Use fq_inv function.

Author: Jean-Pierre Flori

src/sage/libs/flint/fq.pxi

@@ -75,3 +75,7 @@ cdef extern from "flint/fq.h":
     void fq_trace(fmpz_t rop, const fq_t op, const fq_ctx_t ctx)
     void fq_frobenius(fq_t rop, const fq_t op, long e, const fq_ctx_t ctx)
     void fq_norm(fmpz_t rop, const fq_t op, const fq_ctx_t ctx)
+
+    # Templated functions
+ 
+    void fq_div(fq_t rop, const fq_t op1, const fq_t op2, const fq_ctx_t ctx)

src/sage/rings/finite_rings/element_flint_fq.pyx

@@ -400,12 +400,9 @@ cdef class FiniteFieldElement_flint_fq(FinitePolyExtElement):
         if fq_is_zero((<FiniteFieldElement_flint_fq>right).val, self._cparent):
             raise ZeroDivisionError
         cdef FiniteFieldElement_flint_fq x = self._new()
-        cdef fq_t rinv
-        fq_init(rinv, self._cparent)
-        fq_inv(rinv, (<FiniteFieldElement_flint_fq>right).val, self._cparent)
-        fq_mul(x.val, (<FiniteFieldElement_flint_fq>self).val,
-                      rinv, self._cparent)
-        fq_clear(rinv, self._cparent)
+        fq_div(x.val, (<FiniteFieldElement_flint_fq>self).val,
+                      (<FiniteFieldElement_flint_fq>right).val,
+                      self._cparent)
         return x
 
     def is_zero(FiniteFieldElement_flint_fq self):