pysiglib.trees_of_order

pysiglib.trees_of_order#

trees_of_order(dimension, order, *, planar=False)[source]#

Returns all basis elements with exactly order nodes.

For planar=False these are non-planar decorated rooted trees. For planar=True these are ordered forests of decorated planar rooted trees, with order equal to the total number of nodes in the forest. The order matches the native pySigLib coefficient layout.

Parameters:

  • dimension (int) – Path dimension (alphabet size).

  • order (int) – Exact number of nodes.

  • planar (bool) – If True, enumerate ordered forests of planar rooted trees.

Returns:

Tuple of basis elements as tuples in native pySigLib convention.

Return type:

tuple[tuple]

Example:#

import pysiglib

# All single-node trees over dimension 2
t = pysiglib.trees_of_order(2, 1)
print(t) # ((0,), (1,))

Citation#

If you found this library useful in your research, please consider citing the paper:

@article{shmelev2025pysiglib,
  title={pySigLib-Fast Signature-Based Computations on CPU and GPU},
  author={Shmelev, Daniil and Salvi, Cristopher},
  journal={arXiv preprint arXiv:2509.10613},
  year={2025}
}
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