DOC: add examples and extend exisiting dos for polynomial subclasses

6 files changed, 76 insertions, 37 deletions

diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py
index aa2b5b5ea..f14ed988d 100644
--- a/numpy/polynomial/chebyshev.py
+++ b/numpy/polynomial/chebyshev.py
@@ -21,9 +21,10 @@ Arithmetic
 ----------
 - `chebadd` -- add two Chebyshev series.
 - `chebsub` -- subtract one Chebyshev series from another.
+- `chebmulx` -- multiply a Chebyshev series in ``P_i(x)`` by ``x``.
 - `chebmul` -- multiply two Chebyshev series.
 - `chebdiv` -- divide one Chebyshev series by another.
-- `chebpow` -- raise a Chebyshev series to an positive integer power
+- `chebpow` -- raise a Chebyshev series to a positive integer power.
 - `chebval` -- evaluate a Chebyshev series at given points.
 - `chebval2d` -- evaluate a 2D Chebyshev series at given points.
 - `chebval3d` -- evaluate a 3D Chebyshev series at given points.
@@ -579,7 +580,7 @@ def chebadd(c1, c2):
 
     See Also
     --------
-    chebsub, chebmul, chebdiv, chebpow
+    chebsub, chebmulx, chebmul, chebdiv, chebpow
 
     Notes
     -----
@@ -629,7 +630,7 @@ def chebsub(c1, c2):
 
     See Also
     --------
-    chebadd, chebmul, chebdiv, chebpow
+    chebadd, chebmulx, chebmul, chebdiv, chebpow
 
     Notes
     -----
@@ -684,6 +685,12 @@ def chebmulx(c):
 
     .. versionadded:: 1.5.0
 
+    Examples
+    --------
+    >>> from numpy.polynomial import chebyshev as C
+    >>> C.chebmulx([1,2,3])
+    array([ 1.,  2.5,  3.,  1.5,  2.])
+
     """
     # c is a trimmed copy
     [c] = pu.as_series([c])
@@ -722,7 +729,7 @@ def chebmul(c1, c2):
 
     See Also
     --------
-    chebadd, chebsub, chebdiv, chebpow
+    chebadd, chebsub, chebmulx, chebdiv, chebpow
 
     Notes
     -----
@@ -773,7 +780,7 @@ def chebdiv(c1, c2):
 
     See Also
     --------
-    chebadd, chebsub, chebmul, chebpow
+    chebadd, chebsub, chemulx, chebmul, chebpow
 
     Notes
     -----
@@ -841,10 +848,13 @@ def chebpow(c, pow, maxpower=16):
 
     See Also
     --------
-    chebadd, chebsub, chebmul, chebdiv
+    chebadd, chebsub, chebmulx, chebmul, chebdiv
 
     Examples
     --------
+    >>> from numpy.polynomial import chebyshev as C
+    >>> C.chebpow([1, 2, 3, 4], 2)
+    array([15.5, 22. , 16. , 14. , 12.5, 12. ,  8. ])
 
     """
     # c is a trimmed copy
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py
index 8c33ee863..2aed4b34f 100644
--- a/numpy/polynomial/hermite.py
+++ b/numpy/polynomial/hermite.py
@@ -16,11 +16,12 @@ Constants
 
 Arithmetic
 ----------
-- `hermmulx` -- multiply a Hermite series in ``P_i(x)`` by ``x``.
 - `hermadd` -- add two Hermite series.
 - `hermsub` -- subtract one Hermite series from another.
+- `hermmulx` -- multiply a Hermite series in ``P_i(x)`` by ``x``.
 - `hermmul` -- multiply two Hermite series.
 - `hermdiv` -- divide one Hermite series by another.
+- `hermpow` -- raise a Hermite series to a positive integer power.
 - `hermval` -- evaluate a Hermite series at given points.
 - `hermval2d` -- evaluate a 2D Hermite series at given points.
 - `hermval3d` -- evaluate a 3D Hermite series at given points.
@@ -323,7 +324,7 @@ def hermadd(c1, c2):
 
