Poly¶

class Poly¶

The polynomial class used for representing objective functions and constraints.

Methods

`__init__`	__init__
`as_dict`	Return the dictionary representation of the polynomial.
`as_variable`	Return the variable representation of the polynomial.
`asdict`	alias of `as_dict()`
`decode`	Equivalent to `evaluate()`.
`degree`	Return the degree of the polynomial.
`evaluate`	Evaluate the polynomial by substituting variables using the given values.
`is_linear`	Return `True` if the polynomial is linear.
`is_number`	Return `True` if the polynomial is a constant polynomial.
`is_quadratic`	Return `True` if the polynomial is quadratic.
`is_variable`	Return `True` if the polynomial represents a single variable.
`substitute`	Assign numbers or other polynomials to variables in the polynomial.

Attributes

`id`	Variable ID.
`lower_bound`	Lower bound of the variable.
`name`	Variable name.
`type`	Variable type.
`upper_bound`	Upper bound of the variable.
`variables`	List of all variables in the polynomial.

class Iterator¶

__init__(*args, **kwargs)¶

__iter__(self) → Iterator¶

__iter__

戻り値の型:: Iterator

__next__(self) → tuple[tuple[Poly, ...], float]¶

__next__

戻り値の型:: tuple[tuple[Poly, ...], float]

__add__(self, arg: Poly | float, /) → Poly¶

__add__(self, arg: ndarray[], /) → PolyArray[Dim]

__add__(self, arg: Constraint | ConstraintList, /) → Model

__add__

Overload 1.

Args:

arg (amplify.Poly | float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

Overload 3.

Args:

arg (amplify.Constraint | amplify.ConstraintList)

Returns:

amplify.Model:

__and__(self, arg: Poly | bool, /) → Poly¶

__and__(self, arg: ndarray[dtype=bool], /) → PolyArray[Dim]

Logical AND of two polynomials. This is meaningful only for polynomials that take values 0 or 1. __and__

q_0 & q_1 is equivalent to q_0 * q_1.

Overload 1.

Args:

arg (amplify.Poly | bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__bool__(self) → bool¶

Cast a polynomial to a boolean value. Only valid for constant polynomials that take values 0 or 1.

戻り値の型:: bool

__eq__(self, arg: object, /) → bool¶

__eq__

パラメータ:: arg (object)
戻り値の型:: bool

__float__(self) → float¶

Cast a polynomial to a float value. Only valid for constant polynomials.

戻り値の型:: float

__iadd__(self, arg: Poly | float, /) → Poly¶

__iadd__

パラメータ:: arg (Poly | float)
戻り値の型:: Poly

__iand__(self, arg: Poly | bool, /) → Poly¶

__iand__

パラメータ:: arg (Poly | bool)
戻り値の型:: Poly

__imul__(self, arg: Poly | float, /) → Poly¶

__imul__

パラメータ:: arg (Poly | float)
戻り値の型:: Poly

__index__(self) → int¶

Cast a polynomial to an integer. Only valid for constant polynomials.

戻り値の型:: int

__init__(self) → None¶

__init__(self, arg: float, /) → None

__init__(self, arg: Variable, /) → None

__init__

Overload 2.

Args:

arg (float)

Overload 3.

Args:

arg (amplify.Variable)

__int__(self) → int¶

Cast a polynomial to an integer. Only valid for constant polynomials.

戻り値の型:: int

__invert__(self) → Poly¶

Logical NOT of a polynomial. This is meaningful only for polynomials that take values 0 or 1.

~q_0 is equivalent to 1 - q_0.

戻り値の型:: Poly

__ior__(self, arg: Poly | bool, /) → Poly¶

__ior__

パラメータ:: arg (Poly | bool)
戻り値の型:: Poly

__ipow__(self, arg: int, /) → Poly¶

__ipow__

パラメータ:: arg (int)
戻り値の型:: Poly

__isub__(self, arg: Poly | float, /) → Poly¶

__isub__

パラメータ:: arg (Poly | float)
戻り値の型:: Poly

__iter__(self) → Iterator¶

Iterate over the terms in the polynomial.

