make gap objects selectively hashable

src/sage/combinat/designs/gen_quadrangles_with_spread.pyx

@@ -291,20 +291,19 @@ def generalised_quadrangle_hermitian_with_ovoid(const int q):
 
     e1 = [one, zero, zero, zero]  # isotropic point
 
-    points = list(libgap.Orbit(GU, e1, libgap.OnLines))  # all isotropic points
-    pointInt = { x: int(i + 1) for i, x in enumerate(points) }
-    # above we sum 1 because GAP starts at 1
+    points = libgap.Orbit(GU, e1, libgap.OnLines)  # all isotropic points
+    pointInt = {tuple(x): i for i, x in enumerate(points)}
 
     GUp = libgap.Action(GU, points, libgap.OnLines)
 
     e2 = [zero, one, zero, zero]  # another isotropic point
     line = V.Subspace([e1, e2])  # totally isotropic line
-    lineAsPoints = [libgap.Elements(libgap.Basis(b))[0]
+    lineAsPoints = [tuple(libgap.Elements(libgap.Basis(b))[0])
                     for b in libgap.Elements(line.Subspaces(1))]
-    line = libgap.Set([pointInt[p] for p in lineAsPoints])
+    line = libgap.Set([pointInt[p] + 1 for p in lineAsPoints])
 
     lines = libgap.Orbit(GUp, line, libgap.OnSets)  # all isotropic lines
-    lines = [list(map(lambda x: int(x - 1), b)) for b in lines]  # convert to int
+    lines = [[int(x)-1 for x in b] for b in lines]  # convert to int
     # lines defines the GQ H(3, q^2)
 
     # to find an ovoid, we embed H(3,q^2) in H(4,q^2)
@@ -330,9 +329,9 @@ def generalised_quadrangle_hermitian_with_ovoid(const int q):
     # note that p'Jp^q = bx^q + c where p' = (a,b,0,c,d) and p = (0,1,y,x,0)
     ovoid = []
     xq = p[3]**q
-    for p2 in points:
+    for p2, i in pointInt.items():
         if p2[1]*xq + p2[2] == zero:  # p collinear to p2
-            ovoid.append(pointInt[p2] - 1)
+            ovoid.append(i)
 
     D = IncidenceStructure(lines)
     return (D, ovoid)

src/sage/libs/gap/element.pxd

@@ -56,28 +56,31 @@ cdef class GapElement(RingElement):
 
     cpdef GapElement deepcopy(self, bint mut)
 
-cdef class GapElement_Integer(GapElement):
+cdef class GapElement_with_hash(GapElement):
     pass
 
-cdef class GapElement_Rational(GapElement):
+cdef class GapElement_Integer(GapElement_with_hash):
     pass
 
-cdef class GapElement_IntegerMod(GapElement):
+cdef class GapElement_Rational(GapElement_with_hash):
+    pass
+
+cdef class GapElement_IntegerMod(GapElement_with_hash):
     cpdef GapElement_Integer lift(self)
 
-cdef class GapElement_FiniteField(GapElement):
+cdef class GapElement_FiniteField(GapElement_with_hash):
     cpdef GapElement_Integer lift(self)
 
-cdef class GapElement_Cyclotomic(GapElement):
+cdef class GapElement_Cyclotomic(GapElement_with_hash):
     pass
 
 cdef class GapElement_Ring(GapElement):
     pass
 
-cdef class GapElement_String(GapElement):
+cdef class GapElement_String(GapElement_with_hash):
     pass
 
-cdef class GapElement_Boolean(GapElement):
+cdef class GapElement_Boolean(GapElement_with_hash):
     pass
 
 cdef class GapElement_Function(GapElement):
@@ -96,5 +99,5 @@ cdef class GapElement_RecordIterator():
 cdef class GapElement_List(GapElement):
     pass
 
-cdef class GapElement_Permutation(GapElement):
+cdef class GapElement_Permutation(GapElement_with_hash):
     pass

src/sage/libs/gap/element.pyx

@@ -832,17 +832,6 @@ cdef class GapElement(RingElement):
         if not self._compare_by_id:
             raise ValueError('this requires a GAP object whose comparison is by "id"')
 
-    def __hash__(self):
-        """
-        Make hashable.
-
-        EXAMPLES::
-
-            sage: hash(libgap(123))   # random output
-            163512108404620371
-        """
-        return hash(str(self))
-
     cpdef _richcmp_(self, other, int op):
         """
         Compare ``self`` with ``other``.
@@ -1400,6 +1389,23 @@ cdef class GapElement(RingElement):
         raise NotImplementedError('cannot construct equivalent Sage object')
 
 
+cdef class GapElement_with_hash(GapElement):
+    """
+    A GapElement class that provides a hash via the str
+    representation of the object.
+    """
+    def __hash__(self):
+        """
+        Make hashable.
+
+        EXAMPLES::
+
+            sage: hash(libgap(123))   # random output
+            163512108404620371
+        """
+        return hash(str(self))
+
+
 ############################################################################
 ### GapElement_Integer #####################################################
 ############################################################################
@@ -1420,7 +1426,7 @@ cdef GapElement_Integer make_GapElement_Integer(parent, Obj obj):
     return r
 
 
-cdef class GapElement_Integer(GapElement):
+cdef class GapElement_Integer(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP integers.
 
@@ -1656,7 +1662,7 @@ cdef GapElement_IntegerMod make_GapElement_IntegerMod(parent, Obj obj):
     r._initialize(parent, obj)
     return r
 
-cdef class GapElement_IntegerMod(GapElement):
+cdef class GapElement_IntegerMod(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP integers modulo an integer.
 
@@ -1747,7 +1753,7 @@ cdef GapElement_FiniteField make_GapElement_FiniteField(parent, Obj obj):
     return r
 
 
-cdef class GapElement_FiniteField(GapElement):
+cdef class GapElement_FiniteField(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP finite field elements.
 
@@ -1916,7 +1922,7 @@ cdef GapElement_Cyclotomic make_GapElement_Cyclotomic(parent, Obj obj):
     return r
 
 
-cdef class GapElement_Cyclotomic(GapElement):
+cdef class GapElement_Cyclotomic(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP universal cyclotomics.
 
@@ -2001,7 +2007,7 @@ cdef GapElement_Rational make_GapElement_Rational(parent, Obj obj):
     return r
 
 
-cdef class GapElement_Rational(GapElement):
+cdef class GapElement_Rational(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP rational numbers.
 
@@ -2231,7 +2237,7 @@ cdef GapElement_Boolean make_GapElement_Boolean(parent, Obj obj):
     return r
 
 
-cdef class GapElement_Boolean(GapElement):
+cdef class GapElement_Boolean(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP boolean values.
 
@@ -2321,7 +2327,7 @@ cdef GapElement_String make_GapElement_String(parent, Obj obj):
     return r
 
 
-cdef class GapElement_String(GapElement):
+cdef class GapElement_String(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP strings.
 
@@ -2987,7 +2993,7 @@ cdef GapElement_Permutation make_GapElement_Permutation(parent, Obj obj):
     return r
 
 
-cdef class GapElement_Permutation(GapElement):
+cdef class GapElement_Permutation(GapElement_with_hash):
     r"""
     Derived class of GapElement for GAP permutations.