     See Also
     --------
-    hermsub, hermmul, hermdiv, hermpow
+    hermsub, hermmulx, hermmul, hermdiv, hermpow
 
     Notes
     -----
@@ -371,7 +372,7 @@ def hermsub(c1, c2):
 
     See Also
     --------
-    hermadd, hermmul, hermdiv, hermpow
+    hermadd, hermmulx, hermmul, hermdiv, hermpow
 
     Notes
     -----
@@ -417,6 +418,10 @@ def hermmulx(c):
     out : ndarray
         Array representing the result of the multiplication.
 
+    See Also
+    --------
+    hermadd, hermsub, hermmul, hermdiv, hermpow
+
     Notes
     -----
     The multiplication uses the recursion relationship for Hermite
@@ -469,7 +474,7 @@ def hermmul(c1, c2):
 
     See Also
     --------
-    hermadd, hermsub, hermdiv, hermpow
+    hermadd, hermsub, hermmulx, hermdiv, hermpow
 
     Notes
     -----
@@ -537,7 +542,7 @@ def hermdiv(c1, c2):
 
     See Also
     --------
-    hermadd, hermsub, hermmul, hermpow
+    hermadd, hermsub, hermmulx, hermmul, hermpow
 
     Notes
     -----
@@ -606,7 +611,7 @@ def hermpow(c, pow, maxpower=16):
 
     See Also
     --------
-    hermadd, hermsub, hermmul, hermdiv
+    hermadd, hermsub, hermmulx, hermmul, hermdiv
 
     Examples
     --------
diff --git a/numpy/polynomial/hermite_e.py b/numpy/polynomial/hermite_e.py
index 6166c03fd..d4520ad6c 100644
--- a/numpy/polynomial/hermite_e.py
+++ b/numpy/polynomial/hermite_e.py
@@ -16,11 +16,12 @@ Constants
 
 Arithmetic
 ----------
-- `hermemulx` -- multiply a Hermite_e series in ``P_i(x)`` by ``x``.
 - `hermeadd` -- add two Hermite_e series.
 - `hermesub` -- subtract one Hermite_e series from another.
+- `hermemulx` -- multiply a Hermite_e series in ``P_i(x)`` by ``x``.
 - `hermemul` -- multiply two Hermite_e series.
 - `hermediv` -- divide one Hermite_e series by another.
+- `hermepow` -- raise a Hermite_e series to a positive integer power.
 - `hermeval` -- evaluate a Hermite_e series at given points.
 - `hermeval2d` -- evaluate a 2D Hermite_e series at given points.
 - `hermeval3d` -- evaluate a 3D Hermite_e series at given points.
@@ -324,7 +325,7 @@ def hermeadd(c1, c2):
 
     See Also
     --------
-    hermesub, hermemul, hermediv, hermepow
+    hermesub, hermemulx, hermemul, hermediv, hermepow
 
     Notes
     -----
@@ -372,7 +373,7 @@ def hermesub(c1, c2):
 
     See Also
     --------
-    hermeadd, hermemul, hermediv, hermepow
+    hermeadd, hermemulx, hermemul, hermediv, hermepow
 
     Notes
     -----
@@ -470,7 +471,7 @@ def hermemul(c1, c2):
 
     See Also
     --------
-    hermeadd, hermesub, hermediv, hermepow
+    hermeadd, hermesub, hermemulx, hermediv, hermepow
 
     Notes
     -----
@@ -538,7 +539,7 @@ def hermediv(c1, c2):
 
     See Also
     --------
-    hermeadd, hermesub, hermemul, hermepow
+    hermeadd, hermesub, hermemulx, hermemul, hermepow
 
     Notes
     -----
@@ -605,7 +606,7 @@ def hermepow(c, pow, maxpower=16):
 
     See Also
     --------
-    hermeadd, hermesub, hermemul, hermediv
+    hermeadd, hermesub, hermemulx, hermemul, hermediv
 
