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If you replace pol/x with pol//x, then over a large field you'll an error:

NotImplementedError: Division of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.

I'm not sure whether pol/x should raise the same error, but you're welcome to file a bugreport at https://github.com/sagemath/sage/issues anyway.

If you replace pol/x with pol//x, then over a large field you'll see an error:

NotImplementedError: Division of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.

I'm not sure whether pol/x should raise the same error, but you're welcome to file a bugreport at https://github.com/sagemath/sage/issues anyway.

If you replace pol/x with pol//x, then over a large field you'll see an error:

NotImplementedError: Division of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.

I'm not sure whether pol/x should raise the same error, but you're welcome to file a bugreport at https://github.com/sagemath/sage/issues anyway.

See also https://github.com/sagemath/sage/issues/34302