The module or chain complex provided should be over a ring whose degree length (see degreeLength) is the same as the length of the list w. The dot products of w with the multi-degrees occurring will be used to construct the resulting betti tally (see BettiTally). If the option is not specified, then the heft vector of the underlying ring is used, see heft vectors. If the ring has no heft vector, then the weights are taken to be all zero.