ENH: Add static methods basis and cast to the polynomial classes.

The new basis method is a convenient way to return an instance of the basis
function of given degree for the class. It is intended mostly for
pedagogical purposes.

The new cast method provides an alternate way to convert an instance of one
polynomial class to another. It complements the convert instance method.

1 files changed, 80 insertions, 9 deletions

diff --git a/numpy/polynomial/polytemplate.py b/numpy/polynomial/polytemplate.py
index 9d5607467..d8db00f15 100644
--- a/numpy/polynomial/polytemplate.py
+++ b/numpy/polynomial/polytemplate.py
@@ -45,11 +45,11 @@ class $name(pu.PolyBase) :
 
     Attributes
     ----------
-    coef : (N,) array
+    coef : (N,) ndarray
         $name coefficients, from low to high.
-    domain : (2,) array
+    domain : (2,) ndarray
         Domain that is mapped to ``window``.
-    window : (2,) array
+    window : (2,) ndarray
         Window that ``domain`` is mapped to.
 
     Class Attributes
@@ -659,14 +659,19 @@ class $name(pu.PolyBase) :
     def linspace(self, n=100, domain=None):
         """Return x,y values at equally spaced points in domain.
 
-        Returns x, y values at `n` equally spaced points across domain.
-        Here y is the value of the polynomial at the points x.  This is
-        intended as a plotting aid.
+        Returns x, y values at `n` linearly spaced points across domain.
+        Here y is the value of the polynomial at the points x. By default
+        the domain is the same as that of the $name instance.  This method
+        is intended mostly as a plotting aid.
 
         Parameters
         ----------
         n : int, optional
             Number of point pairs to return. The default value is 100.
+        domain : {None, array_like}
+            If not None, the specified domain is used instead of that of
+            the calling instance. It should be of the form ``[beg,end]``.
+            The default is None.
 
         Returns
         -------
@@ -784,7 +789,7 @@ class $name(pu.PolyBase) :
 
         Returns
         -------
-        object : $name
+        object : $name instance
             Series with the specified roots.
 
         See Also
@@ -808,7 +813,7 @@ class $name(pu.PolyBase) :
         Parameters
         ----------
         domain : array_like
-            The resulting array must be if the form ``[beg, end]``, where
+            The resulting array must be of the form ``[beg, end]``, where
             ``beg`` and ``end`` are the endpoints of the domain.
         window : array_like
             The resulting array must be if the form ``[beg, end]``, where
@@ -816,10 +821,76 @@ class $name(pu.PolyBase) :
 
         Returns
         -------
-        identity : $name object
+        identity : $name instance
 
         """
         off, scl = pu.mapparms(window, domain)
         coef = ${nick}line(off, scl)
         return $name(coef, domain, window)
+
+    @staticmethod
+    def basis(deg, domain=$domain, window=$domain):
+        """$name polynomial of degree `deg`.
+
+        Returns an instance of the $name polynomial of degree `d`.
+
+        Parameters
+        ----------
+        deg : int
+            Degree of the $name polynomial. Must be >= 0.
+        domain : array_like
+            The resulting array must be of the form ``[beg, end]``, where
+            ``beg`` and ``end`` are the endpoints of the domain.
+        window : array_like
+            The resulting array must be if the form ``[beg, end]``, where
+            ``beg`` and ``end`` are the endpoints of the window.
+
+        Returns
+        p : $name instance
+
+        Notes
+        -----
+        .. versionadded:: 1.7.0
+
+        """
+        ideg = int(deg)
+        if ideg != deg or ideg < 0:
+            raise ValueError("deg must be non-negative integer")
+        return $name([0]*ideg + [1], domain, window)
+
+    @staticmethod
+    def cast(series, domain=$domain, window=$domain):
+        """Convert instance to equivalent $name series.
+
+        The `series` is expected to be an instance of some polynomial
+        series of one of the types supported by by the numpy.polynomial
+        module, but could be some other class that supports the convert
+        method.
+
+        Parameters
+        ----------
+        series : series
+            The instance series to be converted.
+        domain : array_like
+            The resulting array must be of the form ``[beg, end]``, where
+            ``beg`` and ``end`` are the endpoints of the domain.
+        window : array_like
+            The resulting array must be if the form ``[beg, end]``, where
+            ``beg`` and ``end`` are the endpoints of the window.
+
+        Returns
+        p : $name instance
+            A $name series equal to the `poly` series.
+
+        See Also
+        --------
+        convert -- similar instance method
+
+        Notes
+        -----
+        .. versionadded:: 1.7.0
+
+        """
+        return series.convert(domain, $name, window)
+
 '''.replace('REL_IMPORT', rel_import))