Index

A

abelian_description() (snappy.SymmetryGroup method) AbelianGroup (class in snappy) abelianization() (snappy.SymmetryGroup method) add_vertex_positions_to_horotriangles() (snappy.verify.ComplexCuspCrossSection method) alexander_matrix() (spherogram.Link method) alexander_poly() (spherogram.Link method) alexander_polynomial() (snappy.Manifold method) (snappy.Triangulation method) (spherogram.Link method)

all_crossings_oriented() (spherogram.Link method) all_normalized_translations() (snappy.verify.ComplexCuspCrossSection method) all_translations() (snappy.CuspNeighborhood method) alternating() (spherogram.Link method) AlternatingKnotExteriors (class in snappy)

B

backtrack() (spherogram.Link method) betti_number() (snappy.AbelianGroup method)

black_graph() (spherogram.Link method) braid_word() (spherogram.Link method) browse() (snappy.Manifold method)

C

canonical_retriangulation() (snappy.Manifold method) canonize() (snappy.Manifold method) CensusKnots (in module snappy) center() (snappy.SymmetryGroup method) certified_newton_iteration() (snappy.verify.IntervalNewtonShapesEngine static method) CertifiedShapesEngine (in module snappy.verify) character_variety_vars_and_polys() (snappy.HolonomyGroup method) check_against_manifold() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.Flattenings method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) check_cusp_development_exactly() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method) check_index() (snappy.CuspNeighborhood method) check_logarithmic_edge_equations_and_positivity() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method) check_logarithmic_gluing_equations_and_positively_oriented_tets() (in module snappy.verify.verifyHyperbolicity) check_polynomial_edge_equations_exactly() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method) chern_simons() (snappy.Manifold method) ClosedBraid (class in spherogram) coefficients (snappy.AbelianGroup attribute) commutator_subgroup() (snappy.SymmetryGroup method) complex_length() (snappy.HolonomyGroup method) complex_volume() (snappy.Manifold method) (snappy.ptolemy.coordinates.Flattenings method) complex_volume_numerical() (snappy.ptolemy.coordinates.PtolemyCoordinates method) ComplexCuspCrossSection (class in snappy.verify) ComplexSqrtLinCombination (class in snappy.verify.squareExtensions) compute_decomposition() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method) compute_solutions() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method) compute_tilts() (snappy.verify.RealCuspCrossSection method)

connected_sum() (spherogram.Link method) ConsistencyWithSnapPeaNumericalVerifyError ConsistencyWithSnapPeaType (class in snappy.verify.exceptions) copy() (snappy.Manifold method) (spherogram.Link method) cover() (snappy.Manifold method) cover_info() (snappy.Manifold method) covers() (snappy.Manifold method) cross_ratios() (snappy.ptolemy.coordinates.PtolemyCoordinates method) cross_ratios_numerical() (snappy.ptolemy.coordinates.PtolemyCoordinates method) crossing_entries() (spherogram.Link method) crossing_strands() (spherogram.Link method) CrossRatios (class in snappy.ptolemy.coordinates) CubicalNonorientableClosedCensus (in module snappy) CubicalNonorientableCuspedCensus (in module snappy) CubicalOrientableClosedCensus (in module snappy) CubicalOrientableCuspedCensus (in module snappy) cusp_area_matrix() (snappy.Manifold method) cusp_areas() (snappy.Manifold method) (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method) cusp_info() (snappy.Manifold method) cusp_neighborhood() (snappy.Manifold method) cusp_shapes() (snappy.verify.ComplexCuspCrossSection method) cusp_translations() (snappy.Manifold method) CuspConsistencyType (class in snappy.verify.exceptions) CuspDevelopmentExactVerifyError CuspDevelopmentType (class in snappy.verify.exceptions) CuspEquationExactVerifyError CuspEquationLogLiftNumericalVerifyError CuspEquationType (class in snappy.verify.exceptions) CuspNeighborhood (class in snappy)

