uconf.models.commutative

Commutative operad model.

For n >= 1, Com(n) is rank-one with trivial symmetric action and zero differential. Arity 0 is the zero module.

Classes

Commutative(n, base_ring)

Commutative operad component in fixed arity.

class uconf.models.commutative.Commutative(n, base_ring)

Bases: CombinatorialFreeModule

Commutative operad component in fixed arity.

Parameters:

n (int)

connectivity: ClassVar[int] = 0

All components live in non-negative degrees.

__init__(n, base_ring)

Initialize Com(n) over base_ring.

Parameters:

n (int)

arity()

Return the fixed arity of this operad component.

Return type:

int

static unit(base_ring)

Return the operadic unit in arity 1.

static unit_key()

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

Return type:

tuple

basis_iter(d)

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

Parameters:

d (int)

Return type:

Iterator[Element]

graded_basis

/home/runner/work/uconf/uconf/src/uconf/models/commutative.py (starting at line 94) Return the Family of all basis elements in degree d.

Type:

File

degree_on_basis(basis_element)

Return homological degree of one basis element.

Parameters:

basis_element (tuple)

Return type:

int

static compose(x, input, y)

Operadic composition x \circ_i y.

Parameters:

input (int)

Commutative.Element

alias of Element