fix coersion of libgap FFelements; switch to libgap

With the ticket branch, this works:

sage: F=GF(25)
sage: F(libgap.Z(25)^3)
4*z2 + 3

src/sage/rings/finite_rings/element_givaro.pyx

@@ -66,7 +66,6 @@ import operator
 import sage.arith.all
 import sage.rings.finite_rings.finite_field_constructor as finite_field
 
-import sage.interfaces.gap
 from sage.libs.pari.all import pari
 from cypari2.gen cimport Gen
 from cypari2.stack cimport clear_stack
@@ -431,9 +430,12 @@ cdef class Cache_givaro(Cache_base):
             # Reduce to pari
             e = e.__pari__()
 
+        elif isinstance(e, sage.libs.gap.element.GapElement_FiniteField):
+            return e.sage(ring=self.parent)
+
         elif sage.interfaces.gap.is_GapElement(e):
-            from sage.interfaces.gap import gfq_gap_to_sage
-            return gfq_gap_to_sage(e, self.parent)
+            from sage.libs.gap.libgap import libgap
+            return libgap(e).sage(ring=self.parent)
 
         elif isinstance(e, list):
             if len(e) > self.exponent():
@@ -1637,6 +1639,8 @@ cdef class FiniteField_givaroElement(FinitePolyExtElement):
             'Z(25)^3'
             sage: S(gap('Z(25)^3'))
             4*b + 3
+            sage: S(libgap.Z(25)^3)
+            4*b + 3
         """
         cdef Cache_givaro cache = self._cache
         if self == 0:

src/sage/rings/finite_rings/element_ntl_gf2e.pyx

@@ -46,14 +46,16 @@ from sage.libs.pari.all import pari
 from cypari2.gen cimport Gen
 from cypari2.stack cimport clear_stack
 
-from sage.interfaces.gap import is_GapElement
-
 from sage.misc.randstate import current_randstate
 from sage.arith.long cimport pyobject_to_long
 
 from .element_pari_ffelt import FiniteFieldElement_pari_ffelt
 from .finite_field_ntl_gf2e import FiniteField_ntl_gf2e
 
+from sage.libs.gap.element import GapElement_FiniteField
+
+from sage.interfaces.gap import is_GapElement
+
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 cdef object is_IntegerMod
@@ -364,9 +366,13 @@ cdef class Cache_ntl_gf2e(Cache_base):
             # Reduce to pari
             e = e.__pari__()
 
+        elif isinstance(e, GapElement_FiniteField):
+            return e.sage(ring=self._parent)
+
         elif is_GapElement(e):
-            from sage.interfaces.gap import gfq_gap_to_sage
-            return gfq_gap_to_sage(e, self._parent)
+            from sage.libs.gap.libgap import libgap
+            return libgap(e).sage(ring=self._parent)
+
         else:
             raise TypeError("unable to coerce %r" % type(e))
 
@@ -1174,6 +1180,10 @@ cdef class FiniteField_ntl_gf2eElement(FinitePolyExtElement):
             sage: k.<b> = GF(2^16)
             sage: b._gap_init_()
             'Z(65536)^1'
+            sage: k(gap('Z(2^16)^3+Z(2^16)^5'))
+            b^5 + b^3
+            sage: k(libgap.Z(2^16)^3+libgap.Z(2^16)^5)
+            b^5 + b^3
         """
         F = self._parent
         if not F.is_conway():

src/sage/rings/finite_rings/element_pari_ffelt.pyx

@@ -505,9 +505,15 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):
             self.construct_from(self._parent.polynomial_ring()(x))
 
         elif is_GapElement(x):
-            from sage.interfaces.gap import gfq_gap_to_sage
             try:
-                self.construct_from(gfq_gap_to_sage(x, self._parent))
+                from sage.libs.gap.libgap import libgap
+                self.construct_from(libgap(x).sage(ring=self._parent))
+            except (ValueError, IndexError, TypeError):
+                raise TypeError("no coercion defined")
+
+        elif isinstance(x, sage.libs.gap.element.GapElement_FiniteField):
+            try:
+                self.construct_from(x.sage(ring=self._parent))
             except (ValueError, IndexError, TypeError):
                 raise TypeError("no coercion defined")
 
@@ -1258,16 +1264,20 @@ cdef class FiniteFieldElement_pari_ffelt(FinitePolyExtElement):
 
         EXAMPLES::
 
-            sage: F = FiniteField(2^3, 'a', impl='pari_ffelt')
-            sage: a = F.multiplicative_generator()
-            sage: gap(a) # indirect doctest
+            sage: F = FiniteField(2^3, 'aa', impl='pari_ffelt')
+            sage: aa = F.multiplicative_generator()
+            sage: gap(aa) # indirect doctest
             Z(2^3)
             sage: b = F.multiplicative_generator()
             sage: a = b^3
             sage: gap(a)
             Z(2^3)^3
             sage: gap(a^3)
             Z(2^3)^2
+            sage: F(gap('Z(8)^3'))
+            aa + 1
+            sage: F(libgap.Z(8)^3)
+            aa + 1
 
         You can specify the instance of the Gap interpreter that is used::
 

src/sage/rings/finite_rings/integer_mod_ring.py

@@ -72,7 +72,6 @@
 
 from sage.libs.pari.all import pari, PariError
 
-import sage.interfaces.all
 from sage.misc.cachefunc import cached_method
 
 from sage.structure.factory import UniqueFactory
@@ -1187,9 +1186,8 @@ def _element_constructor_(self, x):
             raise TypeError("error coercing to finite field")
         except TypeError:
             if sage.interfaces.gap.is_GapElement(x):
-                from sage.interfaces.gap import intmod_gap_to_sage
-                y = intmod_gap_to_sage(x)
-                return integer_mod.IntegerMod(self, y)
+                from sage.libs.gap.libgap import libgap
+                return libgap(x).sage()
             raise  # Continue up with the original TypeError
 
     def __iter__(self):