D

deconnect_sum() (spherogram.Link method) degree_to_shapes() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method) dehn_fill() (snappy.Manifold method) determinant() (spherogram.Link method) diamond_coordinate() (snappy.ptolemy.coordinates.PtolemyCoordinates method) digraph() (spherogram.Link method) direct_product_description() (snappy.SymmetryGroup method) dirichlet_domain() (snappy.Manifold method) DirichletDomain (class in snappy)

DodecahedralNonorientableClosedCensus (in module snappy) DodecahedralNonorientableCuspedCensus (in module snappy) DodecahedralOrientableClosedCensus (in module snappy) DodecahedralOrientableCuspedCensus (in module snappy) drill() (snappy.Manifold method) DT_code() (snappy.Manifold method) (spherogram.Link method) dual_curves() (snappy.Manifold method) dual_graph() (spherogram.Link method)

E

edge_list() (snappy.DirichletDomain method) edge_valences() (snappy.Manifold method) EdgeEquationExactVerifyError EdgeEquationLogLiftNumericalVerifyError EdgeEquationType (class in snappy.verify.exceptions) elementary_divisors() (snappy.AbelianGroup method) ensure_disjoint_on_edges() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method) ensure_std_form() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method)

EquationType (class in snappy.verify.exceptions) evaluate_word() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) exactly_checked_canonical_retriangulation() (in module snappy.verify.verifyCanonical) ExactVerifyError expand_until_certified() (snappy.verify.IntervalNewtonShapesEngine method) (snappy.verify.KrawczykShapesEngine method) export_stl() (snappy.DirichletDomain method) exterior() (spherogram.Link method)

F

face_list() (snappy.DirichletDomain method) faces() (spherogram.Link method) filename_base() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method) filled_triangulation() (snappy.Manifold method) find() (snappy.database.ManifoldTable method) find_shapes_as_complex_sqrt_lin_combinations() (in module snappy.verify.squareExtensions)

Flattenings (class in snappy.ptolemy.coordinates) flattenings_numerical() (snappy.ptolemy.coordinates.PtolemyCoordinates method) Ford_domain() (snappy.CuspNeighborhood method) from_snappy_manifold() (snappy.ptolemy.coordinates.CrossRatios static method) from_tetrahedra_shapes_of_manifold() (snappy.ptolemy.coordinates.Flattenings class method) fromManifoldAndShapes() (snappy.verify.RealCuspCrossSection static method) fundamental_group() (snappy.Manifold method)

G

gap_string() (snappy.HolonomyGroup method) generators() (snappy.HolonomyGroup method) generators_in_originals() (snappy.HolonomyGroup method) get_displacement() (snappy.CuspNeighborhood method) get_manifold() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.Flattenings method) (snappy.ptolemy.coordinates.PtolemyCoordinates method)

get_order() (snappy.ptolemy.coordinates.Flattenings method) get_tie() (snappy.CuspNeighborhood method) get_zpq_triple() (snappy.ptolemy.coordinates.Flattenings method) gluing_equations() (snappy.Manifold method) gluing_equations_pgl() (snappy.Manifold method) goeritz_matrix() (spherogram.Link method)

H

has_finite_vertices() (snappy.Manifold method) has_obstruction() (snappy.ptolemy.coordinates.PtolemyCoordinates method) high_precision() (snappy.Manifold method) holonomy_matrix_entries() (snappy.Manifold method) HolonomyGroup (class in snappy) homological_longitude() (snappy.Manifold method) (snappy.Triangulation method)

homology() (snappy.Manifold method) horoballs() (snappy.CuspNeighborhood method) HoroTriangle (snappy.verify.ComplexCuspCrossSection attribute) (snappy.verify.RealCuspCrossSection attribute) HTLinkExteriors (in module snappy) hyperbolic_adjoint_torsion() (snappy.Manifold method) hyperbolic_SLN_torsion() (snappy.Manifold method) hyperbolic_torsion() (snappy.Manifold method)

