Trac #28770: Polyhedra coercion of base rings fails for number fields

Currently coercion of polyhedra with number fields does not work. The
following results in a type error:

{{{
sage: z = QQ['z'].0
sage: K = NumberField(z^2 - 2,'s')
sage: K.gen()*polytopes.simplex(backend='field')
}}}

But the backend can surely handle it, as the following does work:

{{{
sage: z = QQ['z'].0
sage: K = NumberField(z^2 - 2,'s')
sage: K.gen()*polytopes.simplex(backend='field', base_ring=K)
A 3-dimensional polyhedron in (Number Field in s with defining
polynomial z^2 - 2)^4 defined as the convex hull of 4 vertices
}}}

The underlying error:

{{{
sage: z = QQ['z'].0
sage: K = NumberField(z^2 - 2,'s')
sage: parent = polytopes.simplex().parent()
sage: parent._coerce_base_ring(K)
Rational Field
}}}

But it should be `K`.

The problem is that `_coerce_base_ring` of `Polyhedra_base` just takes
the base ring of `K`, which are the rationals.

We fix this, by not taking the base ring, if the object is already a
ring.

URL: https://trac.sagemath.org/28770
Reported by: gh-kliem
Ticket author(s): Jonathan Kliem
Reviewer(s): Léo Brunswic

src/sage/geometry/polyhedron/parent.py

@@ -672,24 +672,46 @@ def _coerce_base_ring(self, other):
             Rational Field
             sage: triangle_QQ._coerce_base_ring(0.5)
             Real Double Field
+
+        TESTS:
+
+        Test that :trac:`28770` is fixed::
+
+            sage: z = QQ['z'].0
+            sage: K = NumberField(z^2 - 2,'s')
+            sage: triangle_QQ._coerce_base_ring(K)
+            Number Field in s with defining polynomial z^2 - 2
+            sage: triangle_QQ._coerce_base_ring(K.gen())
+            Number Field in s with defining polynomial z^2 - 2
+
+            sage: z = QQ['z'].0
+            sage: K = NumberField(z^2 - 2,'s')
+            sage: K.gen()*polytopes.simplex(backend='field')
+            A 3-dimensional polyhedron in (Number Field in s with defining polynomial z^2 - 2)^4 defined as the convex hull of 4 vertices
         """
-        try:
-            other_ring = other.base_ring()
-        except AttributeError:
+        from sage.structure.element import Element
+        if isinstance(other, Element):
+            other = other.parent()
+        if hasattr(other, "is_ring") and other.is_ring():
+            other_ring = other
+        else:
             try:
-                # other is a constant?
-                other_ring = other.parent()
+                other_ring = other.base_ring()
             except AttributeError:
-                other_ring = None
-                for ring in (ZZ, QQ, RDF):
-                    try:
-                        ring.coerce(other)
-                        other_ring = ring
-                        break
-                    except TypeError:
-                        pass
-                if other_ring is None:
-                    raise TypeError('Could not coerce '+str(other)+' into ZZ, QQ, or RDF.')
+                try:
+                    # other is a constant?
+                    other_ring = other.parent()
+                except AttributeError:
+                    other_ring = None
+                    for ring in (ZZ, QQ, RDF):
+                        try:
+                            ring.coerce(other)
+                            other_ring = ring
+                            break
+                        except TypeError:
+                            pass
+                    if other_ring is None:
+                        raise TypeError('Could not coerce '+str(other)+' into ZZ, QQ, or RDF.')
 
         if not other_ring.is_exact():
             other_ring = RDF  # the only supported floating-point numbers for now