Skip to main content
Back to top
Ctrl
+
K
Install
Tutorial
Reference
Examples
Search
Ctrl
+
K
GitHub
Search
Ctrl
+
K
Install
Tutorial
Reference
Examples
GitHub
Section Navigation
algorithms
alternating
alternating_crossings
is_alternating
is_face_alternating
canonical
closure
components_link
link_components
link_components_endpoints
number_of_link_components
connected_sum
cut_set
arc_cut_sets
cut_decomposition
cut_nodes
find_arc_cut_set
cycles
cycles
degree_sequence
degree_sequence
neighbour_sequence
disjoint_union
duality
arc_face_graph
dual_planar_diagram
join
bridge_join
crossing_join
naming
generate_node_names
multiple_unique_new_node_names
number_to_alpha
unique_new_node_name
orientation
all_orientations
orient
orient_edges
unorient
paths
bfs_shortest_path
path_from_endpoint
sanity
sanity_check
skein
crossing_to_vertex
smoothen_crossing
tangle
compose_tangles
is_integer_tangle
rotate
tangle_decompositions
tests
test_canonical
test_canonical
test_canonical_degenerate
test_canonical_degenerate_oriented
test_canonical_knots
test_canonical_knots_oriented
test_canonical_oriented
test_closure
test_closure
test_component_links
test_number_of_link_components
test_cut_set
test_arc_cut_set
test_cut_set_knotoid
test_cut_set_new
test_find_cut_sets
test_order_2
test_degree_sequence
test_deg_seq
test_disjoint_sum
test_disjoint_sum
test_unknots
test_features
test_bridges
test_orientation
test_orientation
test_skein
test_skein
test_sums
helper_test_connected_sum_on_knots
test_all_connected_sums
test_connected_sum
test_disjoint_sum
test_tangles
test_decompose
test_tangle_63
topology
bridges
edges
is_bridge
is_empty_diagram
is_kink
is_knot
is_knotoid
is_leaf
is_link
is_linkoid
is_loop
is_planar_graph
is_unknot
is_unlink
kink_region_iterator
kinks
leafs
loops
number_of_unknots
catalog
diagram_reader
diagram_writer
save_diagram_sets
save_diagrams
DiagramSetWriter
DiagramWriter
example
example_spatial_graph
handcuff_theta
oriented_trefoil
trefoil_knot
trefoil_theta
generate
generate_knot_diagrams
generate_simple_graphs
non_adjacent_combinations
graphs
bouquet
cycle_graph
handcuff_link
parallel_edges
path_graph
star_graph
theta_curve
wheel_graph
invariant_reader
load_invariant_table
invariant_writer
save_invariant_table
InvariantTableWriter
knot_tables
diagram_from_name
get_link_table
handcuff
knot
knot_invariants
knots
link
links
theta
thetas
tests
test_get_knot_by_names
test_get_knot_from_name
test_knot_table_invariants
compare_lazy_non_lazy
helper_lazy_load_diagram_table
helper_load_diagram_table
test_save_diagram_table
test_knots
test_get_knots
test_load_save_diagrams
test_read
test_read_write_diagram
test_read_write_diagram_sets
classes
convert
vertices_to_crossings
endpoint
Endpoint
IngoingEndpoint
OutgoingEndpoint
freezing
freeze
frozen
unfreeze
node
Node
planardiagram
planar_diagram_from_data
OrientedPlanarDiagram
PlanarDiagram
tests
test_endpoint
test_faces
test_faces
test_hopf
test_freezing
test_freeze
test_init
test_knot_name
test_nodes
test_remove_bivalent_vertex
views
ArcView
EndpointView
FaceView
FilteredNodeView
NodeView
drawing
circlepack
CirclePack
InvertAround
InvertPacking
NormalizePacking
acxyz
flower
place
testgrid
draw_matplotlib
average_color
canonically_rotate_layout
compute_PCA
draw
draw_from_layout
export_pdf
export_pdf_groups
export_png
get_style_from_style
to_color
Arrow
draw_tangle
add_corners_and_smoothen
angle_between_points
are_continuation
connect
crossings
draw
draw_smooth
integral
to_zigzag
TangleExpr
TangleProduct
TangleSum
ZigZag
dynamic_network
animate_simulation
plot_bead_frame
plot_force_history
plot_static_frame
simulation
Network
dynamic_simulation
init_network
icp
icp_complex
layout
bezier
circlepack_layout
tests
test_draw
test_draw_bonded
test_draw_bridges
test_draw_knot
test_draw_knotoid
test_draw_theta
test_thetas_sums
