra) fir_window_filter() (in module mathematicskit.special_functions) fisher_exact_test() (in module mathematicskit.statistics) fit() (mathematicskit.numerical_analysis.PolynomialRegression method) fitted_values (mathematicskit.numerical_analysis.RegressionResult attribute) (mathematicskit.statistics.RegressionResult attribute) fitzhugh_nagumo_fixed_point() (in module mathematicskit.ode_dynamics) fitzhugh_nagumo_hopf_currents() (in module mathematicskit.ode_dynamics) FitzHughNagumo (class in mathematicskit.ode_dynamics) fixed_point() (mathematicskit.ode_dynamics.Brusselator method) (mathematicskit.ode_dynamics.LotkaVolterra method) fixed_points (mathematicskit.complex_analysis.MobiusClassification attribute) fixed_points() (mathematicskit.ode_dynamics.LogisticMap method)

FixedPointIteration (class in mathematicskit.numerical_analysis) FixedPointResult (class in mathematicskit.ode_dynamics) (class in mathematicskit.topology) float_bits() (in module mathematicskit.numerical_analysis) FloatBits (class in mathematicskit.numerical_analysis) flow_matrix (mathematicskit.graph_theory.MaxFlowResult attribute) flow_value (mathematicskit.graph_theory.MaxFlowResult attribute) FlowSystem (class in mathematicskit.ode_dynamics) floyd_warshall_shortest_paths() (in module mathematicskit.graph_theory) format (mathematicskit.numerical_analysis.FloatBits attribute) forward_difference() (in module mathematicskit.calculus) fourier_derivative() (in module mathematicskit.pde) fourier_differentiation_matrix() (in module mathematicskit.pde) fourier_sine_coefficients() (in module mathematicskit.pde) fraction_bits (mathematicskit.numerical_analysis.FloatBits attribute) frank_wolfe() (in module mathematicskit.optimization) frenet_serret_frame() (in module mathematicskit.geometry) frequencies (mathematicskit.special_functions.FrequencyResponseResult attribute) (mathematicskit.special_functions.ScalogramResult attribute) frequency_response() (in module mathematicskit.special_functions) FrequencyResponseResult (class in mathematicskit.special_functions) fresnel_integrals() (in module mathematicskit.special_functions) FresnelResult (class in mathematicskit.special_functions) frobenius_norm() (in module mathematicskit.linalg) fully_labeled_triangles() (in module mathematicskit.topology) fun (mathematicskit.optimization.LinearProgramResult attribute) (mathematicskit.optimization.OptimizeResult attribute) (mathematicskit.optimization.ScalarSearchResult attribute) function_evaluations (mathematicskit.numerical_analysis.SystemRootResult attribute) function_value_gap() (in module mathematicskit.optimization) fundamental_group() (in module mathematicskit.topology) FundamentalGroupPresentation (class in mathematicskit.topology)

G

gain (mathematicskit.special_functions.PoleZeroResult attribute) gallager_ldpc_matrix() (in module mathematicskit.information_theory) galton_watson_extinction_probability() (in module mathematicskit.probability) galton_watson_simulate() (in module mathematicskit.probability) GameOfLife (class in mathematicskit.fractals_chaos) GameResult (class in mathematicskit.optimization) Gamma (class in mathematicskit.probability) gamma (mathematicskit.complex_analysis.Contour attribute) gamma_function() (in module mathematicskit.special_functions) gaussian (mathematicskit.geometry.SurfaceCurvatureResult attribute) GaussianQuadrature (class in mathematicskit.calculus) GaussSeidel (class in mathematicskit.linalg) gcd (mathematicskit.number_theory.BezoutResult attribute) (mathematicskit.number_theory.LinearDiophantineResult attribute) gcd() (in module mathematicskit.number_theory) generate() (mathematicskit.fractals_chaos.BarnsleyFern method) (mathematicskit.fractals_chaos.IteratedFunctionSystem method) (mathematicskit.fractals_chaos.SierpinskiCarpet method) (mathematicskit.fractals_chaos.SierpinskiTriangle method) generate_combinations() (in module mathematicskit.combinatorics) generate_permutations() (in module mathematicskit.combinatorics) generated_subgroup() (in module mathematicskit.abstract_algebra) generation_sizes (mathematicskit.probability.BranchingProcessResult attribute) generators (mathematicskit.topology.FundamentalGroupPresentation attribute) genus (mathematicskit.topology.SurfaceClassification attribute)

Geometric (class in mathematicskit.probability) geometric_brownian_motion() (in module mathematicskit.probability) gershgorin_discs() (in module mathematicskit.linalg) GershgorinResult (class in mathematicskit.linalg) GF (class in mathematicskit.abstract_algebra) giant_component_fraction() (in module mathematicskit.graph_theory) gibbs_sampler() (in module mathematicskit.probability) GMRES (class in mathematicskit.linalg) golden_section_search() (in module mathematicskit.optimization) grad (mathematicskit.calculus.Variable attribute) gradient() (in module mathematicskit.calculus) GradientDescent (class in mathematicskit.optimization) GradientDescentLineSearch (class in mathematicskit.optimization) graham_scan() (in module mathematicskit.geometry) gram_schmidt_norms (mathematicskit.number_theory.LLLResult attribute) gram_schmidt_qr() (in module mathematicskit.linalg) Graph (class in mathematicskit.graph_theory) graph (mathematicskit.topology.MapperResult property) gray_code() (in module mathematicskit.combinatorics) greedy_coloring() (in module mathematicskit.graph_theory) grid_graph() (in module mathematicskit.graph_theory) groebner_basis() (in module mathematicskit.abstract_algebra) GroebnerResult (class in mathematicskit.abstract_algebra) group() (mathematicskit.topology.HomologyResult method) group_properties() (in module mathematicskit.abstract_algebra) GroupPropertiesResult (class in mathematicskit.abstract_algebra)

H

hall_condition() (in module mathematicskit.combinatorics) Halley (class in mathematicskit.numerical_analysis) HallResult (class in mathematicskit.combinatorics) hamiltonian_cycle() (in module mathematicskit.graph_theory) hamming_decode() (in module mathematicskit.information_theory) hamming_distance() (in module mathematicskit.information_theory) hamming_encode() (in module mathematicskit.information_theory) hamming_parity_check_matrix() (in module mathematicskit.information_theory) hartley_information() (in module mathematicskit.information_theory) has_monochromatic_triangle() (in module mathematicskit.combinatorics) has_solution (mathematicskit.number_theory.LinearDiophantineResult attribute) hausdorff_distance() (in module mathematicskit.geometry) heat_series_solution() (in module mathematicskit.pde) HeatEquation1D (class in mathematicskit.pde) HeatEquation2D (class in mathematicskit.pde) helix() (in module mathematicskit.geometry) henon_map() (in module mathematicskit.fractals_chaos) hermite_polynomial() (in module mathematicskit.special_functions) HermiteInterpolant (class in mathematicskit.numerical_analysis)

heron_area() (in module mathematicskit.geometry) hessenberg_reduce() (in module mathematicskit.linalg) hilbert_curve() (in module mathematicskit.fractals_chaos) history (mathematicskit.numerical_analysis.RootResult attribute) (mathematicskit.numerical_analysis.SystemRootResult attribute) (mathematicskit.optimization.TourResult attribute) homology() (in module mathematicskit.topology) HomologyResult (class in mathematicskit.topology) homomorphism_image() (in module mathematicskit.abstract_algebra) homomorphism_kernel() (in module mathematicskit.abstract_algebra) HomomorphismResult (class in mathematicskit.abstract_algebra) hopf_limit_cycle_radius() (in module mathematicskit.ode_dynamics) horizontal (mathematicskit.complex_analysis.MappedGrid attribute) horizontal_image (mathematicskit.complex_analysis.MappedGrid attribute) horner() (in module mathematicskit.numerical_analysis) HornerResult (class in mathematicskit.numerical_analysis) householder_qr() (in module mathematicskit.linalg) huffman_code() (in module mathematicskit.information_theory) hypergeometric_2f1() (in module mathematicskit.special_functions) HypothesisTestResult (class in mathematicskit.statistics)

