Revert "hack to make * compose isogenies and isomorphisms correctly"

This reverts commit 6e34c55.

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

@@ -3567,22 +3567,6 @@ def formal(self,prec=20):
     # Overload Morphism methods that we want to
     #
 
-    def _composition_(self, other, homset):
-        r"""
-        Return the composition of this isogeny with another
-        elliptic-curve morphism.
-        """
-        if not isinstance(other, EllipticCurveHom):
-            raise TypeError(f'cannot compose {type(self)!r} with {type(other)!r}')
-
-        # This is a temporary hack: See WeierstrassIsomorphism._composition_.
-        if isinstance(other, WeierstrassIsomorphism):
-            output = copy(self)
-            output._set_pre_isomorphism(other)
-            return output
-
-        return EllipticCurveHom._composition_(self, other, homset)
-
     def is_injective(self):
         r"""
         Return ``True`` if and only if this isogeny has trivial
@@ -3662,6 +3646,36 @@ def is_zero(self):
         """
         return self.degree().is_zero()
 
+    def post_compose(self, left):
+        r"""
+        Return the post-composition of this isogeny with ``left``.
+
+        EXAMPLES::
+
+            sage: E = EllipticCurve(j=GF(7)(0))
+            sage: phi = EllipticCurveIsogeny(E, [ E((0,1)), E((0,-1))])
+            sage: phi.post_compose(phi)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: post-composition of isogenies not yet implemented
+        """
+        raise NotImplementedError("post-composition of isogenies not yet implemented")
+
+    def pre_compose(self, right):
+        r"""
+        Return the pre-composition of this isogeny with ``right``.
+
+        EXAMPLES::
+
+            sage: E = EllipticCurve(j=GF(7)(0))
+            sage: phi = EllipticCurveIsogeny(E, [ E((0,1)), E((0,-1))])
+            sage: phi.pre_compose(phi)
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: pre-composition of isogenies not yet implemented
+        """
+        raise NotImplementedError("pre-composition of isogenies not yet implemented")
+
     def n(self):
         r"""
         Numerical Approximation inherited from Map (through morphism),

src/sage/schemes/elliptic_curves/weierstrass_morphism.py

@@ -394,7 +394,7 @@ def isomorphisms(E, F, JustOne=False):
     return ans
 
 
-class WeierstrassIsomorphism(EllipticCurveHom, baseWI):
+class WeierstrassIsomorphism(baseWI, EllipticCurveHom):
     r"""
     Class representing a Weierstrass isomorphism between two elliptic curves.
     """
@@ -590,10 +590,9 @@ def __invert__(self):
         winv = baseWI.__invert__(self).tuple()
         return WeierstrassIsomorphism(self._codomain, winv, self._domain)
 
-    def _composition_(self, other, homset):
+    def __mul__(self, other):
         r"""
-        Return the composition of this WeierstrassIsomorphism and another
-        elliptic-curve morphism.
+        Return the composition of this WeierstrassIsomorphism and the other,
 
         WeierstrassMorphisms can be composed using ``*`` if the
         codomain & domain match: `(w1*w2)(X)=w1(w2(X))`, so we require
@@ -610,22 +609,11 @@ def _composition_(self, other, homset):
             sage: (w2*w1)(P) == w2(w1(P))
             True
         """
-        if not isinstance(other, EllipticCurveHom):
-            raise TypeError(f'cannot compose {type(self)!r} with {type(other)!r}')
-
-        if isinstance(other, WeierstrassIsomorphism):
-            if self._domain != other._codomain:
-                raise ValueError("Domain of first argument must equal codomain of second")
+        if self._domain == other._codomain:
             w = baseWI.__mul__(self, other)
             return WeierstrassIsomorphism(other._domain, w.tuple(), self._codomain)
-
-        # This is a temporary hack until a new class for composite isogenies has been
-        # implemented and various combinations of EllipticCurveHom instantiations can
-        # be composed in a more uniform and principled way. See #32388.
-        import copy
-        output = copy.copy(other)
-        output._set_post_isomorphism(self)
-        return output
+        else:
+            raise ValueError("Domain of first argument must equal codomain of second")
 
     def __repr__(self):
         r"""