Each term is represented as a tuple of a tuple of variables and a coefficient. For example, the polynomial 3 * x_0 * x_1 - 2 * x_0 + 5 is iterated as ((Poly(x_0), Poly(x_1)), 3.0), ((Poly(x_0),), -2.0), and ((), 5.0).

戻り値の型:: Iterator

__itruediv__(self, arg: float, /) → Poly¶

__itruediv__

パラメータ:: arg (float)
戻り値の型:: Poly

__ixor__(self, arg: Poly | bool, /) → Poly¶

__ixor__

パラメータ:: arg (Poly | bool)
戻り値の型:: Poly

__len__(self) → int¶

Return the number of terms in the polynomial.

戻り値の型:: int

__mul__(self, arg: Poly | float, /) → Poly¶

__mul__(self, arg: ndarray[], /) → PolyArray[Dim]

__mul__

Overload 1.

Args:

arg (amplify.Poly | float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__ne__(self, arg: object, /) → bool¶

__ne__

パラメータ:: arg (object)
戻り値の型:: bool

__neg__(self) → Poly¶

__neg__

戻り値の型:: Poly

__or__(self, arg: Poly | bool, /) → Poly¶

__or__(self, arg: ndarray[dtype=bool], /) → PolyArray[Dim]

Logical OR of two polynomials. This is meaningful only for polynomials that take values 0 or 1. __or__

q_0 | q_1 is equivalent to -q_0 * q_1 + q_0 + q_1.

Overload 1.

Args:

arg (amplify.Poly | bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__pos__(self) → Poly¶

__pos__

戻り値の型:: Poly

__pow__(self, arg: int, /) → Poly¶

__pow__

パラメータ:: arg (int)
戻り値の型:: Poly

__radd__(self, arg: float, /) → Poly¶

__radd__(self, arg: ndarray[], /) → PolyArray[Dim]

__radd__(self, arg: Constraint | ConstraintList, /) → Model

__radd__

Overload 1.

Args:

arg (float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

Overload 3.

Args:

arg (amplify.Constraint | amplify.ConstraintList)

Returns:

amplify.Model:

__rand__(self, arg: bool, /) → Poly¶

__rand__(self, arg: ndarray[dtype=bool], /) → PolyArray[Dim]

__rand__

Overload 1.

Args:

arg (bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__repr__(self) → str¶

__repr__

戻り値の型:: str

__rmul__(self, arg: float, /) → Poly¶

__rmul__(self, arg: ndarray[], /) → PolyArray[Dim]

__rmul__

Overload 1.

Args:

arg (float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__ror__(self, arg: bool, /) → Poly¶

__ror__(self, arg: ndarray[dtype=bool], /) → PolyArray[Dim]

__ror__

Overload 1.

Args:

arg (bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__rsub__(self, arg: float, /) → Poly¶

__rsub__(self, arg: ndarray[], /) → PolyArray[Dim]

__rsub__

Overload 1.

Args:

arg (float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__rxor__(self, arg: bool, /) → Poly¶

__rxor__(self, arg: ndarray[dtype=bool], /) → PolyArray[Dim]

__rxor__

Overload 1.

Args:

arg (bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__str__(self) → str¶

__str__

戻り値の型:: str

__sub__(self, arg: Poly | float, /) → Poly¶

__sub__(self, arg: ndarray[], /) → PolyArray[Dim]

__sub__

Overload 1.

Args:

arg (amplify.Poly | float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__truediv__(self, arg: float, /) → Poly¶

__truediv__(self, arg: ndarray[], /) → PolyArray[Dim]

__truediv__

Overload 1.

Args:

arg (float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__xor__(self, arg: Poly | bool, /) → Poly¶

__xor__(self, arg: ndarray[dtype=bool], /) → PolyArray[Dim]

Logical XOR of two polynomials. This is meaningful only for polynomials that take values 0 or 1. __xor__

q_0 ^ q_1 is equivalent to -2 * q_0 * q_1 + q_0 + q_1.