I

identity (mathematicskit.abstract_algebra.GroupPropertiesResult attribute) identity() (mathematicskit.abstract_algebra.CyclicGroup method) (mathematicskit.abstract_algebra.FiniteGroup method) (mathematicskit.abstract_algebra.PermutationGroup method) (mathematicskit.abstract_algebra.QuaternionGroup method) (mathematicskit.abstract_algebra.QuotientGroup method) (mathematicskit.abstract_algebra.Subgroup method) image (mathematicskit.abstract_algebra.HomomorphismResult attribute) implicit_euler_integrate() (in module mathematicskit.integrators) implicit_euler_step() (in module mathematicskit.integrators) importance_sampling_integrate() (in module mathematicskit.probability) in_ideal() (in module mathematicskit.abstract_algebra) index (mathematicskit.topology.CriticalPointsResult attribute) index() (mathematicskit.topology.SimplicialComplex method) indices (mathematicskit.geometry.ClosestPairResult attribute) induced_subcomplex() (mathematicskit.topology.SimplicialComplex method) inner_product() (in module mathematicskit.special_functions) input_distribution (mathematicskit.information_theory.ChannelCapacityResult attribute) integer_linear_program() (in module mathematicskit.optimization) integer_partitions() (in module mathematicskit.combinatorics) integer_relation() (in module mathematicskit.number_theory) integral (mathematicskit.complex_analysis.ResidueTheoremResult attribute) integrate() (mathematicskit.calculus.AdaptiveQuadrature method) (mathematicskit.calculus.ClenshawCurtisQuadrature method) (mathematicskit.calculus.GaussianQuadrature method) (mathematicskit.calculus.Quadrature method) (mathematicskit.calculus.RiemannSum method) (mathematicskit.calculus.RombergQuadrature method) (mathematicskit.calculus.SimpsonsRule method) (mathematicskit.calculus.TanhSinhQuadrature method) (mathematicskit.calculus.TrapezoidalRule method) (mathematicskit.ode_dynamics.FlowSystem method) integrated_autocorrelation_time() (in module mathematicskit.probability) interior (mathematicskit.geometry.LatticePolygonResult attribute) interior_point_lp() (in module mathematicskit.optimization) Interpolant (class in mathematicskit.numerical_analysis) invariant_factors (mathematicskit.topology.SmithNormalFormResult property) inverse() (mathematicskit.abstract_algebra.CyclicGroup method) (mathematicskit.abstract_algebra.FiniteGroup method) (mathematicskit.abstract_algebra.GF method) (mathematicskit.abstract_algebra.PermutationGroup method) (mathematicskit.abstract_algebra.QuaternionGroup method) (mathematicskit.abstract_algebra.QuotientGroup method) (mathematicskit.abstract_algebra.Subgroup method)

inverse_discrete_wavelet_transform() (in module mathematicskit.special_functions) inverse_iteration() (in module mathematicskit.linalg) inverse_laplace_stehfest() (in module mathematicskit.special_functions) inverse_laplace_talbot() (in module mathematicskit.special_functions) inverse_z_transform() (in module mathematicskit.special_functions) is_abelian (mathematicskit.abstract_algebra.GroupPropertiesResult attribute) is_abelian() (mathematicskit.abstract_algebra.FiniteGroup method) is_absolutely_stable() (in module mathematicskit.integrators) is_cyclic() (in module mathematicskit.abstract_algebra) is_homomorphism (mathematicskit.abstract_algebra.HomomorphismResult attribute) is_homomorphism() (in module mathematicskit.abstract_algebra) is_irreducible() (in module mathematicskit.abstract_algebra) is_latin_square() (in module mathematicskit.combinatorics) is_normal_subgroup() (in module mathematicskit.abstract_algebra) is_on_curve() (mathematicskit.number_theory.EllipticCurve method) is_orientable() (in module mathematicskit.topology) is_prime_miller_rabin() (in module mathematicskit.number_theory) is_prime_trial_division() (in module mathematicskit.number_theory) is_solvable() (in module mathematicskit.abstract_algebra) is_sperner_labeling() (in module mathematicskit.topology) is_stable (mathematicskit.special_functions.PoleZeroResult attribute) is_symmetric() (in module mathematicskit.linalg) is_symmetric_positive_definite() (in module mathematicskit.linalg) is_zero() (mathematicskit.abstract_algebra.MultivariatePolynomial method) items (mathematicskit.optimization.KnapsackResult attribute) iterate() (mathematicskit.ode_dynamics.LogisticMap method) IteratedFunctionSystem (class in mathematicskit.fractals_chaos) iterations (mathematicskit.fractals_chaos.EscapeTimeResult attribute) (mathematicskit.graph_theory.PageRankResult attribute) (mathematicskit.information_theory.BitFlipResult attribute) (mathematicskit.information_theory.ChannelCapacityResult attribute) (mathematicskit.linalg.EigenResult attribute) (mathematicskit.linalg.IterativeSolveResult attribute) (mathematicskit.number_theory.PollardRhoResult attribute) (mathematicskit.numerical_analysis.MinimaxResult attribute) (mathematicskit.numerical_analysis.RootResult attribute) (mathematicskit.numerical_analysis.SystemRootResult attribute) (mathematicskit.optimization.OptimizeResult attribute) (mathematicskit.optimization.ScalarSearchResult attribute) IterativeLinearSolver (class in mathematicskit.linalg) IterativeRootFinder (class in mathematicskit.numerical_analysis) IterativeSolveResult (class in mathematicskit.linalg)

J

jackknife() (in module mathematicskit.statistics) JackknifeResult (class in mathematicskit.statistics) jacobi_elliptic_functions() (in module mathematicskit.special_functions) jacobi_spectral_radius() (in module mathematicskit.linalg) jacobi_symbol() (in module mathematicskit.number_theory) jacobian (mathematicskit.ode_dynamics.FixedPointResult attribute)

JacobiEllipticResult (class in mathematicskit.special_functions) JacobiIteration (class in mathematicskit.linalg) james_stein_estimator() (in module mathematicskit.statistics) joint_entropy() (in module mathematicskit.information_theory) joukowski_map() (in module mathematicskit.complex_analysis) julia_set() (in module mathematicskit.fractals_chaos)

K

k (mathematicskit.probability.TailBoundResult attribute) kahan_sum() (in module mathematicskit.numerical_analysis) kernel (mathematicskit.abstract_algebra.HomomorphismResult attribute) kind (mathematicskit.complex_analysis.MobiusClassification attribute) kkt (mathematicskit.optimization.LagrangeResult attribute) KKTResult (class in mathematicskit.optimization) kl_divergence() (in module mathematicskit.information_theory) klein_bottle() (in module mathematicskit.topology) knapsack() (in module mathematicskit.optimization)

KnapsackResult (class in mathematicskit.optimization) koch_curve() (in module mathematicskit.fractals_chaos) koch_snowflake() (in module mathematicskit.fractals_chaos) kolmogorov_smirnov_test() (in module mathematicskit.statistics) kraft_sum() (in module mathematicskit.information_theory) kruskal_mst() (in module mathematicskit.graph_theory) kuramoto_lorentzian_order_parameter() (in module mathematicskit.ode_dynamics) kuramoto_order_parameter() (in module mathematicskit.ode_dynamics) KuramotoModel (class in mathematicskit.ode_dynamics) kurtosis (mathematicskit.statistics.DescriptiveStatsResult attribute)

