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Apparently, though r is a unit in the polynomial ring, it is not necessarilly equal to 1, but it is a polynomial of degree 0, so you can assert instead r.is_unit() and replace inv = GF(inv_bar) with inv = GF(inv_bar)/GF(r) or inv = GF(inv_bar/GF.base_ring()(r)) if you do not ant to rely on division in GF to redefine it.

Apparently, though r is a unit in the polynomial ring, it is not necessarilly equal to 1, but it is a polynomial of degree 0, so you can assert instead r.is_unit() and replace inv = GF(inv_bar) with inv = GF(inv_bar)/GF(r) or inv = GF(inv_bar/GF.base_ring()(r)) if you do not ant want to rely on division in GF to redefine it.