Inversion in P-Computable Fields

We consider fields computable in polynomial time (P-computable). We prove that under some assumptions about a P-computable field \( (A, +, \cdot ) \) of characteristic 0, there exists a P-computable field \( (B, +, \cdot ) \cong (A, +, \cdot ) \) , in which \(x^{-1}\) is not a primitive recursive function. In particular, this holds for the field \( \mathbb Q \) of rational numbers.