     Examples
     --------
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py
index 0e4554071..a116d20a7 100644
--- a/numpy/polynomial/laguerre.py
+++ b/numpy/polynomial/laguerre.py
@@ -16,11 +16,12 @@ Constants
 
 Arithmetic
 ----------
-- `lagmulx` -- multiply a Laguerre series in ``P_i(x)`` by ``x``.
 - `lagadd` -- add two Laguerre series.
 - `lagsub` -- subtract one Laguerre series from another.
+- `lagmulx` -- multiply a Laguerre series in ``P_i(x)`` by ``x``.
 - `lagmul` -- multiply two Laguerre series.
 - `lagdiv` -- divide one Laguerre series by another.
+- `lagpow` -- raise a Laguerre series to a positive integer power.
 - `lagval` -- evaluate a Laguerre series at given points.
 - `lagval2d` -- evaluate a 2D Laguerre series at given points.
 - `lagval3d` -- evaluate a 3D Laguerre series at given points.
@@ -320,7 +321,7 @@ def lagadd(c1, c2):
 
     See Also
     --------
-    lagsub, lagmul, lagdiv, lagpow
+    lagsub, lagmulx, lagmul, lagdiv, lagpow
 
     Notes
     -----
@@ -369,7 +370,7 @@ def lagsub(c1, c2):
 
     See Also
     --------
-    lagadd, lagmul, lagdiv, lagpow
+    lagadd, lagmulx, lagmul, lagdiv, lagpow
 
     Notes
     -----
@@ -415,6 +416,10 @@ def lagmulx(c):
     out : ndarray
         Array representing the result of the multiplication.
 
+    See Also
+    --------
+    lagadd, lagsub, lagmul, lagdiv, lagpow
+
     Notes
     -----
     The multiplication uses the recursion relationship for Laguerre
@@ -468,7 +473,7 @@ def lagmul(c1, c2):
 
     See Also
     --------
-    lagadd, lagsub, lagdiv, lagpow
+    lagadd, lagsub, lagmulx, lagdiv, lagpow
 
     Notes
     -----
@@ -536,7 +541,7 @@ def lagdiv(c1, c2):
 
     See Also
     --------
-    lagadd, lagsub, lagmul, lagpow
+    lagadd, lagsub, lagmulx, lagmul, lagpow
 
     Notes
     -----
@@ -603,7 +608,7 @@ def lagpow(c, pow, maxpower=16):
 
     See Also
     --------
-    lagadd, lagsub, lagmul, lagdiv
+    lagadd, lagsub, lagmulx, lagmul, lagdiv
 
     Examples
     --------
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py
index 0a20707e6..e741ce0f8 100644
--- a/numpy/polynomial/legendre.py
+++ b/numpy/polynomial/legendre.py
@@ -27,12 +27,12 @@ Arithmetic
 .. autosummary::
    :toctree: generated/
 
-   legmulx              multiply a Legendre series in P_i(x) by x.
    legadd               add two Legendre series.
    legsub               subtract one Legendre series from another.
+   legmulx              multiply a Legendre series in ``P_i(x)`` by ``x``.
    legmul               multiply two Legendre series.
    legdiv               divide one Legendre series by another.
-   legpow               raise a Legendre series to an positive integer power
+   legpow               raise a Legendre series to an positive integer power.
    legval               evaluate a Legendre series at given points.
    legval2d             evaluate a 2D Legendre series at given points.
    legval3d             evaluate a 3D Legendre series at given points.
@@ -351,7 +351,7 @@ def legadd(c1, c2):
 
     See Also
     --------
-    legsub, legmul, legdiv, legpow
+    legsub, legmulx, legmul, legdiv, legpow
 
     Notes
     -----
@@ -401,7 +401,7 @@ def legsub(c1, c2):
 
     See Also
     --------
-    legadd, legmul, legdiv, legpow
+    legadd, legmulx, legmul, legdiv, legpow
 
     Notes
     -----
@@ -451,6 +451,10 @@ def legmulx(c):
     out : ndarray
         Array representing the result of the multiplication.
 
