uconf.models.associative

Associative operad model on permutation basis elements.

The component in arity n is the free module on S_n (for n >= 1), with zero differential.

Classes

Associative(n, base_ring)

Associative operad component in fixed arity.
class uconf.models.associative.Associative(n, base_ring)[source]

Bases: CombinatorialFreeModule

Associative operad component in fixed arity.

Parameters:

n (int)

connectivity: ClassVar[int] = 0

All components live in non-negative degrees.

__init__(n, base_ring)[source]

Initialize Ass(n) over base_ring.

Parameters:

n (int)

arity()[source]

Return the fixed arity of this operad component.

Return type:

int

static unit(base_ring)[source]

Return the operadic unit in arity 1.

static unit_key()[source]

Return the basis key of the unit element in arity 1.

Return type:

tuple

basis_iter(d)[source]

Iterate over basis elements in this arity and the given degree.

Parameters:

d (int)

Return type:

Iterator[Element]

planar_basis_iter(d)[source]

Iterate over planar basis elements in this arity and the given degree.

Parameters:

d (int)

Return type:

Iterator[Element]

graded_basis[source]

/home/runner/work/uconf/uconf/src/uconf/models/associative.py (starting at line 115) Return the Family of all basis elements in degree d.

Type:

File

graded_planar_basis[source]

/home/runner/work/uconf/uconf/src/uconf/models/associative.py (starting at line 120) Return the Family of planar basis elements in degree d.

Type:

File

degree_on_basis(basis_element)[source]

Return homological degree of one basis element.

Parameters:

basis_element (tuple)

Return type:

int

static compose(x, input, y)[source]

Operadic composition x \circ_i y.

Parameters:
Associative.Element[source]

alias of Element