L

L (mathematicskit.linalg.CholeskyResult attribute) (mathematicskit.linalg.LUResult attribute) labels (mathematicskit.graph_theory.ComponentsResult attribute) lagrange_stationary_point() (in module mathematicskit.optimization) LagrangeInterpolant (class in mathematicskit.numerical_analysis) LagrangeResult (class in mathematicskit.optimization) laguerre_polynomial() (in module mathematicskit.special_functions) lambert_w() (in module mathematicskit.special_functions) lanczos_eigsh() (in module mathematicskit.linalg) laplace_transform() (in module mathematicskit.special_functions) laplacian (mathematicskit.graph_theory.SpectralResult attribute) laplacian_1d() (in module mathematicskit.pde) laplacian_2d() (in module mathematicskit.pde) lattice_point_counts() (in module mathematicskit.geometry) LatticePolygonResult (class in mathematicskit.geometry) laurent_coefficients() (in module mathematicskit.complex_analysis) LaurentSeriesResult (class in mathematicskit.complex_analysis) law_of_large_numbers_trace() (in module mathematicskit.probability) lcm() (in module mathematicskit.number_theory) leading_term() (mathematicskit.abstract_algebra.MultivariatePolynomial method) leapfrog_integrate() (in module mathematicskit.integrators) leapfrog_step() (in module mathematicskit.integrators) least_squares_lstsq() (in module mathematicskit.linalg) least_squares_normal_equations() (in module mathematicskit.linalg) least_squares_qr() (in module mathematicskit.linalg) LeastSquaresResult (class in mathematicskit.linalg) (class in mathematicskit.optimization) lebesgue_constant() (in module mathematicskit.numerical_analysis) lefschetz_number() (in module mathematicskit.topology) left_cosets() (in module mathematicskit.abstract_algebra) legendre_nodes_and_weights() (in module mathematicskit.calculus) legendre_polynomial() (in module mathematicskit.special_functions) legendre_symbol() (in module mathematicskit.number_theory) length (mathematicskit.optimization.TourResult attribute) lenstra_ecm() (in module mathematicskit.number_theory) levenberg_marquardt() (in module mathematicskit.optimization) likelihood_ratio_test() (in module mathematicskit.statistics) limit (mathematicskit.pde.StabilityResult attribute) Linear2D (class in mathematicskit.ode_dynamics) linear_program() (in module mathematicskit.optimization) linear_regression() (in module mathematicskit.statistics)

LinearDiophantineResult (class in mathematicskit.number_theory) LinearProgramResult (class in mathematicskit.optimization) link() (mathematicskit.topology.SimplicialComplex method) linking_number() (in module mathematicskit.topology) lll_reduce() (in module mathematicskit.number_theory) LLLResult (class in mathematicskit.number_theory) location (mathematicskit.ode_dynamics.FixedPointResult attribute) log() (mathematicskit.calculus.Dual method) (mathematicskit.calculus.Variable method) log2_size (mathematicskit.information_theory.TypicalSetResult attribute) log_gamma_function() (in module mathematicskit.special_functions) log_likelihood (mathematicskit.statistics.MaximumLikelihoodResult attribute) logarithmic_integral() (in module mathematicskit.number_theory) logistic_growth_solution() (in module mathematicskit.ode_dynamics) LogisticGrowth (class in mathematicskit.ode_dynamics) LogisticMap (class in mathematicskit.ode_dynamics) longest_decreasing_subsequence() (in module mathematicskit.combinatorics) longest_increasing_subsequence() (in module mathematicskit.combinatorics) lorenz_fixed_points() (in module mathematicskit.ode_dynamics) LorenzSystem (class in mathematicskit.ode_dynamics) lotka_volterra_invariant() (in module mathematicskit.ode_dynamics) LotkaVolterra (class in mathematicskit.ode_dynamics) lower (mathematicskit.calculus.ExhaustionResult attribute) (mathematicskit.statistics.BootstrapResult attribute) (mathematicskit.statistics.ConfidenceIntervalResult attribute) lower_bounds (mathematicskit.information_theory.ChannelCapacityResult attribute) lower_star_filtration() (in module mathematicskit.topology) lsystem() (in module mathematicskit.fractals_chaos) lu_decompose() (in module mathematicskit.linalg) lu_det() (in module mathematicskit.linalg) lu_solve() (in module mathematicskit.linalg) lu_solve_system() (in module mathematicskit.linalg) lucas_lehmer() (in module mathematicskit.number_theory) LUResult (class in mathematicskit.linalg) lyapunov_exponent_1d_map() (in module mathematicskit.fractals_chaos) lyapunov_exponent_flow() (in module mathematicskit.fractals_chaos) lyapunov_quadratic_form() (in module mathematicskit.ode_dynamics) LyapunovFunctionResult (class in mathematicskit.ode_dynamics) lz78_compressed_bits() (in module mathematicskit.information_theory) lz78_decode() (in module mathematicskit.information_theory) lz78_encode() (in module mathematicskit.information_theory)

M

machine_epsilon() (in module mathematicskit.numerical_analysis) maclaurin_coefficients() (in module mathematicskit.calculus) magnitude (mathematicskit.special_functions.FrequencyResponseResult attribute) mandelbrot_set() (in module mathematicskit.fractals_chaos) mann_whitney_u_test() (in module mathematicskit.statistics) map_grid() (in module mathematicskit.complex_analysis) MappedGrid (class in mathematicskit.complex_analysis) mapper_graph() (in module mathematicskit.topology) MapperResult (class in mathematicskit.topology) MarkovChain (class in mathematicskit.probability) matching (mathematicskit.combinatorics.HallResult attribute) mathematicskit.abstract_algebra module mathematicskit.calculus module mathematicskit.combinatorics module mathematicskit.complex_analysis module mathematicskit.fractals_chaos module mathematicskit.geometry module mathematicskit.graph_theory module mathematicskit.information_theory module mathematicskit.integrators module mathematicskit.linalg module mathematicskit.number_theory module mathematicskit.numerical_analysis module mathematicskit.ode_dynamics module mathematicskit.optimization module mathematicskit.pde module mathematicskit.probability module mathematicskit.special_functions module mathematicskit.statistics module mathematicskit.topology module mathieu_characteristic_a() (in module mathematicskit.special_functions) mathieu_characteristic_b() (in module mathematicskit.special_functions) mathieu_even() (in module mathematicskit.special_functions) mathieu_odd() (in module mathematicskit.special_functions) matrix_polynomial() (in module mathematicskit.linalg) max_amplification() (in module mathematicskit.pde) max_dimension (mathematicskit.topology.PersistenceDiagram property) max_error (mathematicskit.numerical_analysis.MinimaxResult attribute) (mathematicskit.special_functions.ConvolutionComparisonResult attribute) max_error_naive_vs_numpy (mathematicskit.special_functions.FFTComparisonResult attribute) max_error_radix2_vs_numpy (mathematicskit.special_functions.FFTComparisonResult attribute) max_flow_min_cut() (in module mathematicskit.graph_theory) max_iter (mathematicskit.fractals_chaos.EscapeTimeResult attribute) max_rms_residual (mathematicskit.integrators.BVPResult attribute) max_stable_dt() (mathematicskit.pde.BurgersEquation1D method) (mathematicskit.pde.HeatEquation1D method) (mathematicskit.pde.HeatEquation2D method) (mathematicskit.pde.MethodOfLinesPDE method) (mathematicskit.pde.WaveEquation1D method) MaxFlowResult (class in mathematicskit.graph_theory) maxima (mathematicskit.topology.CriticalPointsResult attribute) maximal_simplices (mathematicskit.topology.SimplicialComplex property) maximum (mathematicskit.statistics.DescriptiveStatsResult attribute) maximum_likelihood_fit() (in module mathematicskit.statistics) maximum_matching() (in module mathematicskit.combinatorics) MaximumLikelihoodResult (class in mathematicskit.statistics) mayer_vietoris() (in module mathematicskit.topology) MayerVietorisResult (class in mathematicskit.topology) MCMCResult (class in mathematicskit.probability) mean (mathematicskit.geometry.SurfaceCurvatureResult attribute) (mathematicskit.probability.ContinuousDistribution property) (mathematicskit.probability.DiscreteDistribution property) (mathematicskit.statistics.ARModelResult attribute) (mathematicskit.statistics.DescriptiveStatsResult attribute) (mathematicskit.statistics.PCAResult attribute) mean_confidence_interval() (in module mathematicskit.statistics) median (mathematicskit.statistics.DescriptiveStatsResult attribute) message (mathematicskit.integrators.BVPResult attribute) (mathematicskit.optimization.LeastSquaresResult attribute) (mathematicskit.optimization.LinearProgramResult attribute) method (mathematicskit.calculus.DerivativeResult attribute) (mathematicskit.calculus.QuadratureResult attribute) (mathematicskit.geometry.ConvexHullResult attribute) (mathematicskit.graph_theory.ColoringResult attribute) (mathematicskit.graph_theory.MSTResult attribute) (mathematicskit.graph_theory.ShortestPathResult attribute) (mathematicskit.linalg.EigenResult attribute) (mathematicskit.linalg.GaussSeidel attribute) (mathematicskit.linalg.IterativeSolveResult attribute) (mathematicskit.linalg.JacobiIteration attribute) (mathematicskit.linalg.LeastSquaresResult attribute) (mathematicskit.linalg.QRResult attribute) (mathematicskit.linalg.SOR attribute) (mathematicskit.numerical_analysis.RootResult attribute) (mathematicskit.numerical_analysis.SystemRootResult attribute) (mathematicskit.ode_dynamics.OdeTrajectory attribute) (mathematicskit.optimization.OptimizeResult attribute) (mathematicskit.optimization.TourResult attribute) (mathematicskit.pde.EllipticSolution attribute) (mathematicskit.pde.PDESolution attribute) (mathematicskit.probability.MCMCResult attribute) (mathematicskit.probability.MonteCarloResult attribute) (mathematicskit.probability.SDEResult attribute) (mathematicskit.statistics.BootstrapResult attribute) (mathematicskit.statistics.ConfidenceIntervalResult attribute) (mathematicskit.statistics.CorrelationResult attribute) (mathematicskit.statistics.HypothesisTestResult attribute) (mathematicskit.statistics.MultipleTestingResult attribute)

