coordinates.base.class_expression

coordinates.base.class_expression(name: str | None = None) → classmethod

Mark a class method as a symbolic expression (“class expression”) in a coordinate system.

Class expressions are symbolic methods that define expressions such as metric tensors, Jacobians, or differential geometry terms. When decorated with this function, the method is automatically registered during class construction and evaluated on demand via get_class_expression().

The decorated method must be a @classmethod with the following signature:

def some_expr(cls, *axes_symbols, **parameter_symbols): ...

Parameters:

name (str, optional) – A custom name to assign to the expression. If omitted, the method name is used.

Returns:

The decorated class method with metadata attached for registration and deferred evaluation.

Return type:

classmethod

Notes

• The decorator only works on methods already marked as @classmethod.

• Registered expressions are stored on the class and evaluated once when first accessed.

• Use get_class_expression(name)() to access the expression symbolically.

Example

class MySystem(CoordinateSystemBase):
    __AXES__ = ["r", "theta"]
    __PARAMETERS__ = {}

    @class_expression()
    @classmethod
    def metric_tensor(cls, r, theta):
        return sp.Matrix([[1, 0], [0, r**2]])

expr = MySystem.get_class_expression("metric_tensor")
print(expr)  # => Matrix([[1, 0], [0, r**2]])