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.

rmul_with_projection(x, y, lg)

Similar to rmul(x, y), except that this version calls mul_with_projection instead of *.

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.

rmul_return_type(X, Y)

Computes the return type of rmul_with_projection(x, y, lg), where x isa X and y isa Y. This can also be used to obtain the return type of rmul(x, y), although rmul(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(rmul_with_projection, Tuple{X, Y, LG}), where lg isa LG.