MethodOfLinesPDE (class in mathematicskit.pde) metropolis_hastings() (in module mathematicskit.probability) mgf() (mathematicskit.probability.Beta method) (mathematicskit.probability.Binomial method) (mathematicskit.probability.ContinuousDistribution method) (mathematicskit.probability.DiscreteDistribution method) (mathematicskit.probability.Exponential method) (mathematicskit.probability.Gamma method) (mathematicskit.probability.Geometric method) (mathematicskit.probability.Normal method) (mathematicskit.probability.Poisson method) (mathematicskit.probability.Uniform method) min_cut (mathematicskit.graph_theory.MaxFlowResult attribute) min_enclosing_circle() (in module mathematicskit.geometry) minima (mathematicskit.topology.CriticalPointsResult attribute) MinimaxResult (class in mathematicskit.numerical_analysis) minimize() (mathematicskit.optimization.Adam method) (mathematicskit.optimization.BFGS method) (mathematicskit.optimization.GradientDescent method) (mathematicskit.optimization.GradientDescentLineSearch method) (mathematicskit.optimization.NelderMead method) (mathematicskit.optimization.NesterovAcceleratedGradient method) (mathematicskit.optimization.NewtonMethod method) (mathematicskit.optimization.NonlinearConjugateGradient method) (mathematicskit.optimization.PenaltyMethod method) (mathematicskit.optimization.UnconstrainedOptimizer method) minimum (mathematicskit.statistics.DescriptiveStatsResult attribute) minimum_ebn0() (in module mathematicskit.information_theory) mobius() (in module mathematicskit.number_theory) mobius_strip() (in module mathematicskit.topology) mobius_transform() (in module mathematicskit.complex_analysis) MobiusClassification (class in mathematicskit.complex_analysis) mod_inverse() (in module mathematicskit.number_theory) module mathematicskit.abstract_algebra mathematicskit.calculus mathematicskit.combinatorics mathematicskit.complex_analysis mathematicskit.fractals_chaos mathematicskit.geometry mathematicskit.graph_theory mathematicskit.information_theory mathematicskit.integrators mathematicskit.linalg mathematicskit.number_theory mathematicskit.numerical_analysis mathematicskit.ode_dynamics mathematicskit.optimization mathematicskit.pde mathematicskit.probability mathematicskit.special_functions mathematicskit.statistics mathematicskit.topology modulus (mathematicskit.number_theory.CRTResult attribute) monic() (mathematicskit.abstract_algebra.MultivariatePolynomial method) monte_carlo_integrate() (in module mathematicskit.probability) MonteCarloResult (class in mathematicskit.probability) morlet_cwt() (in module mathematicskit.special_functions) MSTResult (class in mathematicskit.graph_theory) multigrid_poisson_2d() (in module mathematicskit.pde) multinomial_coefficient() (in module mathematicskit.combinatorics) MultipleTestingResult (class in mathematicskit.statistics) multipliers (mathematicskit.optimization.LagrangeResult attribute) multiply() (mathematicskit.abstract_algebra.GF method) (mathematicskit.number_theory.EllipticCurve method) multivariate_divide() (in module mathematicskit.abstract_algebra) MultivariatePolynomial (class in mathematicskit.abstract_algebra) mutual_information() (in module mathematicskit.information_theory)

N

n (mathematicskit.combinatorics.YoungDiagram property) (mathematicskit.information_theory.TypicalSetResult attribute) (mathematicskit.statistics.CorrelationResult attribute) (mathematicskit.statistics.DescriptiveStatsResult attribute) (mathematicskit.topology.FixedPointResult attribute) (mathematicskit.topology.TriangleGrid attribute) n_components (mathematicskit.graph_theory.ComponentsResult attribute) n_drops (mathematicskit.probability.BuffonNeedleResult attribute) n_evaluations (mathematicskit.calculus.QuadratureResult attribute) n_expanded (mathematicskit.graph_theory.SearchResult attribute) n_params (mathematicskit.statistics.MaximumLikelihoodResult attribute) n_samples (mathematicskit.probability.MonteCarloResult attribute) naive_result (mathematicskit.special_functions.FFTComparisonResult attribute) naive_time (mathematicskit.special_functions.FFTComparisonResult attribute) name (mathematicskit.topology.SurfaceClassification attribute) negate() (mathematicskit.number_theory.EllipticCurve method) neighbors() (mathematicskit.graph_theory.Graph method) NelderMead (class in mathematicskit.optimization) NesterovAcceleratedGradient (class in mathematicskit.optimization) NewtonDividedDifference (class in mathematicskit.numerical_analysis)

NewtonMethod (class in mathematicskit.optimization) NewtonRaphson (class in mathematicskit.numerical_analysis) NewtonSystem (class in mathematicskit.numerical_analysis) nfev (mathematicskit.optimization.LeastSquaresResult attribute) (mathematicskit.optimization.ScalarSearchResult attribute) njit() (in module mathematicskit.integrators) node_values (mathematicskit.topology.MapperResult attribute) nodes (mathematicskit.topology.MapperResult attribute) noise_variance (mathematicskit.statistics.ARModelResult attribute) Nonlinear2D (class in mathematicskit.ode_dynamics) NonlinearConjugateGradient (class in mathematicskit.optimization) Normal (class in mathematicskit.probability) normal (mathematicskit.geometry.CurveFrameResult attribute) num_colors (mathematicskit.graph_theory.ColoringResult attribute) num_row_swaps (mathematicskit.linalg.LUResult attribute) number (mathematicskit.pde.StabilityResult attribute) numerical_jacobian() (in module mathematicskit.numerical_analysis) (in module mathematicskit.ode_dynamics) numpy_result (mathematicskit.special_functions.FFTComparisonResult attribute) numpy_time (mathematicskit.special_functions.FFTComparisonResult attribute)

O

odd_degree_vertices() (in module mathematicskit.graph_theory) OdeTrajectory (class in mathematicskit.ode_dynamics) one_sample_t_test() (in module mathematicskit.statistics) one_sample_z_test() (in module mathematicskit.statistics) one_way_anova() (in module mathematicskit.statistics) operate() (mathematicskit.abstract_algebra.CyclicGroup method) (mathematicskit.abstract_algebra.FiniteGroup method) (mathematicskit.abstract_algebra.PermutationGroup method) (mathematicskit.abstract_algebra.QuaternionGroup method) (mathematicskit.abstract_algebra.QuotientGroup method) (mathematicskit.abstract_algebra.Subgroup method) optimal_sor_omega() (in module mathematicskit.linalg)

