Interval exchange transformations¶
Permutations¶
- Interval exchange constructors
- Permutation template
FlippedPermutationFlippedPermutationIETFlippedPermutationLIFlippedRauzyDiagramOrientablePermutationIETOrientablePermutationIET.arf_invariant()OrientablePermutationIET.attached_in_degree()OrientablePermutationIET.attached_out_degree()OrientablePermutationIET.backward_rauzy_move()OrientablePermutationIET.decompose()OrientablePermutationIET.erase_marked_points()OrientablePermutationIET.genus()OrientablePermutationIET.heights_cone()OrientablePermutationIET.intersection_matrix()OrientablePermutationIET.invariant_density_rauzy()OrientablePermutationIET.is_cylindric()OrientablePermutationIET.is_hyperelliptic()OrientablePermutationIET.is_identity()OrientablePermutationIET.is_standard()OrientablePermutationIET.marked_profile()OrientablePermutationIET.marking()OrientablePermutationIET.masur_polygon()OrientablePermutationIET.order_of_rauzy_action()OrientablePermutationIET.profile()OrientablePermutationIET.rauzy_move()OrientablePermutationIET.stratum()OrientablePermutationIET.stratum_component()OrientablePermutationIET.suspension_cone()OrientablePermutationIET.to_cylindric()OrientablePermutationIET.to_origami()OrientablePermutationIET.to_permutation()OrientablePermutationIET.to_standard()
OrientablePermutationLIPermutationPermutation.alphabet()Permutation.cover()Permutation.flips()Permutation.horizontal_inverse()Permutation.interval_diagram()Permutation.left_right_inverse()Permutation.length()Permutation.length_bottom()Permutation.length_top()Permutation.letters()Permutation.lr_inverse()Permutation.regular_cover()Permutation.str()Permutation.symmetric()Permutation.tb_inverse()Permutation.top_bottom_inverse()Permutation.vertical_inverse()
PermutationIETPermutationLIPermutationLI.erase_marked_points()PermutationLI.genus()PermutationLI.has_rauzy_move()PermutationLI.is_cylindric()PermutationLI.is_hyperelliptic()PermutationLI.is_irreducible()PermutationLI.marked_profile()PermutationLI.marking()PermutationLI.orientation_cover()PermutationLI.profile()PermutationLI.stratum_component()PermutationLI.to_cylindric()PermutationLI.twin()PermutationLI.twin_list()
RauzyDiagramRauzyDiagram.PathRauzyDiagram.alphabet()RauzyDiagram.cardinality()RauzyDiagram.complete()RauzyDiagram.edge_iterator()RauzyDiagram.edge_to_loser()RauzyDiagram.edge_to_matrix()RauzyDiagram.edge_to_winner()RauzyDiagram.edge_types()RauzyDiagram.edge_types_index()RauzyDiagram.edges()RauzyDiagram.graph()RauzyDiagram.letters()RauzyDiagram.path()RauzyDiagram.vertex_iterator()RauzyDiagram.vertices()
cylindric_canonical()interval_conversion()labelize_flip()side_conversion()to_fat_graphs()
- Labelled permutations
- Reduced permutations
- Rauzy class cardinality
bidecompositions()c()check_marking()check_std_marking()collapse()d()delta_irr()delta_std()gamma_irr()gamma_std()marking_iterator()number_of_irreducible_permutations()number_of_standard_permutations()spin_difference_for_irreducible_permutations()spin_difference_for_standard_permutations()split()
- Covering construction
PermutationCoverPermutationCover.automorphism_groupPermutationCover.base()PermutationCover.covering_data()PermutationCover.covering_data_tuple()PermutationCover.degree()PermutationCover.genus()PermutationCover.groupPermutationCover.interval_diagram()PermutationCover.is_orientable()PermutationCover.isotypic_projection_matrix()PermutationCover.isotypic_projectors()PermutationCover.lyapunov_exponents_H_plus()PermutationCover.masur_polygon()PermutationCover.monodromyPermutationCover.profile()PermutationCover.stratum()
RegularCoverto_gap()
Interval exchange transformations¶
- Interval exchange transformations
IntervalExchangeTransformationIntervalExchangeTransformation.backward_rauzy_move()IntervalExchangeTransformation.base_ring()IntervalExchangeTransformation.domain_singularities()IntervalExchangeTransformation.erase_marked_points()IntervalExchangeTransformation.in_which_interval()IntervalExchangeTransformation.inverse()IntervalExchangeTransformation.is_identity()IntervalExchangeTransformation.length()IntervalExchangeTransformation.lengths()IntervalExchangeTransformation.normalize()IntervalExchangeTransformation.permutation()IntervalExchangeTransformation.plot()IntervalExchangeTransformation.plot_function()IntervalExchangeTransformation.plot_towers()IntervalExchangeTransformation.plot_two_intervals()IntervalExchangeTransformation.range_singularities()IntervalExchangeTransformation.rauzy_move()IntervalExchangeTransformation.recoding()IntervalExchangeTransformation.sah_arnoux_fathi_invariant()IntervalExchangeTransformation.show()IntervalExchangeTransformation.singularities()IntervalExchangeTransformation.translations()IntervalExchangeTransformation.vector_space()IntervalExchangeTransformation.zorich_move()
wedge()
- Integral interval exchanges
- Interval exchange families
- Flip sequences
IETFlipSequenceIETFlipSequence.close()IETFlipSequence.dual_substitution()IETFlipSequence.end()IETFlipSequence.find_closure()IETFlipSequence.interval_substitution()IETFlipSequence.is_closed()IETFlipSequence.is_complete()IETFlipSequence.is_full()IETFlipSequence.is_loop()IETFlipSequence.left_right_inverse()IETFlipSequence.losers()IETFlipSequence.matrix()IETFlipSequence.orbit_substitution()IETFlipSequence.rauzy_move()IETFlipSequence.relabel()IETFlipSequence.self_similar_iet()IETFlipSequence.self_similar_interval_exchange_transformation()IETFlipSequence.start()IETFlipSequence.substitution()IETFlipSequence.top_bottom_inverse()IETFlipSequence.winners()IETFlipSequence.winners_losers()