Given two dictionaries containing key -> list of values mapping create intersection mapping common keys to dot product of values.

intersect_values.py

from itertools import product

def intersect_values(left, right):
  intersection = left.viewkeys() & right.viewkeys()
  return {key: list(product(left[key], right[key])) for key in intersection}
  
assert intersect_values({'A': [1, 2], 'B': [5]}, {'A': [3, 7]}) == {'A': [(1, 3), (1, 7), (2, 3), (2, 7)]}