monomial.py

from pymwp import Monomial

Monomial

Monomial(
    scalar: str = UNIT_MWP,
    deltas: Optional[Union[List[DELTA], DELTA]] = None,
    *args: Optional[DELTA]
)

A monomial is a pair made of:

1. scalar - a value in the semi-ring
2. a sorted list of deltas, where an index occurs at most once.

Deltas are coded as pairs \((i,j)\) with:

• \(i\) the value and
• \(j\) the index in the domain (infinite product)

We will have that \((i,j)\) will be equal to the unit of the semi-ring iff the \(j^{th}\) input is equal to \(i\) (so, the \(j^{th}\) choice is \(i\)).

We will make the assumption that the deltas of delta is sorted and no two deltas can have the same index.

Attributes:

Name	Type	Description
scalar	str	Monomial scalar.
deltas	List[DELTA]	List of deltas.

Create a monomial.

Example

Create a monomial.

mono = Monomial()

Create monomial with scalar \(m\) explicitly.

mono = Monomial('m')

Create monomial with scalar \(w\) and two deltas.

mono = Monomial('w', (0, 0), (1, 1))

Parameters:

Name	Type	Description	Default
scalar	str	Monomial scalar.	UNIT_MWP
deltas	Optional[Union[List[DELTA], DELTA]]	A delta or a list of deltas.	None
*args	Optional[DELTA]	Arbitrary number of subsequent deltas.	()

choice_scalar

choice_scalar(*choices: int) -> Optional[str]

Determine if given sequence of choices matches monomial.

Parameters:

Name	Type	Description	Default
choices	int	Tuple of choices.	()

Returns:

Type	Description
Optional[str]	Monomial's scalar if structure matches choices and None otherwise.

contains

contains(m: Monomial) -> bool

Check if all deltas of m are in deltas of self.

Parameters:

Name	Type	Description	Default
m	Monomial	A monomial to search for intersection.	required

Returns:

Type	Description
bool	False if one delta of m not in self, True otherwise.

copy

copy() -> Monomial

Make a deep copy of a monomial.

inclusion

inclusion(monomial: Monomial) -> SetInclusion

Gives info about inclusion of self monomial with monomial.

Parameters:

Name	Type	Description	Default
monomial	Monomial	A monomial to see inclusion.	required

Returns:

Type	Description
SetInclusion	CONTAINS if self contains monomial, INCLUDED if self is included in monomial, and EMPTY none of them.

insert_delta staticmethod

insert_delta(sorted_deltas: List[DELTA], delta: DELTA) -> List[DELTA]

Takes as input a sorted list of deltas and a delta.

Check if two deltas have the same index:

If they do, and if they:

• disagree on the value expected, returns [] (empty list)
• agree on the value expected, returns the original deltas

If they don't:

• add the new delta in the deltas "at the right position".

Parameters:

Name	Type	Description	Default
sorted_deltas	List[DELTA]	List of deltas where to perform insert.	required
delta	DELTA	The delta value to be inserted.	required

Returns:

Type	Description
List[DELTA]	updated list of deltas.

insert_deltas staticmethod

insert_deltas(monomial: Monomial, deltas: List[DELTA]) -> None

Insert new deltas into monomial list of deltas.

Parameters:

Name	Type	Description	Default
monomial	Monomial	The monomial into whose list of deltas values will be inserted.	required
deltas	List[DELTA]	List of deltas to insert into monomial.	required

prod

prod(monomial: Monomial) -> Monomial

Prod combines two monomials where one is this monomial (self) and the second is an argument.

The attributes of the resulting monomial are determined as follows:

• output scalar is a product of the input scalars
• two lists of deltas are merged according to rules of insert_delta

Parameters:

Name	Type	Description	Default
monomial	Monomial	The second monomial.	required

Returns:

Type	Description
Monomial	A new Monomial that is a product of two monomials.

show

show() -> None

Display scalar and the list of deltas.

to_dict

to_dict() -> dict

Get dictionary representation of a monomial.