projective_morphism.py: Add a test to ensure sagemath#35797 fixed: Re…

…turn a version of the point with normalized coordinates

src/sage/schemes/projective/projective_morphism.py

@@ -915,6 +915,18 @@ def normalize_coordinates(self, **kwds):
              3-adic Field with capped relative precision 20
               Defn: Defined on coordinates by sending (x : y) to
                     (x^2 + (2 + O(3^20))*y^2 : (3 + O(3^21))*x*y)
+
+        ::
+
+            sage: R.<x> = QQ[]
+            sage: K.<a> = NumberField(3*x^2 + 1)
+            sage: P.<z,w> = ProjectiveSpace(K, 1)
+            sage: f = DynamicalSystem_projective([a*(z^2 + w^2), 1/3*z*w])
+            sage: f.normalize_coordinates(); f
+            Dynamical System of Projective Space of dimension 1 over
+            Number Field in a with defining polynomial 3*x^2 + 1
+            Defn: Defined on coordinates by sending (z : w) to
+                    ((3*a)*z^2 + (3*a)*w^2 : z*w)
         """
         # if ideal or valuation is specified, we scale according the norm defined by the ideal/valuation
         ideal = kwds.pop('ideal', None)
@@ -968,14 +980,12 @@ def normalize_coordinates(self, **kwds):
             return
 
         R = self.domain().base_ring()
-
-        # clear any denominators from the coefficients
         N = self.codomain().ambient_space().dimension_relative() + 1
 
+        # Only clear denominators from the coefficients in the ring of integers
         if R in NumberFields():
             if not all([self[i] in R.maximal_order() for i in range(N)]):
-                LCM = lcm([self[i].denominator() for i in range(N)])
-                self.scale_by(LCM)
+                self.scale_by(lcm([self[i].denominator() for i in range(N)]))
 
         # There are cases, such as the example above over GF(7),
         # where we want to compute GCDs, but NOT in the case