BinaryPoly¶

class BinaryPoly¶

ベースクラス: Poly

A polynomial of binary variables. Deprecated alias of Poly.

Amplify v1 gives the variable its type when the generator makes it, so the polynomial no longer carries the type. This class still works, and it emits a DeprecationWarning.

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¶

戻り値の型:: Iterator

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

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 a polynomial, a number, an array, or a constraint to the polynomial.

The result is a Poly for a polynomial or a number, a PolyArray for an array, and a Model for a Constraint or a ConstraintList.

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.

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¶

Tell whether the two sides are the same polynomial.

This compares the terms, so it gives a bool and not a constraint. Use equal_to() to make a constraint that asks for equality.

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
例外:: ValueError -- The polynomial is not a constant.

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

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

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

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

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

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
例外:: ValueError -- The polynomial is not a constant.

__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
例外:: ValueError -- The polynomial is not a constant.

__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¶

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

__ipow__(self, arg: int, /) → Poly¶

Raise the polynomial to a power in place. The exponent must be an integer that is 0 or larger.

パラメータ:: arg (int)
戻り値の型:: Poly
例外:: ValueError -- The exponent is negative.

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

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¶

パラメータ:: arg (float)
戻り値の型:: Poly

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

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]

Multiply the polynomial by a polynomial or by a number.

Overload 1.

Args:

arg (amplify.Poly | float)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__ne__(self, arg: object, /) → bool¶

Tell whether the two sides are different polynomials.

This is the negation of ==. It gives a bool and not a constraint.

パラメータ:: arg (object)
戻り値の型:: bool

__neg__(self) → Poly¶

Give the polynomial in which every coefficient has the opposite sign.

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.

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¶

Give a copy of the polynomial.

戻り値の型:: Poly

__pow__(self, arg: int, /) → Poly¶

Raise the polynomial to a power. The exponent must be an integer that is 0 or larger.

パラメータ:: arg (int)
戻り値の型:: Poly
例外:: ValueError -- The exponent is negative.

__radd__(self, arg: float, /) → Poly¶

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

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

Add a polynomial, a number, an array, or a constraint to the polynomial.

The result is a Poly for a polynomial or a number, a PolyArray for an array, and a Model for a Constraint or a ConstraintList.

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]

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

q_0 & q_1 is equivalent to q_0 * q_1.

Overload 1.

Args:

arg (bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__repr__(self) → str¶

戻り値の型:: str

__rmul__(self, arg: float, /) → Poly¶

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

Multiply the polynomial by a polynomial or by a number.

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]

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

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

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]

Subtract the polynomial from a number.

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]

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

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

Overload 1.

Args:

arg (bool)

Returns:

amplify.Poly:

Overload 2.

Args:

arg (ndarray)

Returns:

amplify.PolyArray[Dim]:

__str__(self) → str¶

戻り値の型:: str

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

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

Subtract a polynomial or a number from the polynomial.

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]

Divide the polynomial by a number.

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.

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
例外:: RuntimeError -- The polynomial is not a single 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().

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.

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

When the keyword argument default is absent, a variable that values does not contain takes the default value of its type:

a binary variable takes 0;
an Ising variable takes -1;
an integer or a real variable takes 0 when its bounds contain 0, the upper bound when they do not, and the lower bound when it has no upper bound.

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:

Raises:

ValueError: values comes from another VariableGenerator than the one that made the variables of this polynomial.

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

__deprecated__ = 'BinaryPoly is deprecated since amplify v1.0.0 and will no longer support in the near future.\nUse Poly instead. Please see the migration guide for details: https://amplify.fixstars.com/docs/amplify/v1/migration.html'¶

property id¶

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

戻り値の型:: int
例外:: RuntimeError -- The polynomial is not a single variable.

property lower_bound¶

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

戻り値の型:: float | None
例外:: RuntimeError -- The polynomial is not a single variable.

property name¶

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

戻り値の型:: str
例外:: RuntimeError -- The polynomial is not a single variable.

property type¶

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

戻り値の型:: VariableType
例外:: RuntimeError -- The polynomial is not a single variable.

property upper_bound¶

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

戻り値の型:: float | None
例外:: RuntimeError -- The polynomial is not a single variable.

property variables¶

List of all variables in the polynomial.

戻り値の型:: list[Variable]