sage: F = GF(2^4)
sage: R.<x> = PolynomialRing(F)
sage: f = x^5 + x^2 + 1
sage: h = 1
sage: H.lift_x(1)
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
Cell In [19], line 1
----> 1 H.lift_x(Integer(1))

File ~/sage/sage-10.2/src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py:269, in HyperellipticCurve_generic.lift_x(self, x, all)
    267             return [self.point([x, (-b+d)/2, one], check=False) for d in D.sqrt(all=True)]
    268         else:
--> 269             return self.point([x, (-b+D.sqrt())/2, one], check=False)
    270 if all:
    271     return []

File ~/sage/sage-10.2/src/sage/structure/element.pyx:1742, in sage.structure.element.Element.__truediv__()
   1740 
   1741         try:
-> 1742             return coercion_model.bin_op(left, right, truediv)
   1743         except TypeError:
   1744             return NotImplemented

File ~/sage/sage-10.2/src/sage/structure/coerce.pyx:1232, in sage.structure.coerce.CoercionModel.bin_op()
   1230     self._record_exception()
   1231 else:
-> 1232     return PyObject_CallObject(op, xy)
   1233 
   1234 if op is mul:

File ~/sage/sage-10.2/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
   1735 cdef int cl = classify_elements(left, right)
   1736 if HAVE_SAME_PARENT(cl):
-> 1737     return (<Element>left)._div_(right)
   1738 if BOTH_ARE_ELEMENT(cl):
   1739     return coercion_model.bin_op(left, right, truediv)

File ~/sage/sage-10.2/src/sage/rings/finite_rings/element_givaro.pyx:1128, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._div_()
   1126 cdef int r = 0
   1127 if (<FiniteField_givaroElement>right).element == 0:
-> 1128     raise ZeroDivisionError('division by zero in finite field')
   1129 self._cache.objectptr.div(r, self.element,
   1130                           (<FiniteField_givaroElement>right).element)

ZeroDivisionError: division by zero in finite field