tutte_layout
tutte_layout
invariants
affine_index
affine_index_polynomial
alexander
alexander_polynomial
arrow
arrow_polynomial
disoriented_smoothing
bracket
bracket_polynomial
kauffman_bracket_skein_module
cache
Cache
homflypt
homflypt_polynomial
homflypt_polynomial_az
homflypt_polynomial_lm
homflypt_polynomial_vz
homflypt_polynomial_xyz
simplify_to_2_face
jones
jones_polynomial
kauffman
kauffman_polynomial
mock_alexander
mock_alexander_polynomial
module
Module
tests
test_homflypt
test_homflypt
test_jones
test_jones
test_tutte
test_deletion_contraction_cycle
test_deletion_contraction_parallel_edges
test_deletion_contraction_square_with_diagonal
test_yamada
test_thetas_recursive
test_yamada_examples_from_paper
test_yamada_moriuchi
test_yamada_reidemeister
tutte
deletion_contraction
tutte_polynomial
unplugging
writhe
yamada
yamada_polynomial
manipulation
attributes
clear_attributes
clear_diagram_attributes
clear_endpoint_attributes
clear_node_attributes
contract
contract_arc
insert
insert_arc
insert_arc2
insert_endpoint
insert_loop
insert_new_leaf
parallelize_arc
permute
permute_node
remove
remove_arc
remove_bivalent_vertex
remove_bivalent_vertices
remove_empty_nodes
remove_loops
remove_unknots
rewire
pull_and_plug_endpoint
replug_endpoint
swap_endpoints
subdivide
subdivide_arc
subdivide_arcs_around_node
subdivide_endpoint
subdivide_endpoint_by_crossing
symmetry
flip
mirror
tests
test_contract
test_contract_edge
test_contract_edge_attributes
test_insert
test_insert_attr
test_remove
test_remove_edge
notation
dispatcher
from_notation_dispatcher
to_notation_dispatcher
dt
from_dt_notation
to_dt_notation
em
from_condensed_em_notation
from_em_notation
to_condensed_em_notation
to_em_notation
native
from_knotpy_notation
to_knotpy_notation
pd
from_condensed_pd_notation
from_pd_notation
to_condensed_pd_notation
to_pd_notation
plantri
from_plantri_notation
to_plantri_notation
tests
test_notation
test_native_notation_from
test_native_notation_to
test_native_notation_to_from
test_plantri
test_from_plantri
reidemeister
choose_random_reidemeister_moves
detect_move_type
find_all_reidemeister_moves
make_all_reidemeister_moves
make_random_reidemeister_move
make_reidemeister_move
randomize_diagram
utils
algebra
laurent_polynomial_to_tuples
poly2str
reciprocal
str2poly
cache
Cache
chunked
combinatorics
combinations_with_limited_repetitions
iterable_depth
lexicographical_minimal_cyclic_rotation_shift
parted_permutations
union
decorators
total_ordering_from_compare
dict_utils
common_dict
compare_dicts
invert_dict
invert_dict_of_sets
invert_multi_dict
invert_nested_dict
ClassifierDict
JointDict
LazyEvalDict
LazyLoadDict
LazyLoadEvalDict
identitydict
disjoint_union_set
DisjointSetUnion
func_utils
min_elements_by
geometry
antipode
bisect
bisector
bounding_box
circle_through_points
inverse_point_through_circle
is_angle_between
middle
perpendicular_arc
perpendicular_arc_through_point
perpendicular_line
split
tangent_line
weighted_circle_center_mean
BoundingBox
Circle
CircularArc
Line
PolySegment
Segment
list_utils
flatten_nested_list
module
module
multiprogressbar
Bar
FakeBar
ProgressTracker
multiprogressbar2
Bar
FakeBar
ProgressBar
ProgressTracker
parsing
parse_arc
parse_arcs
parse_endpoint
parse_spaced_rows
universal_list_of_lists_parser
set_utils
powerset
LeveledSet
statistics
print_bar_chart
string_utils
multi_replace
nested_split
string_to_nested_tuple_with_prefixes
test
test_dict
test_dict
test_dsu
test_dsu
test_lazy_dict
test_lazy_eval
test_lazy_load
test_lazy_load_eval
test_module
test_module
test_parser
test_universal_list_of_lists_parser
test_set_utils
test_leveled_set
test_value_partitioner
mod2
mod3
test_value_partitioner
Reference
catalog
knot_tables
knots
knots
#
knots
(
crossings
:
int
|
tuple
[
int
,
int
]
|
None
=
None
)
#
On this page
knots()
