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Variable

Represents a symbolic variable within an optimization environment.

A Variable is the fundamental building block of algebraic expressions used in optimization models. Each variable is tied to an Environment which scopes its lifecycle and expression context. Variables can be typed and optionally bounded.

Parameters:

Name Type Description Default
name str

The name of the variable.

 required
env Environment

The environment in which this variable is created. If not provided, the current environment from the context manager is used.

 ...
vtype Vtype

The variable type (e.g., Vtype.Real, Vtype.Integer, etc.). Defaults to Vtype.Binary.

 ...
bounds Bounds

Bounds restricting the range of the variable. Only applicable for Real and Integer variables.

 ...

Examples:

>>> from luna_quantum import Variable, Environment, Vtype, Bounds
>>> with Environment():
...     x = Variable("x")
...     y = Variable("y", vtype=Vtype.Integer, bounds=Bounds(0, 5))
...     expr = 2 * x + y - 1
Arithmetic Overloads

Variables support standard arithmetic operations:

  • Addition: x + y, x + 2, 2 + x
  • Subtraction: x - y, 3 - x
  • Multiplication: x * y, 2 * x, x * 2

All expressions return Expression objects and preserve symbolic structure.

Notes
  • A Variable is bound to a specific Environment instance.
  • Variables are immutable; all operations yield new Expression objects.
  • Variables carry their environment, but the environment does not own the variable.

bounds property 

bounds: Bounds

Get the bounds of the variable.

id property 

id: int

name property 

name: str

Get the name of the variable.

vtype property 

vtype: Vtype

__add__ method descriptor 

__add__(value) -> Expression

Return self+value.

__eq__ method descriptor 

__eq__(value) -> Constraint

Return self==value.

__ge__ method descriptor 

__ge__(value) -> Constraint

Return self>=value.

__hash__ method descriptor 

__hash__() -> int

Return hash(self).

__init__ 

__init__(name: str) -> None

__init__(name: str, *, env: Environment) -> None

__init__(name: str, *, env: Environment, vtype: Vtype) -> None

__init__(name: str, *, vtype: Vtype) -> None

__init__(name: str, *, vtype: Vtype, bounds: Bounds) -> None

__init__(name: str, *, vtype: Vtype, bounds: Bounds, env: Environment) -> None

__init__(
    name: str,
    *,
    vtype: Vtype | None = ...,
    bounds: Bounds | None = ...,
    env: Environment | None = ...,
) -> None

Initialize a new Variable.

See class-level docstring for full usage.

Raises:

Type Description
NoActiveEnvironmentFoundError

If no active environment is found and none is explicitly provided.
VariableExistsError

If a variable with the same name already exists in the environment.
VariableCreationError

If the variable is tried to be created with incompatible bounds.

__le__ method descriptor 

__le__(value) -> Constraint

Return self<=value.

__mul__ method descriptor 

__mul__(value) -> Expression

Return self*value.

__neg__ method descriptor 

__neg__() -> Expression

-self

__pow__ method descriptor 

__pow__(value, mod=None) -> Expression

Return pow(self, value, mod).

__radd__ method descriptor 

__radd__(value) -> Expression

Return value+self.

__repr__ method descriptor 

__repr__() -> str

Return repr(self).

__rmul__ method descriptor 

__rmul__(value) -> Expression

Return value*self.

__rsub__ method descriptor 

__rsub__(value) -> Expression

Return value-self.

__str__ method descriptor 

__str__() -> str

Return str(self).

__sub__ method descriptor 

__sub__(value) -> Expression

Return self-value.