Geometry

mul_with_projection(x, y, lg)

Similar to x * y, except that this version automatically projects y to avoid DimensionMismatch errors for AxisTensors. For example, if x is a covector along the Covariant3Axis (e.g., Covariant3Vector(1)'), then y will be projected onto the Contravariant3Axis. In general, the first axis of y will be projected onto the dual of the last axis of x.

mul_return_type(X, Y)

Computes the return type of mul_with_projection(x, y, lg), where x isa X and y isa Y. This can also be used to obtain the return type of x * y, although x * y will throw an error when projection is necessary.

Note that this is equivalent to calling the internal function _return_type: Base._return_type(mul_with_projection, Tuple{X, Y, LG}), where lg isa LG.