I

IcosahedralNonorientableClosedCensus (in module snappy) IcosahedralOrientableClosedCensus (in module snappy) identify() (snappy.database.ManifoldTable method) (snappy.Manifold method) imag() (snappy.verify.squareExtensions.ComplexSqrtLinCombination method) in_radius() (snappy.DirichletDomain method) induced_representation() (snappy.ptolemy.coordinates.CrossRatios method) InequalityNumericalVerifyError init_hyperbolic_structure() (snappy.Manifold method) inside_view() (snappy.Manifold method) interval_checked_canonical_triangulation() (in module snappy.verify.verifyCanonical) interval_vector_is_contained_in() (snappy.verify.IntervalNewtonShapesEngine static method) (snappy.verify.KrawczykShapesEngine static method) interval_vector_mid_points() (snappy.verify.IntervalNewtonShapesEngine static method) (snappy.verify.KrawczykShapesEngine static method) interval_vector_union() (snappy.verify.IntervalNewtonShapesEngine static method) (snappy.verify.KrawczykShapesEngine static method) IntervalNewtonShapesEngine (class in snappy.verify) invariant_trace_field_gens() (snappy.Manifold method) is_abelian() (snappy.SymmetryGroup method)

is_alternating() (spherogram.Link method) is_amphicheiral() (snappy.SymmetryGroup method) is_dihedral() (snappy.SymmetryGroup method) is_direct_product() (snappy.SymmetryGroup method) is_full_group() (snappy.SymmetryGroup method) is_geometric() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) is_induced_from_psl2() (snappy.ptolemy.coordinates.CrossRatios method) is_invertible_knot() (snappy.SymmetryGroup method) is_isometric_to() (snappy.Manifold method) is_orientable() (snappy.Manifold method) is_planar() (spherogram.Link method) is_polyhedral() (snappy.SymmetryGroup method) is_pu_2_1_representation() (snappy.ptolemy.coordinates.CrossRatios method) is_real() (snappy.ptolemy.coordinates.CrossRatios method) is_S5() (snappy.SymmetryGroup method) is_two_bridge() (snappy.Manifold method) isometries() (snappy.SymmetryGroup method) isometry_signature() (snappy.Manifold method) isomorphisms_to() (snappy.Manifold method) IsZeroExactVerifyError

J

jones_polynomial() (spherogram.Link method)

K

keys() (snappy.database.ManifoldTable method) KLPProjection() (spherogram.Link method) knot_floer_homology() (spherogram.Link method)

knot_group() (spherogram.Link method) krawczyk_interval() (snappy.verify.KrawczykShapesEngine method) KrawczykShapesEngine (class in snappy.verify)

L

length_spectrum() (snappy.Manifold method) length_spectrum_dicts() (snappy.DirichletDomain method) lift_vertex_positions_of_horotriangles() (snappy.verify.ComplexCuspCrossSection method) Link (class in spherogram) link() (snappy.Manifold method) LinkExteriors (in module snappy) linking_matrix() (spherogram.Link method) linking_number() (spherogram.Link method)

log_gluing_LHS_derivatives() (snappy.verify.IntervalNewtonShapesEngine static method) (snappy.verify.KrawczykShapesEngine method) log_gluing_LHS_derivatives_sparse() (snappy.verify.KrawczykShapesEngine method) log_gluing_LHSs() (snappy.verify.IntervalNewtonShapesEngine static method) (snappy.verify.KrawczykShapesEngine method) LogLiftNumericalVerifyError long_edge() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) longitude() (snappy.HolonomyGroup method)

