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I think the problem is that you compute with symbolic matrices. Computations there can easily blow up horribly and I expect that is what's happening. The line:

FFTc.change_ring(CC)

produces a new matrix with complex-float entries, but since you don't assign it to anything, the resulting matrix just gets lost. You continue working with the symbolic matrix after that, and I think that just grinds to a halt due to explosion of intermediate expressions. Perhaps you meant to compute with a float approximation to the matrix instead?

Note that computing a "kernel" of a float matrix generally doesn't work, because numerically matrices of non-maximal rank aren't really distinguishable from maximal rank ones. Also computing the "inverse" numerically is generally tricky and requires special measures to get a bit of numerical stability. Sage unfortunately doesn't do that by default (in part because you're probably doing something wrong if you're computing an inverse numerically).