OptimizeResult (class in mathematicskit.optimization) orbits() (in module mathematicskit.abstract_algebra) order (mathematicskit.abstract_algebra.FiniteGroup property) (mathematicskit.abstract_algebra.GF property) (mathematicskit.abstract_algebra.GroebnerResult attribute) (mathematicskit.abstract_algebra.GroupPropertiesResult attribute) order() (mathematicskit.number_theory.EllipticCurve method) order_statistic() (in module mathematicskit.statistics) orders (mathematicskit.complex_analysis.LaurentSeriesResult attribute) orientable (mathematicskit.topology.SurfaceClassification attribute) ornstein_uhlenbeck() (in module mathematicskit.probability) orthogonal_latin_square_pair() (in module mathematicskit.combinatorics) orthogonality_error() (in module mathematicskit.linalg)

P

p (mathematicskit.abstract_algebra.SylowResult attribute) P (mathematicskit.linalg.LUResult attribute) (mathematicskit.ode_dynamics.LyapunovFunctionResult attribute) p_value (mathematicskit.statistics.CorrelationResult attribute) (mathematicskit.statistics.HypothesisTestResult attribute) p_values (mathematicskit.statistics.RegressionResult attribute) PadeApproximant (class in mathematicskit.numerical_analysis) pagerank() (in module mathematicskit.graph_theory) PageRankResult (class in mathematicskit.graph_theory) pairs (mathematicskit.graph_theory.BipartiteMatchingResult attribute) (mathematicskit.topology.PersistenceDiagram attribute) params (mathematicskit.ode_dynamics.FlowSystem attribute) (mathematicskit.pde.MethodOfLinesPDE attribute) (mathematicskit.statistics.MaximumLikelihoodResult attribute) partial_sums() (in module mathematicskit.calculus) partition_function() (in module mathematicskit.combinatorics) parts (mathematicskit.combinatorics.YoungDiagram attribute) pascals_triangle() (in module mathematicskit.combinatorics) path (mathematicskit.graph_theory.SearchResult attribute) (mathematicskit.optimization.OptimizeResult attribute) path_graph() (in module mathematicskit.graph_theory) paths (mathematicskit.probability.BrownianMotionResult attribute) (mathematicskit.probability.SDEResult attribute) PCAResult (class in mathematicskit.statistics) PDESolution (class in mathematicskit.pde) pdf() (mathematicskit.probability.Beta method) (mathematicskit.probability.ContinuousDistribution method) (mathematicskit.probability.Exponential method) (mathematicskit.probability.Gamma method) (mathematicskit.probability.Normal method) (mathematicskit.probability.Uniform method) pearson_correlation() (in module mathematicskit.statistics) PellResult (class in mathematicskit.number_theory) PenaltyMethod (class in mathematicskit.optimization) penrose_residuals() (in module mathematicskit.linalg) PermutationGroup (class in mathematicskit.abstract_algebra) permutations_count() (in module mathematicskit.combinatorics) persistence() (mathematicskit.topology.PersistenceDiagram method) PersistenceDiagram (class in mathematicskit.topology) persistent_homology() (in module mathematicskit.topology) phase (mathematicskit.special_functions.FrequencyResponseResult attribute) pi_estimate (mathematicskit.probability.BuffonNeedleResult attribute) pick_area (mathematicskit.geometry.LatticePolygonResult property) pitchfork_fixed_points() (in module mathematicskit.ode_dynamics) planar_betti_numbers() (in module mathematicskit.topology) pmf() (mathematicskit.probability.Binomial method) (mathematicskit.probability.DiscreteDistribution method) (mathematicskit.probability.Geometric method) (mathematicskit.probability.Poisson method) point (mathematicskit.topology.FixedPointResult attribute)

point_in_polygon() (in module mathematicskit.geometry) point_order() (mathematicskit.number_theory.EllipticCurve method) points (mathematicskit.geometry.ConvexHullResult attribute) (mathematicskit.geometry.SurfaceCurvatureResult attribute) (mathematicskit.geometry.TriangulationResult attribute) (mathematicskit.geometry.VoronoiResult attribute) (mathematicskit.topology.TriangleGrid attribute) points() (mathematicskit.complex_analysis.Contour method) (mathematicskit.number_theory.EllipticCurve method) Poisson (class in mathematicskit.probability) poles (mathematicskit.complex_analysis.ResidueTheoremResult attribute) (mathematicskit.special_functions.PoleZeroResult attribute) poles_zeros() (in module mathematicskit.special_functions) PoleZeroResult (class in mathematicskit.special_functions) pollard_rho() (in module mathematicskit.number_theory) PollardRhoResult (class in mathematicskit.number_theory) poly_add() (in module mathematicskit.abstract_algebra) poly_divmod() (in module mathematicskit.abstract_algebra) poly_gcd() (in module mathematicskit.abstract_algebra) poly_mul() (in module mathematicskit.abstract_algebra) poly_sub() (in module mathematicskit.abstract_algebra) polygon_area() (in module mathematicskit.geometry) polygon_centroid() (in module mathematicskit.geometry) polygon_contour() (in module mathematicskit.complex_analysis) polyhedron_counts() (in module mathematicskit.geometry) PolyhedronResult (class in mathematicskit.geometry) Polynomial (class in mathematicskit.abstract_algebra) PolynomialRegression (class in mathematicskit.numerical_analysis) position (mathematicskit.geometry.CurveFrameResult attribute) positive_definite (mathematicskit.ode_dynamics.LyapunovFunctionResult attribute) power_iteration() (in module mathematicskit.linalg) ppf() (mathematicskit.probability.ContinuousDistribution method) (mathematicskit.probability.DiscreteDistribution method) predecessors (mathematicskit.graph_theory.ShortestPathResult attribute) predict() (mathematicskit.numerical_analysis.PolynomialRegression method) predicted (mathematicskit.complex_analysis.ResidueTheoremResult attribute) predicted_union (mathematicskit.topology.MayerVietorisResult property) PrefixCode (class in mathematicskit.information_theory) prim_mst() (in module mathematicskit.graph_theory) primal_feasible (mathematicskit.optimization.KKTResult attribute) prime_counting() (in module mathematicskit.number_theory) prime_factorization() (in module mathematicskit.number_theory) primes_in_progression() (in module mathematicskit.number_theory) principal_component_analysis() (in module mathematicskit.statistics) probabilities (mathematicskit.information_theory.PrefixCode attribute) probability (mathematicskit.information_theory.TypicalSetResult attribute) projective_plane() (in module mathematicskit.topology) proportion_confidence_interval() (in module mathematicskit.statistics) prufer_decode() (in module mathematicskit.combinatorics) prufer_encode() (in module mathematicskit.combinatorics) pseudoinverse() (in module mathematicskit.linalg)

Q

Q (mathematicskit.linalg.QRResult attribute) (mathematicskit.ode_dynamics.LyapunovFunctionResult attribute) q1 (mathematicskit.statistics.DescriptiveStatsResult attribute) q3 (mathematicskit.statistics.DescriptiveStatsResult attribute) QRResult (class in mathematicskit.linalg) quadratic_bowl() (in module mathematicskit.optimization) quadratic_bowl_grad() (in module mathematicskit.optimization) quadratic_bowl_hess() (in module mathematicskit.optimization)

quadratic_roots() (in module mathematicskit.numerical_analysis) Quadrature (class in mathematicskit.calculus) QuadratureResult (class in mathematicskit.calculus) quantity (mathematicskit.pde.StabilityResult attribute) QuaternionGroup (class in mathematicskit.abstract_algebra) quotient (mathematicskit.numerical_analysis.HornerResult attribute) quotient_group() (in module mathematicskit.abstract_algebra) QuotientGroup (class in mathematicskit.abstract_algebra)

