Trac #11719: Add is_monomial() to power series and laurent series rin…

…g elements

It should be trivial to check if a power/laurent series ring element is
a monomial or not.  It is not.

URL: http://trac.sagemath.org/11719
Reported by: boothby
Ticket author(s): Tom Boothby, Ralf Stephan
Reviewer(s): Peter Bruin

src/sage/rings/laurent_series_ring_element.pyx

@@ -202,6 +202,28 @@ cdef class LaurentSeries(AlgebraElement):
         """
         return self.__u.is_zero()
 
+    def is_monomial(self):
+        """
+        Return True if this element is a monomial.  That is, if self is
+        `x^n` for some integer `n`.
+
+        EXAMPLES::
+
+            sage: k.<z> = LaurentSeriesRing(QQ, 'z')
+            sage: (30*z).is_monomial()
+            False
+            sage: k(1).is_monomial()
+            True
+            sage: (z+1).is_monomial()
+            False
+            sage: (z^-2909).is_monomial()
+            True
+            sage: (3*z^-2909).is_monomial()
+            False
+        """
+
+        return self.__u.is_monomial()
+
     def __nonzero__(self):
         return not not self.__u
 

src/sage/rings/polynomial/laurent_polynomial.pyx

@@ -650,6 +650,28 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial_generic):
         self.__u *= c
         return self
 
+    def is_monomial(self):
+        """
+        Return True if this element is a monomial.  That is, if self is
+        `x^n` for some integer `n`.
+
+        EXAMPLES::
+
+            sage: k.<z> = LaurentPolynomialRing(QQ)
+            sage: z.is_monomial()
+            True
+            sage: k(1).is_monomial()
+            True
+            sage: (z+1).is_monomial()
+            False
+            sage: (z^-2909).is_monomial()
+            True
+            sage: (38*z^-2909).is_monomial()
+            False
+        """
+
+        return self.__u.is_monomial()
+
     def __pow__(_self, r, dummy):
         """
         EXAMPLES::
@@ -1867,6 +1889,28 @@ cdef class LaurentPolynomial_mpair(LaurentPolynomial_generic):
             ans._poly -= right._poly
         return ans
 
+    def is_monomial(self):
+        """
+        Return 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: (z^-2909).is_monomial()
+            True
+            sage: (38*z^-2909).is_monomial()
+            False
+        """
+
+        d = self._poly.dict()
+        return len(d) == 1 and 1 in d.values()
+
     cpdef ModuleElement _neg_(self):
         """
         Returns -self.

src/sage/rings/power_series_ring_element.pyx

@@ -1104,6 +1104,28 @@ cdef class PowerSeries(AlgebraElement):
     def __rshift__(self, n):
         return self.parent()(self.polynomial() >> n, self.prec())
 
+    def is_monomial(self):
+        """
+        Return True if this element is a monomial.  That is, if self is
+        `x^n` for some non-negative integer `n`.
+
+        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
+            sage: (3*z^2909).is_monomial()
+            False
+        """
+
+        return self.polynomial().is_monomial()
+
     def is_square(self):
         """
         Returns True if this function has a square root in this ring, e.g.