consider a function
$$f(x_1, x_2, \ldots, x_n) $$
is it possible to compute the period of the function as a vector
$$\langle l_1, l_2, \ldots, l_n\rangle$$
where each $l$ denotes the period of the function for that corresponding variable?
furthermore,
can some generalization of the fourier transform be used to compute this period vector?
and if so,
Is the time complexity of running the multivariable version of the quantum fourier transform still polynomial in the bit complexity of a function being evaluated?
Its a compound question, I'll upvote answers to any part, and best answers will be the ones that are best quality and maximize the parts being answered, although I feel each question follows naturally from the one before it.