R

R (mathematicskit.linalg.QRResult attribute) r0 (mathematicskit.ode_dynamics.SIRModel property) r_squared (mathematicskit.numerical_analysis.RegressionResult attribute) (mathematicskit.statistics.RegressionResult attribute) radii (mathematicskit.linalg.GershgorinResult attribute) radius (mathematicskit.complex_analysis.LaurentSeriesResult attribute) (mathematicskit.geometry.CircleResult attribute) radix2_result (mathematicskit.special_functions.FFTComparisonResult attribute) radix2_time (mathematicskit.special_functions.FFTComparisonResult attribute) random_code_error_rate() (in module mathematicskit.information_theory) random_graph() (in module mathematicskit.graph_theory) random_spd_matrix() (in module mathematicskit.linalg) random_sperner_labeling() (in module mathematicskit.topology) random_walk_return_fraction() (in module mathematicskit.probability) rank (mathematicskit.topology.SmithNormalFormResult property) rank_inclusion (mathematicskit.topology.MayerVietorisResult attribute) rank_mod_p() (in module mathematicskit.topology) rate_distortion_binary() (in module mathematicskit.information_theory) rate_distortion_gaussian() (in module mathematicskit.information_theory) real (mathematicskit.calculus.Dual attribute) reference (mathematicskit.numerical_analysis.MinimaxResult attribute) reflection (mathematicskit.abstract_algebra.DihedralGroup property) regions (mathematicskit.geometry.VoronoiResult attribute) RegressionResult (class in mathematicskit.numerical_analysis) (class in mathematicskit.statistics) reject_null() (mathematicskit.statistics.HypothesisTestResult method) rejected (mathematicskit.statistics.MultipleTestingResult attribute) relations (mathematicskit.topology.FundamentalGroupPresentation attribute) remez_minimax() (in module mathematicskit.numerical_analysis) replicates (mathematicskit.statistics.JackknifeResult attribute) reset() (mathematicskit.ode_dynamics.FlowSystem method) residual (mathematicskit.complex_analysis.CauchyRiemannResult property) (mathematicskit.topology.FixedPointResult attribute) residual_history (mathematicskit.linalg.IterativeSolveResult attribute) residual_norm (mathematicskit.linalg.LeastSquaresResult attribute) (mathematicskit.pde.EllipticSolution attribute) residual_norms (mathematicskit.numerical_analysis.SystemRootResult attribute) residuals (mathematicskit.numerical_analysis.RegressionResult attribute) (mathematicskit.optimization.LeastSquaresResult attribute) (mathematicskit.statistics.RegressionResult attribute) residue (mathematicskit.number_theory.CRTResult attribute) residue() (in module mathematicskit.complex_analysis) residue_theorem() (in module mathematicskit.complex_analysis) residues (mathematicskit.complex_analysis.ResidueTheoremResult attribute) ResidueTheoremResult (class in mathematicskit.complex_analysis)

response (mathematicskit.special_functions.FrequencyResponseResult attribute) return_probability_1d() (in module mathematicskit.probability) rgb (mathematicskit.complex_analysis.DomainColoringResult attribute) rhs() (mathematicskit.ode_dynamics.Brusselator method) (mathematicskit.ode_dynamics.DuffingOscillator method) (mathematicskit.ode_dynamics.FitzHughNagumo method) (mathematicskit.ode_dynamics.FlowSystem method) (mathematicskit.ode_dynamics.KuramotoModel method) (mathematicskit.ode_dynamics.Linear2D method) (mathematicskit.ode_dynamics.LogisticGrowth method) (mathematicskit.ode_dynamics.LorenzSystem method) (mathematicskit.ode_dynamics.LotkaVolterra method) (mathematicskit.ode_dynamics.Nonlinear2D method) (mathematicskit.ode_dynamics.RosslerSystem method) (mathematicskit.ode_dynamics.SIRModel method) (mathematicskit.ode_dynamics.VanDerPolOscillator method) (mathematicskit.pde.MethodOfLinesPDE method) richardson_extrapolation() (in module mathematicskit.calculus) ridge_points (mathematicskit.geometry.VoronoiResult attribute) riemann_zeta() (in module mathematicskit.special_functions) RiemannSum (class in mathematicskit.calculus) rk4_integrate() (in module mathematicskit.integrators) rk4_step() (in module mathematicskit.integrators) robbins_monro() (in module mathematicskit.optimization) RombergQuadrature (class in mathematicskit.calculus) root (mathematicskit.numerical_analysis.RootResult attribute) (mathematicskit.numerical_analysis.SystemRootResult attribute) root_condition_numbers() (in module mathematicskit.numerical_analysis) RootResult (class in mathematicskit.numerical_analysis) rosenbrock() (in module mathematicskit.optimization) rosenbrock_grad() (in module mathematicskit.optimization) rosenbrock_hess() (in module mathematicskit.optimization) rossler_fixed_points() (in module mathematicskit.ode_dynamics) RosslerSystem (class in mathematicskit.ode_dynamics) rotation (mathematicskit.abstract_algebra.DihedralGroup property) rouche_condition() (in module mathematicskit.complex_analysis) row_strategy (mathematicskit.optimization.GameResult attribute) rows (mathematicskit.graph_theory.AssignmentResult attribute) rs_decode_erasures() (in module mathematicskit.abstract_algebra) rs_encode() (in module mathematicskit.abstract_algebra) rule_of_succession() (in module mathematicskit.probability) rules_out_periodic_orbits (mathematicskit.ode_dynamics.BendixsonResult attribute) run() (mathematicskit.fractals_chaos.CellularAutomaton method) runge_function() (in module mathematicskit.numerical_analysis) runge_phenomenon_errors() (in module mathematicskit.numerical_analysis)

S

S (mathematicskit.linalg.SVDResult attribute) s (mathematicskit.special_functions.FresnelResult attribute) s_pairs (mathematicskit.abstract_algebra.GroebnerResult attribute) s_polynomial() (in module mathematicskit.abstract_algebra) saddle_node_fixed_points() (in module mathematicskit.ode_dynamics) saddles (mathematicskit.topology.CriticalPointsResult attribute) sample() (mathematicskit.probability.ContinuousDistribution method) (mathematicskit.probability.DiscreteDistribution method) samples (mathematicskit.probability.MCMCResult attribute) satisfied (mathematicskit.combinatorics.HallResult attribute) (mathematicskit.optimization.KKTResult attribute) ScalarSearchResult (class in mathematicskit.optimization) scales (mathematicskit.special_functions.ScalogramResult attribute) ScalogramResult (class in mathematicskit.special_functions) scheme (mathematicskit.pde.StabilityResult attribute) schur_decompose() (in module mathematicskit.linalg) SchurResult (class in mathematicskit.linalg) scores (mathematicskit.graph_theory.PageRankResult attribute) (mathematicskit.statistics.PCAResult attribute) SDEResult (class in mathematicskit.probability) SearchResult (class in mathematicskit.graph_theory) Secant (class in mathematicskit.numerical_analysis) second_derivative_at_nodes() (mathematicskit.numerical_analysis.CubicSpline method) segment_intersection() (in module mathematicskit.geometry) series (mathematicskit.abstract_algebra.CompositionSeriesResult attribute) shannon_fano_code() (in module mathematicskit.information_theory) ShortestPathResult (class in mathematicskit.graph_theory) sides (mathematicskit.calculus.ExhaustionResult attribute) SierpinskiCarpet (class in mathematicskit.fractals_chaos) SierpinskiTriangle (class in mathematicskit.fractals_chaos) sieve_of_eratosthenes() (in module mathematicskit.number_theory) sign (mathematicskit.numerical_analysis.FloatBits attribute) significand (mathematicskit.numerical_analysis.FloatBits attribute) similarity_dimension() (in module mathematicskit.fractals_chaos) simple_random_walk() (in module mathematicskit.probability) simplex() (in module mathematicskit.topology) simplices (mathematicskit.geometry.ConvexHullResult attribute) (mathematicskit.geometry.TriangulationResult attribute) (mathematicskit.topology.Filtration attribute) simplices() (mathematicskit.topology.SimplicialComplex method) simplicial_product() (in module mathematicskit.topology) SimplicialComplex (class in mathematicskit.topology) SimpsonsRule (class in mathematicskit.calculus) simulate_ar() (in module mathematicskit.statistics) simulated_annealing() (in module mathematicskit.optimization) sin() (mathematicskit.calculus.Dual method) (mathematicskit.calculus.Variable method) singular_values (mathematicskit.statistics.PCAResult attribute) sir_final_size() (in module mathematicskit.ode_dynamics) sir_peak_infected() (in module mathematicskit.ode_dynamics) SIRModel (class in mathematicskit.ode_dynamics) size (mathematicskit.graph_theory.BipartiteMatchingResult property) sizes (mathematicskit.graph_theory.ComponentsResult attribute) skeleton() (mathematicskit.topology.SimplicialComplex method) skewness (mathematicskit.statistics.DescriptiveStatsResult attribute) smith_normal_form() (in module mathematicskit.topology) SmithNormalFormResult (class in mathematicskit.topology) sn (mathematicskit.special_functions.JacobiEllipticResult attribute) snapshot() (mathematicskit.pde.PDESolution method) sol (mathematicskit.integrators.BVPResult attribute) solve() (mathematicskit.linalg.ConjugateGradient method) (mathematicskit.linalg.GMRES method) (mathematicskit.linalg.IterativeLinearSolver method) (mathematicskit.linalg.SOR method) (mathematicskit.numerical_analysis.Bisection method) (mathematicskit.numerical_analysis.Broyden method) (mathematicskit.numerical_analysis.FixedPointIteration method) (mathematicskit.numerical_analysis.Halley method) (mathematicskit.numerical_analysis.IterativeRootFinder method) (mathematicskit.numerical_analysis.NewtonRaphson method) (mathematicskit.numerical_analysis.NewtonSystem method) (mathematicskit.numerical_analysis.Secant method) (mathematicskit.numerical_analysis.Steffensen method) (mathematicskit.pde.AdvectionEquation1D method) (mathematicskit.pde.BurgersConservationLaw1D method) (mathematicskit.pde.MethodOfLinesPDE method) (mathematicskit.pde.WaveEquation1D method)