+    See Also
+    --------
+    legadd, legmul, legmul, legdiv, legpow
+
     Notes
     -----
     The multiplication uses the recursion relationship for Legendre
@@ -460,6 +464,12 @@ def legmulx(c):
 
       xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1)
 
+    Examples
+    --------
+    >>> from numpy.polynomial import legendre as L
+    >>> L.legmulx([1,2,3])
+    array([ 0.66666667, 2.2, 1.33333333, 1.8])
+
     """
     # c is a trimmed copy
     [c] = pu.as_series([c])
@@ -500,7 +510,7 @@ def legmul(c1, c2):
 
     See Also
     --------
-    legadd, legsub, legdiv, legpow
+    legadd, legsub, legmulx, legdiv, legpow
 
     Notes
     -----
@@ -570,7 +580,7 @@ def legdiv(c1, c2):
 
     See Also
     --------
-    legadd, legsub, legmul, legpow
+    legadd, legsub, legmulx, legmul, legpow
 
     Notes
     -----
@@ -640,7 +650,7 @@ def legpow(c, pow, maxpower=16):
 
     See Also
     --------
-    legadd, legsub, legmul, legdiv
+    legadd, legsub, legmulx, legmul, legdiv
 
     Examples
     --------
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py
index 7c43e658a..8807904ae 100644
--- a/numpy/polynomial/polynomial.py
+++ b/numpy/polynomial/polynomial.py
@@ -18,9 +18,10 @@ Arithmetic
 ----------
 - `polyadd` -- add two polynomials.
 - `polysub` -- subtract one polynomial from another.
+- `polymulx` -- multiply a polynomial in ``P_i(x)`` by ``x``.
 - `polymul` -- multiply two polynomials.
 - `polydiv` -- divide one polynomial by another.
-- `polypow` -- raise a polynomial to an positive integer power
+- `polypow` -- raise a polynomial to an positive integer power.
 - `polyval` -- evaluate a polynomial at given points.
 - `polyval2d` -- evaluate a 2D polynomial at given points.
 - `polyval3d` -- evaluate a 3D polynomial at given points.
@@ -224,7 +225,7 @@ def polyadd(c1, c2):
 
     See Also
     --------
-    polysub, polymul, polydiv, polypow
+    polysub, polymulx, polymul, polydiv, polypow
 
     Examples
     --------
@@ -269,7 +270,7 @@ def polysub(c1, c2):
 
     See Also
     --------
-    polyadd, polymul, polydiv, polypow
+    polyadd, polymulx, polymul, polydiv, polypow
 
     Examples
     --------
@@ -312,6 +313,10 @@ def polymulx(c):
     out : ndarray
         Array representing the result of the multiplication.
 
+    See Also
+    --------
+    polyadd, polysub, polymul, polydiv, polypow
+
     Notes
     -----
 
@@ -351,7 +356,7 @@ def polymul(c1, c2):
 
     See Also
     --------
-    polyadd, polysub, polydiv, polypow
+    polyadd, polysub, polymulx, polydiv, polypow
 
     Examples
     --------
@@ -388,7 +393,7 @@ def polydiv(c1, c2):
 
     See Also
     --------
-    polyadd, polysub, polymul, polypow
+    polyadd, polysub, polymulx, polymul, polypow
 
     Examples
     --------
@@ -450,10 +455,13 @@ def polypow(c, pow, maxpower=None):
 
     See Also
     --------
-    polyadd, polysub, polymul, polydiv
+    polyadd, polysub, polymulx, polymul, polydiv
 
     Examples
     --------
+    >>> from numpy.polynomial import polynomial as P
+    >>> P.polypow([1,2,3], 2)
+    array([ 1., 4., 10., 12., 9.])
 
     """
     # c is a trimmed copy