M

magma_string() (snappy.HolonomyGroup method) Manifold (class in snappy) manifold() (snappy.CuspNeighborhood method) (snappy.DirichletDomain method) ManifoldTable (class in snappy.database) mat_solve() (snappy.verify.IntervalNewtonShapesEngine static method) matrix_times_sparse() (snappy.verify.KrawczykShapesEngine static method) max_reach() (snappy.CuspNeighborhood method) meridian() (snappy.HolonomyGroup method) middle_edge() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) mirror() (spherogram.Link method) module snappy snappy.ptolemy snappy.snap snappy.verify snappy.verify.exceptions snappy.verify.squareExtensions spherogram

morse_diagram() (spherogram.Link method) morse_number() (spherogram.Link method) move_fixed_point_to_zero() (snappy.verify.ComplexCuspCrossSection method) move_lifted_vertex_positions_to_zero_first() (snappy.verify.ComplexCuspCrossSection method) multiply_and_simplify_terms_in_RUR() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) multiply_elements() (snappy.SymmetryGroup method) multiply_terms_in_RUR() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method)

N

N() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.Flattenings method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) name() (snappy.Manifold method) newton_iteration() (snappy.verify.IntervalNewtonShapesEngine static method) next() (snappy.AlternatingKnotExteriors method) (snappy.NonalternatingKnotExteriors method) NonalternatingKnotExteriors (class in snappy) NonorientableClosedCensus (in module snappy) NonorientableCuspedCensus (in module snappy) NonZeroDimensionalComponent (class in snappy.ptolemy.component) normal_boundary_slopes() (snappy.Manifold method) (snappy.Triangulation method) normal_surfaces() (snappy.Manifold method) (snappy.Triangulation method) normalize_cusps() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method)

num_cusps() (snappy.CuspNeighborhood method) (snappy.Manifold method) num_edges() (snappy.DirichletDomain method) num_faces() (snappy.DirichletDomain method) num_finite_vertices() (snappy.DirichletDomain method) num_generators() (snappy.HolonomyGroup method) num_ideal_vertices() (snappy.DirichletDomain method) num_original_generators() (snappy.HolonomyGroup method) num_relators() (snappy.HolonomyGroup method) num_tetrahedra() (snappy.Manifold method) (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.Flattenings method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) num_vertices() (snappy.DirichletDomain method) number_field() (snappy.ptolemy.coordinates.PtolemyCoordinates method) numerical() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) NumericalVerifyError

O

O31() (snappy.HolonomyGroup method) OctahedralNonorientableCuspedCensus (in module snappy) OctahedralOrientableCuspedCensus (in module snappy) optimize_overcrossings() (spherogram.Link method) order() (snappy.AbelianGroup method) (snappy.SymmetryGroup method)

OrientableClosedCensus (in module snappy) OrientableCuspedCensus (in module snappy) orientation_cover() (snappy.Manifold method) original_generators() (snappy.HolonomyGroup method) original_index() (snappy.CuspNeighborhood method) out_radius() (snappy.DirichletDomain method) overstrands() (spherogram.Link method)

P

pairing_matrices() (snappy.DirichletDomain method) PD_code() (spherogram.Link method) peer_code() (spherogram.Link method) peripheral_curves() (snappy.HolonomyGroup method) pickle() (snappy.Manifold method) plink() (snappy.Manifold method) polished_holonomy() (snappy.Manifold method)

polyhedral_description() (snappy.SymmetryGroup method) ptolemy_generalized_obstruction_classes() (snappy.Manifold method) ptolemy_obstruction_classes() (snappy.Manifold method) ptolemy_variety() (snappy.Manifold method) PtolemyCoordinates (class in snappy.ptolemy.coordinates) PtolemyVariety (class in snappy.ptolemy.ptolemyVariety) py_eval_section() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method)

R

random_link() (in module spherogram) randomize() (snappy.Manifold method) rank() (snappy.AbelianGroup method) ratio_coordinate() (snappy.ptolemy.coordinates.PtolemyCoordinates method) reach() (snappy.CuspNeighborhood method)

read_tilts() (snappy.verify.RealCuspCrossSection method) real() (snappy.verify.squareExtensions.ComplexSqrtLinCombination method) RealCuspCrossSection (class in snappy.verify) relators() (snappy.HolonomyGroup method) reverse_orientation() (snappy.Manifold method)