solve_assignment() (in module mathematicskit.graph_theory) solve_laplace_2d() (in module mathematicskit.pde) solve_linear_diophantine() (in module mathematicskit.number_theory) solve_pell_equation() (in module mathematicskit.number_theory) solve_poisson_1d() (in module mathematicskit.pde) solve_poisson_2d() (in module mathematicskit.pde) solve_theta() (mathematicskit.pde.HeatEquation1D method) (mathematicskit.pde.HeatEquation2D method) solve_zero_sum_game() (in module mathematicskit.optimization) solver_result (mathematicskit.pde.EllipticSolution attribute) SOR (class in mathematicskit.linalg) spearman_correlation() (in module mathematicskit.statistics) spectral_analysis() (in module mathematicskit.graph_theory) SpectralResult (class in mathematicskit.graph_theory) sphere() (in module mathematicskit.topology) sphere_surface() (in module mathematicskit.geometry) sqrt() (mathematicskit.calculus.Dual method) sqrt_mod() (in module mathematicskit.number_theory) st_petersburg_certainty_equivalent() (in module mathematicskit.probability) st_petersburg_payoffs() (in module mathematicskit.probability) stability() (mathematicskit.pde.MethodOfLinesPDE method) stability_function() (in module mathematicskit.integrators) StabilityResult (class in mathematicskit.pde) stable (mathematicskit.ode_dynamics.FixedPointResult attribute) (mathematicskit.pde.StabilityResult attribute) standard_errors (mathematicskit.statistics.RegressionResult attribute) state (mathematicskit.fractals_chaos.CellularAutomaton attribute) state0 (mathematicskit.pde.MethodOfLinesPDE attribute) stationarity_residual (mathematicskit.optimization.KKTResult attribute) stationary_distribution() (mathematicskit.probability.MarkovChain method) stationary_distribution_power_iteration() (mathematicskit.probability.MarkovChain method) statistic (mathematicskit.statistics.HypothesisTestResult attribute) std (mathematicskit.probability.ContinuousDistribution property) (mathematicskit.probability.DiscreteDistribution property) (mathematicskit.statistics.DescriptiveStatsResult attribute) std_error (mathematicskit.probability.MonteCarloResult attribute) (mathematicskit.statistics.BootstrapResult attribute) (mathematicskit.statistics.JackknifeResult attribute) Steffensen (class in mathematicskit.numerical_analysis) stehfest_coefficients() (in module mathematicskit.special_functions) step (mathematicskit.calculus.DerivativeResult attribute) step() (mathematicskit.fractals_chaos.CellularAutomaton method) (mathematicskit.fractals_chaos.ElementaryCA method) (mathematicskit.fractals_chaos.GameOfLife method) (mathematicskit.pde.AdvectionEquation1D method) (mathematicskit.pde.BurgersConservationLaw1D method) stiff_integrate() (in module mathematicskit.integrators) stirling_factorial() (in module mathematicskit.special_functions) stirling_first_kind() (in module mathematicskit.combinatorics) stirling_log_gamma() (in module mathematicskit.special_functions) stirling_second_kind() (in module mathematicskit.combinatorics) stroboscopic_poincare_section() (in module mathematicskit.ode_dynamics) Subgroup (class in mathematicskit.abstract_algebra) subgroups (mathematicskit.abstract_algebra.SylowResult attribute) success (mathematicskit.integrators.BVPResult attribute) (mathematicskit.optimization.LeastSquaresResult attribute) (mathematicskit.optimization.LinearProgramResult attribute) sum_of_four_squares() (in module mathematicskit.number_theory) sum_of_powers() (in module mathematicskit.combinatorics) sum_of_two_squares() (in module mathematicskit.number_theory) surface_curvature() (in module mathematicskit.geometry) SurfaceClassification (class in mathematicskit.topology) SurfaceCurvatureResult (class in mathematicskit.geometry) svd_decompose() (in module mathematicskit.linalg) SVDResult (class in mathematicskit.linalg) swaps (mathematicskit.number_theory.LLLResult attribute) sylow_order (mathematicskit.abstract_algebra.SylowResult attribute) sylow_subgroups() (in module mathematicskit.abstract_algebra) SylowResult (class in mathematicskit.abstract_algebra) SystemRootResult (class in mathematicskit.numerical_analysis)

T

t (mathematicskit.geometry.CurveFrameResult attribute) T (mathematicskit.linalg.SchurResult attribute) t (mathematicskit.ode_dynamics.OdeTrajectory attribute) (mathematicskit.pde.PDESolution attribute) (mathematicskit.special_functions.FresnelResult attribute) t_statistics (mathematicskit.statistics.RegressionResult attribute) table (mathematicskit.abstract_algebra.CharacterTableResult attribute) (mathematicskit.optimization.KnapsackResult attribute) TailBoundResult (class in mathematicskit.probability) tangent (mathematicskit.geometry.CurveFrameResult attribute) TanhSinhQuadrature (class in mathematicskit.calculus) taylor_remainder_bound() (in module mathematicskit.calculus) terms (mathematicskit.abstract_algebra.MultivariatePolynomial attribute) (mathematicskit.number_theory.ContinuedFractionResult attribute) times (mathematicskit.probability.BrownianMotionResult attribute) (mathematicskit.probability.SDEResult attribute) (mathematicskit.special_functions.ScalogramResult attribute) to_sparse() (mathematicskit.graph_theory.Graph method) torsion (mathematicskit.geometry.CurveFrameResult attribute) (mathematicskit.topology.HomologyResult attribute) torus() (in module mathematicskit.topology) torus_surface() (in module mathematicskit.geometry) total_cost (mathematicskit.graph_theory.AssignmentResult attribute) total_degree (mathematicskit.abstract_algebra.MultivariatePolynomial property) total_variation() (in module mathematicskit.pde)

