Ticket #11719: trac_11719.patch

sage/rings/laurent_series_ring_element.pyx

@@ -202 +202 @@
             1
         """
         return self.__u.is_zero()
-        
+
+
+    def is_monomial(self):
+        """
+        Returns True if this element is a monomial.  That is, if self is
+        `a*x^n` for some non-negative integer `n` and some coefficient `a`
+        in the base ring.
+
+        EXAMPLES::
+
+            sage: k.<z> = LaurentSeriesRing(QQ, 'z')
+            sage: (30*z).is_monomial()
+            True
+            sage: k(1).is_monomial()
+            True
+            sage: (z+1).is_monomial()
+            False
+            sage: (3*z^-2909).is_monomial()
+            True
+        """
+
+        return self.__u.is_monomial()
+
     def __nonzero__(self):
         return not not self.__u
         

sage/rings/polynomial/laurent_polynomial.pyx

@@ -583 +583 @@
     cpdef ModuleElement _ilmul_(self, RingElement c):
         self.__u *= c
         return self
+
+    def is_monomial(self):
+        """
+        Returns True if this element is a monomial.  That is, if self is
+        `a*x^n` for some integer `n` and some coefficient `a` in the base
+        ring.
+
+        EXAMPLES::
+
+            sage: k.<z> = LaurentPolynomialRing(QQ)
+            sage: z.is_monomial()
+            True
+            sage: k(1).is_monomial()
+            True
+            sage: (z+1).is_monomial()
+            False
+            sage: (38*z^-2909).is_monomial()
+            True
+        """
+
+        return self.__u.is_monomial()
                              
     def __pow__(_self, r, dummy):
         """
@@ -1328 +1349 @@
             ans._poly -= right._poly
         return ans
 
+    def is_monomial(self):
+        """
+        Returns True if this element is a monomial.
+
+        EXAMPLES::
+
+            sage: k.<y,z> = LaurentPolynomialRing(QQ)
+            sage: z.is_monomial()
+            True
+            sage: k(1).is_monomial()
+            True
+            sage: (z+1).is_monomial()
+            False
+            sage: (38*z^-2909).is_monomial()
+            True
+        """
+
+        return len(self._poly.dict()) <= 1
+
     cpdef ModuleElement _neg_(self):
         """
         Returns -self.

sage/rings/power_series_ring_element.pyx

@@ -1052 +1052 @@
     def __rshift__(self, n):
         return self.parent()(self.polynomial() >> n, self.prec())
 
+    def is_monomial(self):
+        """
+        Returns True if this element is a monomial.  That is, if self is
+        `a*x^n` for some non-negative integer `n` and some coefficient `a`
+        in the base ring.
+
+        EXAMPLES::
+
+            sage: k.<z> = PowerSeriesRing(QQ, 'z')
+            sage: z.is_monomial()
+            True
+            sage: k(1).is_monomial()
+            True
+            sage: (z+1).is_monomial()
+            False
+            sage: (z^2909).is_monomial()
+            True
+        """
+
+        return self.polynomial().is_monomial()
+
     def is_square(self):
         """
         Returns True if this function has a square root in this ring, e.g.