Tangle class

#include <sources/headers/Tangles.h>

Constructors, destructors, conversion operators

Tangle(const File& file)

construct tangle from File file

Tangle(std::string input, Cut top_orient, bool auto_correct = true)

standard constructor

Public functions

auto add(const std::string& twists) const -> Tangle

add a tangle twists to the bottom of the tangle. The format of twists is as the first component of tangle_input.

auto bot_orient() const -> std::vector<bool>

bottom Cut

template<typename Coeff>

auto CobComplex(Complex<CobObj, CobMor, Coeff> cx = {}, const bool& with_feedback = true) const -> Complex<CobObj, CobMor, Coeff>

computes the cobordism complex for a tangle

auto complete_symmetry() const -> Tangle

completes a symmetric knot to a full knot

auto complexity() const -> size_t

complexity of the tangle; equal to the sum of the cubes of the lengths of all cuts

void doubled()

double each strand of a tangle diagram. For example, this can be used to generate four-ended tangles from 1-1-knots. For those knots, the framing of the resulting cap-trivial tangle is chosen such that the linking number between the two strands is 0 and the -filling is the unknot filling.

auto draw_svg_orient(const Cut& cut, const int& ycoord, const int& pref_orient = 2) const -> std::string

svg-string adding orientations according to cut at the y-coordinate ycoord ; pref_orient is the preferred orientation, which is 0 (down), 1 (up) or 2 (both).

auto draw_svg_slice(const unsigned int& si, const unsigned int& level) const -> std::string

svg-string for a single slice

auto draw_svg_slice_fill(const std::vector<Slice>& sliceL, const unsigned int& max, const unsigned int& level) const -> std::string

svg-string adding all vertical strands in a slice with a crossing

void flip_orient_at_index(int i)

changes the orientation of the strand at the index i at the bottom of the tangle, counted from the left, starting with 0

auto is_symmetric() const -> bool

true iff symmetry is true

auto n_ended(const size_t& n) -> bool

true if tangle is n-ended and has at least one top tangle end (which is the reduction point) and one bottom tangle end

void print(const bool& orient = 1) const

prints a string represenation of a tangle into the terminal. orient is as in to_string().

auto quotient() const -> Tangle

computes the quotient of a symmetric knot under a strong inversion

void record_new_orientations(const File& file) const

adds a comment to file which records the top Cut; this is used if the input tangle was inconsistent and the constructor changed the top cut to fix orientations.

void simplify_diagram()

attempt to simplify a tangle diagram. This is currently only implemented for non-symmetric tangles. This function relies on simplify().

auto tanglestring() const -> std::string

convert tangle back into input string, the first component of tangle_input

void to_file(const File& file) const

generates a file file.kht which specifies the tangle in the format tangle_input and adds metadata

auto to_string(const int& index, const bool& orient) const -> std::string

string representation of a single slice of the tangle. If orient is 1, all strands are oriented, otherwise only the orientations of caps (↶/↷) are included.

void to_svg(const std::string& metadata, const std::string& name, const bool& orient = false, const bool& transparent = false) const

create svg file of the tangle diagram

auto top_orient() const -> std::vector<bool>

top Cut

auto writhe() const -> int

signed number of crossings

Function documentation