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

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.

name property

name: str

Get the name of the variable.

__init__

__init__(name: str) -> None

__init__(name: str, *, env: Environment) -> 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.