dt#

Functions

flatten_nested_list(nested)

Recursively flatten a list of arbitrary depth into a flat list.

from_dt_notation(notation[, oriented])

Parse DT notation (knot or link) and return a diagram.

to_dt_notation(k)

Serialize a knot/link diagram to DT notation.
from_dt_notation(notation, oriented=False)#

Parse DT notation (knot or link) and return a diagram.

This currently parses and validates the input but does not finish the DT→diagram construction (the original code also stopped mid-way). For now, non-empty inputs raise a clear NotImplementedError instead of silently printing and returning None.

Accepts:

  • A string with rows separated by commas/semicolons/spaces (e.g. "4 -6 2" or "4 -6 2 ; 8 -10 12")

  • A list of ints (knot) → will be wrapped as a single-component link

  • A list of lists of ints (link)

Parameters:

  • notation (str | Iterable[int] | Iterable[Iterable[int]]) – DT notation (string or nested iterables of ints).

  • oriented (bool) – If True, returns an oriented diagram instance; if False, an unoriented one.

Returns:

PlanarDiagram | OrientedPlanarDiagram – Empty diagram if input is empty.

Raises:

  • ValueError – If parsing fails.

  • NotImplementedError – For non-empty inputs until the constructor is completed.

Notes

  • The unfinished part in the original code explored endpoint placement options but never built the final diagram. This version preserves behavior safely by raising a clear exception.

to_dt_notation(k)#

Serialize a knot/link diagram to DT notation.

For knots, returns a single tuple of signed odd labels. For links, returns a tuple of tuples (one per component), following the usual conventions: - Label even indices along the traversal at each crossing on the incoming over endpoint. - The sign of the paired odd label is positive/negative based on the local crossing orientation.

Parameters:

k – Planar or oriented diagram.

Returns:

tuple – For a knot, (l1, l2, ..., l_{2n}). For a link, ((...), (...), ...).

Raises:

ValueError – If the diagram is not a knot/link in a way compatible with DT.

Return type:

Tuple[Tuple[int, …], …] | Tuple[int, …]