mathematicskit 0.6.0

Added

• mathematicskit.topology, an 18th domain:

  • SimplicialComplex, with signed boundary matrices, links, skeleta,
    induced subcomplexes, unions and intersections.
  • Triangulations: simplex, sphere, circle, torus,
    klein_bottle, mobius_strip and projective_plane.
  • Constructions: barycentric_subdivision and simplicial_product.
  • Homology: smith_normal_form (SmithNormalFormResult),
    betti_numbers over Q or Z/p, homology with torsion
    (HomologyResult), and mayer_vietoris (MayerVietorisResult).
  • The fundamental group: fundamental_group
    (FundamentalGroupPresentation) and abelianization.
  • Surfaces: is_orientable, boundary_components, classify_surface
    (SurfaceClassification), and critical_points
    (CriticalPointsResult).
  • Fixed points: triangle_grid, random_sperner_labeling,
    is_sperner_labeling, fully_labeled_triangles,
    brouwer_fixed_point (FixedPointResult), vector_field_index,
    and lefschetz_number.
  • Curves: linking_number and turning_number.
  • Point clouds: vietoris_rips_complex, vietoris_rips_filtration,
    cech_complex, lower_star_filtration (Filtration), and
    mapper_graph (MapperResult).
  • Persistence: persistent_homology (PersistenceDiagram) and
    bottleneck_distance.
  • Utilities: clique_simplices, rank_mod_p and
    planar_betti_numbers.
  • Visualizers: plot_complex, plot_persistence_diagram,
    plot_barcode and plot_mapper_graph.

  Its history page has 22 breakthroughs, from Gauss's linking number
  (1833) to Mapper (2007), each with its own gallery example.

• mathematicskit.information_theory, a 17th domain: entropy,
  binary_entropy, joint_entropy, conditional_entropy,
  mutual_information, kl_divergence and hartley_information (via
  scipy.stats.entropy); source coding with typical_set,
  kraft_sum, canonical_code, shannon_fano_code, huffman_code
  (returning a PrefixCode), elias_gamma_encode/elias_gamma_decode,
  arithmetic_encode/arithmetic_decode/arithmetic_intervals and
  lz78_encode/lz78_decode/lz78_compressed_bits; channels with
  bsc_capacity, bec_capacity, awgn_capacity, minimum_ebn0,
  blahut_arimoto (ChannelCapacityResult), random_code_error_rate,
  rate_distortion_binary and rate_distortion_gaussian; channel codes
  with hamming_encode/hamming_decode, convolutional_encode,
  viterbi_decode, gallager_ldpc_matrix and bit_flip_decode
  (BitFlipResult); bsc_transmit and hamming_distance; and the
  plot_code_tree and plot_information_diagram visualizers. Its
  history page has 20 breakthroughs, from Hartley (1928) to Lempel-Ziv
  (1977-1978), each with its own gallery example.

• Markov chain Monte Carlo in mathematicskit.probability:
  metropolis_hastings (random-walk or general asymmetric proposals with
  the Hastings correction) and gibbs_sampler, returning an
  MCMCResult, plus integrated_autocorrelation_time and
  chain_effective_sample_size for correlated chains.

• Stochastic differential equations in mathematicskit.probability:
  euler_maruyama, geometric_brownian_motion (exact Itô solution or
  Euler-Maruyama on the same Brownian path) and ornstein_uhlenbeck,
  returning an SDEResult.

• mathematicskit.statistics.principal_component_analysis via
  numpy.linalg.svd (PCAResult), and time series: autocorrelation,
  yule_walker (AR(p) fitting by scipy.linalg.solve_toeplitz,
  ARModelResult), simulate_ar and ar_autocorrelation.

• mathematicskit.graph_theory.eulerian_circuit, eulerian_trail and
  odd_degree_vertices: Hierholzer's algorithm, for undirected and
  directed graphs.

• In mathematicskit.optimization: simulated_annealing; the travelling
  salesman problem (tsp_nearest_neighbor, tsp_two_opt, the exact
  tsp_held_karp, distance_matrix, tour_length, TourResult); and
  interior_point_lp, a primal-dual path-following LP solver that
  records the central path. linear_program takes a new method
  argument (default "highs", unchanged) to select HiGHS's simplex or
  interior-point solver.

• In mathematicskit.number_theory: EllipticCurve (group law, point
  multiplication and counting over GF(p)) and Lenstra's lenstra_ecm
  (ECMResult); lll_reduce (exact-rational LLL, LLLResult) and
  integer_relation.

• In mathematicskit.abstract_algebra: conjugacy_classes and
  character_table (Burnside's algorithm, CharacterTableResult);
  MultivariatePolynomial over Q or GF(p) with lex/grlex/grevlex
  orders, multivariate_divide, s_polynomial, groebner_basis
  (Buchberger's algorithm, reduced basis, GroebnerResult) and
  in_ideal.

• History breakthroughs, each with its own gallery example: Itô and
  Maruyama's stochastic differential equations (1944-1955) and
  Metropolis-Hastings and the Gibbs sampler (1970-1984) in probability;
  Pearson and Hotelling's principal components (1901-1933) and Yule's
  autoregressive model (1927) in statistics; Hierholzer's Eulerian
  circuits (1873) in graph theory; Held and Karp's travelling salesman
  algorithm (1962), simulated annealing (1983) and Karmarkar's
  interior-point method (1984) in optimization; LLL lattice reduction
  (1982) and Lenstra's elliptic-curve factorization (1987) in number
  theory; and Frobenius's group characters (1896) and Buchberger's
  Gröbner bases (1965) in abstract algebra.

• Animations of the algorithms at work, each an animate_* visualizer
  that takes a result and returns a matplotlib.animation.FuncAnimation:
  numerical_analysis.visualizers.animate_root_finding (Newton's
  tangents against bisection's bracket, with the errors side by side),
  optimization.visualizers.animate_optimizer_paths (iterate paths over
  the contours, frames spaced geometrically in the iteration count),
  linalg.visualizers.animate_power_iteration,
  pde.visualizers.animate_solution (1D curves or 2D fields, with an
  optional exact-solution overlay),
  fractals_chaos.visualizers.animate_life, and
  ode_dynamics.visualizers.animate_logistic_cobweb (the cobweb as r
  grows, beside the bifurcation diagram). Seven new gallery examples
  play them, and the gallery now embeds animations as JavaScript
  players (to_jshtml), so neither the docs build nor JupyterLite needs
  ffmpeg.

• Bisection records the bracket behind each midpoint in
  extra["brackets"], and power_iteration records every iterate in
  extra["vectors"].

• The README and the docs home page show how to install from
  conda-forge (conda install -c conda-forge mathematicskit numba).