S

sage() (snappy.HolonomyGroup method) sage_link() (spherogram.Link method) save() (snappy.DirichletDomain method) (snappy.Manifold method) scale_cusps() (snappy.verify.ComplexCuspCrossSection method) (snappy.verify.RealCuspCrossSection method) seifert_matrix() (spherogram.Link method) set_displacement() (snappy.CuspNeighborhood method) set_name() (snappy.Manifold method) set_peripheral_curves() (snappy.Manifold method) set_target_holonomy() (snappy.Manifold method) set_tetrahedra_shapes() (snappy.Manifold method) set_tie() (snappy.CuspNeighborhood method) ShapePositiveImaginaryPartNumericalVerifyError ShapeType (class in snappy.verify.exceptions) short_edge() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) short_slopes() (snappy.Manifold method) siblings() (snappy.database.ManifoldTable method) sign() (snappy.verify.squareExtensions.SqrtLinCombination method) sign_with_interval() (snappy.verify.squareExtensions.SqrtLinCombination method) signature() (spherogram.Link method) simplify() (snappy.Manifold method) (spherogram.Link method) SL2C() (snappy.HolonomyGroup method) slice_obstruction_HKL() (snappy.Manifold method) (snappy.Triangulation method)

snappy module snappy.ptolemy module snappy.snap module snappy.verify module snappy.verify.exceptions module snappy.verify.squareExtensions module solution_type() (snappy.Manifold method) solutions_from_magma() (in module snappy.ptolemy) solutions_from_magma_file() (in module snappy.ptolemy) spherogram module spine_radius() (snappy.DirichletDomain method) split() (snappy.Manifold method) split_link_diagram() (spherogram.Link method) splitting_surfaces() (snappy.Manifold method) SqrtLinCombination (class in snappy.verify.squareExtensions) stopper() (snappy.CuspNeighborhood method) stopping_displacement() (snappy.CuspNeighborhood method) sublink() (spherogram.Link method) symmetric_triangulation() (snappy.Manifold method) symmetry_group() (snappy.Manifold method) SymmetryGroup (class in snappy)

T

tetrahedra_field_gens() (snappy.Manifold method) tetrahedra_shapes() (snappy.Manifold method) TetrahedralNonorientableCuspedCensus (in module snappy) TetrahedralOrientableCuspedCensus (in module snappy) TiltInequalityNumericalVerifyError TiltIsZeroExactVerifyError TiltProvenPositiveNumericalVerifyError TiltType (class in snappy.verify.exceptions) to_magma() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method)

to_magma_file() (snappy.ptolemy.ptolemyVariety.PtolemyVariety method) to_PUR() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method) topology() (snappy.CuspNeighborhood method) trace_field_gens() (snappy.Manifold method) translations() (snappy.CuspNeighborhood method) Triangulation (class in snappy) triangulation() (snappy.CuspNeighborhood method) (snappy.DirichletDomain method) triangulation_isosig() (snappy.Manifold method)

U

use_field_conversion() (snappy.CuspNeighborhood method) (snappy.DirichletDomain method) (snappy.HolonomyGroup class method) (snappy.Manifold method)

V

verified_canonical_retriangulation() (in module snappy.verify) verify_hyperbolicity() (snappy.Manifold method) VerifyErrorBase vertex_list() (snappy.DirichletDomain method) view() (snappy.CuspNeighborhood method) (snappy.DirichletDomain method) (spherogram.Link method)

volume() (snappy.CuspNeighborhood method) (snappy.DirichletDomain method) (snappy.Manifold method) volume_numerical() (snappy.ptolemy.coordinates.CrossRatios method) (snappy.ptolemy.coordinates.PtolemyCoordinates method)

W

white_graph() (spherogram.Link method) with_hyperbolic_structure() (snappy.Manifold method)

without_hyperbolic_structure() (snappy.Manifold method) writhe() (spherogram.Link method)

X

x_coordinate() (snappy.ptolemy.coordinates.CrossRatios method)