Overload 1.

Args:

arg (amplify.Poly | bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

as_dict(self) → dict[tuple[int, ...], float]¶

Return the dictionary representation of the polynomial.

The polynomial is represented as a dictionary where keys are tuples of variable indices and values are coefficients. For example, the polynomial 3 * x_0 - 2 * x_0 * x_1 + 5 will be represented as {(): 5, (0,): 3, (0, 1): -2}.

戻り値の型:: dict[tuple[int, ...], float]

as_variable(self) → Variable¶

Return the variable representation of the polynomial. Only valid for polynomials that represent a single variable.

戻り値の型:: Variable

asdict(self) → dict[tuple[int, ...], float]¶

alias of as_dict()

戻り値の型:: dict[tuple[int, ...], float]

decode(self, values: Values) → float¶

decode(self, values: Values, default: float) → float

decode(self, values: Values, default: None) → Poly

Equivalent to evaluate(). decode decode

This method is deprecated since Amplify v1.0.0 and will be removed in a future version. Please see the migration guide for details: https://amplify.fixstars.com/docs/amplify/v1/migration.html

Overload 1.

Args:

values (amplify.Values)

Returns:

float:

Overload 2.

Args:

values (amplify.Values)
default (float)

Returns:

float:

Overload 3.

Args:

values (amplify.Values)
default (None)

Returns:

amplify.Poly:

degree(self) → int¶

Return the degree of the polynomial.

戻り値の型:: int

evaluate(self, values: Values) → float¶

evaluate(self, values: Values, default: float) → float

evaluate(self, values: Values, default: None) → Poly

Evaluate the polynomial by substituting variables using the given values. evaluate evaluate

This method is usually used to obtain optimization results in array form.

If the keyword argument default is not specified, variables that are not specified in values will be substituted by a reasonable default value.

If the keyword argument default is specified with a float value, variables that are not specified in values will be substituted by that value.

If the keyword argument default is specified with None, variables that are not specified in values will remain as symbolic variables without substitution.

Overload 1.

Args:

values (amplify.Values): Values obtained from optimization results, e.g. result.best.values.

Returns:

float:

Overload 2.

Args:

values (amplify.Values): Values that can be obtained from optimization results, e.g. result.best.values.
default (float): The default value for variables not specified in values.

Returns:

float:

Overload 3.

Args:

values (amplify.Values): Values obtained from optimization results, e.g. result.best.values.
default (None): Set to None to keep variables not specified in values symbolic.

Returns:

amplify.Poly:

is_linear(self) → bool¶

Return True if the polynomial is linear.

戻り値の型:: bool

is_number(self) → bool¶

Return True if the polynomial is a constant polynomial.

戻り値の型:: bool

is_quadratic(self) → bool¶

Return True if the polynomial is quadratic.

戻り値の型:: bool

is_variable(self) → bool¶

Return True if the polynomial represents a single variable.

戻り値の型:: bool

Assign numbers or other polynomials to variables in the polynomial.

パラメータ:: mapping (Mapping[Poly, Poly | float | int] | Mapping[Variable, Poly | float | int]) -- Key-value pairs of variables and replacement values. Each value can be a number or another polynomial.
戻り値の型:: Poly

property id¶

Variable ID. Only valid for polynomials that represent a single variable.

戻り値の型:: int

property lower_bound¶

Lower bound of the variable. Only valid for polynomials that represent a single variable.

戻り値の型:: float | None

property name¶

Variable name. Only valid for polynomials that represent a single variable.

戻り値の型:: str

property type¶

Variable type. Only valid for polynomials that represent a single variable.

戻り値の型:: VariableType

property upper_bound¶

Upper bound of the variable. Only valid for polynomials that represent a single variable.

戻り値の型:: float | None

property variables¶

List of all variables in the polynomial.

戻り値の型:: list[Variable]