Arcs class

wrapper for arc representation of tangles

Constructors, destructors, conversion operators

Arcs(std::vector<TE> arcs)
standard constructor
Arcs(TE size)
constructor of the identity tangle with 'size' strands

Public functions

void addCap(const TE& i)
add two extra ends before the $i^\text{th}$ tangle end and connect them by an arc.
void addCup(const TE& i)
join the $i^\text{th}$ tangle end to the next and removing the new closed component if there is one.
auto addCupGCC(const TE& i) const -> bool
true if the two ends were connected (=new closed component); false if the two ends belonged to different arcs
auto check() const -> bool
true if the object is a well-defined crossingless tangle
auto components_to(const Arcs& a2) const -> IndexLL
list of components from one crossingless tangle to another
auto operator!=(const Arcs& arcs2) const -> bool
true if idempotents differ (ignore gradings)
auto operator==(const Arcs& arcs2) const -> bool
true if idempotents coincide (ignore gradings)
auto pairs() const -> std::vector<std::pair<TE, TE>>
converts arc-format (Arcs) into pair-format, which consists of all pairs $(i,j)$ with $i<j$ for which the tangle connects the tangle ends $i$ to $j$ .
void print() const
print representative of a cobordism object in terminal
void rotate(const TE& top)
convert arcs by rotating the first 'top' tangle ends : Arcs representing a one-sided tangle with 0 top tangle ends are converted into arcs representing a two-sided tangle with 'top' top tangle strands and vice versa. This is done by rotating the first 'top' tangle strands by 180 degrees. This function does not check, if the input arcs are valid. It simply reverses the order of the first 'top' elements and then relabels the entries if they are < 'top'.
auto to_string() const -> std::string
string representative of a cobordism object

Friends

void expand_gens_if_needed(const int& n)
computes more entries for PCA::gens if PCA::max_strands < n
void expand_vec_if_needed(const int& n)
computes more entries for PCA::vec if PCA::max < n