gh-40808: add Newton polytopes in one variable
    
in order to have the same behaviour as in several variables

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40808
Reported by: Frédéric Chapoton
Reviewer(s): Martin Rubey

Author: Release Manager

src/sage/rings/polynomial/multi_polynomial.pyx

@@ -1232,9 +1232,7 @@ cdef class MPolynomial(CommutativePolynomial):
             ((0, 2), (1, 1), (2, 0))
         """
         from sage.geometry.polyhedron.constructor import Polyhedron
-        e = self.exponents()
-        P = Polyhedron(vertices=e, base_ring=ZZ)
-        return P
+        return Polyhedron(vertices=self.exponents(), base_ring=ZZ)
 
     def __iter__(self):
         r"""

src/sage/rings/polynomial/polynomial_element.pyx

@@ -1188,6 +1188,29 @@ cdef class Polynomial(CommutativePolynomial):
         """
         return self[i]
 
+    def newton_polytope(self):
+        r"""
+        Return the Newton polytope of this polynomial.
+
+        EXAMPLES::
+
+            sage: R.<x> = QQ[]
+            sage: f = 42 + x + x^3
+            sage: P = f.newton_polytope(); P                                            # needs sage.geometry.polyhedron
+            A 1-dimensional polyhedron in ZZ^1 defined as the convex hull of 2 vertices
+
+        TESTS::
+
+            sage: R.<x> = QQ[]
+            sage: R(0).newton_polytope()                                                # needs sage.geometry.polyhedron
+            The empty polyhedron in ZZ^0
+            sage: R(1).newton_polytope()                                                # needs sage.geometry.polyhedron
+            A 0-dimensional polyhedron in ZZ^1 defined as the convex hull of 1 vertex
+        """
+        from sage.geometry.polyhedron.constructor import Polyhedron
+        return Polyhedron(vertices=[(e,) for e in self.exponents()],
+                          base_ring=ZZ)
+
     def __iter__(self):
         """
         EXAMPLES::