Interaction decomposition

[opeltre]

Implement projection to homology classes via local iFFT

H(x) = sum_k h(k) x(k)

where x(k) = prod_i ei^(ki xi)

This extends the representation of local observables as polynomials in the binary case, +-1 being replaced by Nth-roots of unity.

[opeltre]

In practice this corresponds to a large batch of small iFT transforms: best implemented as a sparse matrix of diagonal iFT blocks

[opeltre]

Note that we have then:

h(k) = sum_x H(x) k(x)

where k(x) = prod_i ei^(ki xi) / Ni

with mass factor Ni