total_weight (mathematicskit.graph_theory.MSTResult attribute) tour (mathematicskit.optimization.TourResult attribute) tour_length() (in module mathematicskit.optimization) TourResult (class in mathematicskit.optimization) toy_float_system() (in module mathematicskit.numerical_analysis) trace_squared (mathematicskit.complex_analysis.MobiusClassification attribute) transfer_function() (in module mathematicskit.special_functions) transforms (mathematicskit.fractals_chaos.IteratedFunctionSystem attribute) TrapezoidalRule (class in mathematicskit.calculus) triangle (mathematicskit.topology.FixedPointResult attribute) triangle_grid() (in module mathematicskit.topology) TriangleGrid (class in mathematicskit.topology) triangles (mathematicskit.topology.TriangleGrid attribute) TriangulationResult (class in mathematicskit.geometry) truncation_error() (in module mathematicskit.calculus) tsp_held_karp() (in module mathematicskit.optimization) tsp_nearest_neighbor() (in module mathematicskit.optimization) tsp_two_opt() (in module mathematicskit.optimization) turan_graph() (in module mathematicskit.graph_theory) turan_number() (in module mathematicskit.graph_theory) turning_number() (in module mathematicskit.topology) turtle_path() (in module mathematicskit.fractals_chaos) two_sample_t_test() (in module mathematicskit.statistics) two_sample_z_test() (in module mathematicskit.statistics) typical_set() (in module mathematicskit.information_theory) TypicalSetResult (class in mathematicskit.information_theory)

U

u (mathematicskit.geometry.SurfaceCurvatureResult attribute) U (mathematicskit.linalg.LUResult attribute) (mathematicskit.linalg.SVDResult attribute) u (mathematicskit.pde.EllipticSolution attribute) (mathematicskit.pde.PDESolution attribute) U (mathematicskit.topology.SmithNormalFormResult attribute) u_x (mathematicskit.complex_analysis.CauchyRiemannResult attribute) u_y (mathematicskit.complex_analysis.CauchyRiemannResult attribute)

ulp() (in module mathematicskit.numerical_analysis) UnconstrainedOptimizer (class in mathematicskit.optimization) Uniform (class in mathematicskit.probability) uniform_grid() (in module mathematicskit.pde) union_size_inclusion_exclusion() (in module mathematicskit.combinatorics) upper (mathematicskit.calculus.ExhaustionResult attribute) (mathematicskit.statistics.BootstrapResult attribute) (mathematicskit.statistics.ConfidenceIntervalResult attribute) upper_bounds (mathematicskit.information_theory.ChannelCapacityResult attribute)

V

v (mathematicskit.geometry.SurfaceCurvatureResult attribute) V (mathematicskit.topology.SmithNormalFormResult attribute) v_x (mathematicskit.complex_analysis.CauchyRiemannResult attribute) v_y (mathematicskit.complex_analysis.CauchyRiemannResult attribute) value (mathematicskit.calculus.DerivativeResult attribute) (mathematicskit.calculus.QuadratureResult attribute) (mathematicskit.calculus.Variable attribute) (mathematicskit.numerical_analysis.FloatBits attribute) (mathematicskit.numerical_analysis.HornerResult attribute) (mathematicskit.optimization.GameResult attribute) (mathematicskit.optimization.KnapsackResult attribute) values (mathematicskit.topology.Filtration attribute) VanDerPolOscillator (class in mathematicskit.ode_dynamics) Variable (class in mathematicskit.calculus) variables() (mathematicskit.abstract_algebra.MultivariatePolynomial class method) variance (mathematicskit.probability.ContinuousDistribution property) (mathematicskit.probability.DiscreteDistribution property) (mathematicskit.statistics.DescriptiveStatsResult attribute) variance_confidence_interval() (in module mathematicskit.statistics)

vector_field_grid() (in module mathematicskit.ode_dynamics) vector_field_index() (in module mathematicskit.topology) velocity_verlet_integrate() (in module mathematicskit.integrators) velocity_verlet_step() (in module mathematicskit.integrators) verify_kkt() (in module mathematicskit.optimization) vertex_cover (mathematicskit.graph_theory.BipartiteMatchingResult attribute) vertical (mathematicskit.complex_analysis.MappedGrid attribute) vertical_image (mathematicskit.complex_analysis.MappedGrid attribute) vertices (mathematicskit.geometry.ConvexHullResult attribute) (mathematicskit.geometry.PolyhedronResult attribute) (mathematicskit.geometry.VoronoiResult attribute) (mathematicskit.topology.SimplicialComplex property) vietoris_rips_complex() (in module mathematicskit.topology) vietoris_rips_filtration() (in module mathematicskit.topology) violating_subset (mathematicskit.combinatorics.HallResult attribute) viterbi_decode() (in module mathematicskit.information_theory) volume (mathematicskit.geometry.ConvexHullResult attribute) voronoi_diagram() (in module mathematicskit.geometry) VoronoiResult (class in mathematicskit.geometry) Vt (mathematicskit.linalg.SVDResult attribute)

W

w (mathematicskit.complex_analysis.DomainColoringResult attribute) WaveEquation1D (class in mathematicskit.pde) wavelet (mathematicskit.special_functions.WaveletDecompositionResult attribute) wavelet_filters() (in module mathematicskit.special_functions) WaveletDecompositionResult (class in mathematicskit.special_functions) weierstrass_function() (in module mathematicskit.fractals_chaos) weight (mathematicskit.optimization.KnapsackResult attribute)

width() (mathematicskit.statistics.ConfidenceIntervalResult method) wiener (mathematicskit.probability.SDEResult attribute) wilcoxon_signed_rank_test() (in module mathematicskit.statistics) wilkinson_polynomial() (in module mathematicskit.numerical_analysis) winding_number() (in module mathematicskit.complex_analysis) winding_numbers (mathematicskit.complex_analysis.ResidueTheoremResult attribute) word() (mathematicskit.topology.FundamentalGroupPresentation method)

X

x (mathematicskit.integrators.BVPResult attribute) (mathematicskit.linalg.IterativeSolveResult attribute) (mathematicskit.number_theory.BezoutResult attribute) (mathematicskit.number_theory.PellResult attribute) X (mathematicskit.ode_dynamics.BendixsonResult attribute) x (mathematicskit.optimization.KKTResult attribute) (mathematicskit.optimization.LagrangeResult attribute) (mathematicskit.optimization.LeastSquaresResult attribute) (mathematicskit.optimization.LinearProgramResult attribute) (mathematicskit.optimization.OptimizeResult attribute) (mathematicskit.optimization.ScalarSearchResult attribute) (mathematicskit.pde.EllipticSolution attribute) (mathematicskit.pde.MethodOfLinesPDE attribute) (mathematicskit.pde.PDESolution attribute) (mathematicskit.special_functions.AiryResult attribute)

x0 (mathematicskit.number_theory.LinearDiophantineResult attribute) x_step (mathematicskit.number_theory.LinearDiophantineResult attribute)

Y

y (mathematicskit.integrators.BVPResult attribute) (mathematicskit.number_theory.BezoutResult attribute) (mathematicskit.number_theory.PellResult attribute) Y (mathematicskit.ode_dynamics.BendixsonResult attribute) y (mathematicskit.ode_dynamics.OdeTrajectory attribute) (mathematicskit.pde.EllipticSolution attribute) (mathematicskit.pde.MethodOfLinesPDE attribute) (mathematicskit.pde.PDESolution attribute)

y0 (mathematicskit.number_theory.LinearDiophantineResult attribute) y_step (mathematicskit.number_theory.LinearDiophantineResult attribute) yoshida4_integrate() (in module mathematicskit.integrators) yoshida4_step() (in module mathematicskit.integrators) YoungDiagram (class in mathematicskit.combinatorics) yule_walker() (in module mathematicskit.statistics)

Z

z (mathematicskit.complex_analysis.DomainColoringResult attribute) Z (mathematicskit.linalg.SchurResult attribute)

z_transform() (in module mathematicskit.special_functions) zero_reductions (mathematicskit.abstract_algebra.GroebnerResult attribute) zeros (mathematicskit.special_functions.PoleZeroResult attribute)