# Transforming multi-tape Turing machines to equivalent single-tape Turing machines

We know that multi-tape Turing machines have the same computational power as single-tape ones. So every $$k$$-tape Turing machine has an equivalent single-tape Turing machine.

About the computability and complexity analysis of such a transformation:

Is there a computable function that receives as input an arbitrary multi-tape Turing machine and returns an equivalent single-tape Turing machine in polynomial time and polynomial space?