MAINT: Move duplicate implementations of ABCPolyBase._fromroots into polyutils

Every implementation is the same right now, other than calling different line / mul functions.

Found by LGTM.

7 files changed, 36 insertions, 90 deletions

diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py
index e8efe1cb9..70527ec79 100644
--- a/numpy/polynomial/chebyshev.py
+++ b/numpy/polynomial/chebyshev.py
@@ -541,21 +541,7 @@ def chebfromroots(roots):
     array([1.5+0.j, 0. +0.j, 0.5+0.j])
 
     """
-    if len(roots) == 0:
-        return np.ones(1)
-    else:
-        [roots] = pu.as_series([roots], trim=False)
-        roots.sort()
-        p = [chebline(-r, 1) for r in roots]
-        n = len(p)
-        while n > 1:
-            m, r = divmod(n, 2)
-            tmp = [chebmul(p[i], p[i+m]) for i in range(m)]
-            if r:
-                tmp[0] = chebmul(tmp[0], p[-1])
-            p = tmp
-            n = m
-        return p[0]
+    return pu._fromroots(chebline, chebmul, roots)
 
 
 def chebadd(c1, c2):
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py
index 93c9fc564..1dd2563bb 100644
--- a/numpy/polynomial/hermite.py
+++ b/numpy/polynomial/hermite.py
@@ -286,21 +286,7 @@ def hermfromroots(roots):
     array([0.+0.j, 0.+0.j])
 
     """
-    if len(roots) == 0:
-        return np.ones(1)
-    else:
-        [roots] = pu.as_series([roots], trim=False)
-        roots.sort()
-        p = [hermline(-r, 1) for r in roots]
-        n = len(p)
-        while n > 1:
-            m, r = divmod(n, 2)
-            tmp = [hermmul(p[i], p[i+m]) for i in range(m)]
-            if r:
-                tmp[0] = hermmul(tmp[0], p[-1])
-            p = tmp
-            n = m
-        return p[0]
+    return pu._fromroots(hermline, hermmul, roots)
 
 
 def hermadd(c1, c2):
diff --git a/numpy/polynomial/hermite_e.py b/numpy/polynomial/hermite_e.py
index f6ba64301..282d5da90 100644
--- a/numpy/polynomial/hermite_e.py
+++ b/numpy/polynomial/hermite_e.py
@@ -287,21 +287,7 @@ def hermefromroots(roots):
     array([0.+0.j, 0.+0.j])
 
     """
-    if len(roots) == 0:
-        return np.ones(1)
-    else:
-        [roots] = pu.as_series([roots], trim=False)
-        roots.sort()
-        p = [hermeline(-r, 1) for r in roots]
-        n = len(p)
-        while n > 1:
-            m, r = divmod(n, 2)
-            tmp = [hermemul(p[i], p[i+m]) for i in range(m)]
-            if r:
-                tmp[0] = hermemul(tmp[0], p[-1])
-            p = tmp
-            n = m
-        return p[0]
+    return pu._fromroots(hermeline, hermemul, roots)
 
 
 def hermeadd(c1, c2):
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py
index fbd8e8ab7..337c71dd3 100644
--- a/numpy/polynomial/laguerre.py
+++ b/numpy/polynomial/laguerre.py
@@ -283,21 +283,7 @@ def lagfromroots(roots):
     array([0.+0.j, 0.+0.j])
 
     """
-    if len(roots) == 0:
-        return np.ones(1)
-    else:
-        [roots] = pu.as_series([roots], trim=False)
-        roots.sort()
-        p = [lagline(-r, 1) for r in roots]
-        n = len(p)
-        while n > 1:
-            m, r = divmod(n, 2)
-            tmp = [lagmul(p[i], p[i+m]) for i in range(m)]
-            if r:
-                tmp[0] = lagmul(tmp[0], p[-1])
-            p = tmp
-            n = m
-        return p[0]
+    return pu._fromroots(lagline, lagmul, roots)
 
 
 def lagadd(c1, c2):
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py
index b5e4c9bef..0037f3ad0 100644
--- a/numpy/polynomial/legendre.py
+++ b/numpy/polynomial/legendre.py
@@ -314,21 +314,7 @@ def legfromroots(roots):
     array([ 1.33333333+0.j,  0.00000000+0.j,  0.66666667+0.j]) # may vary
 
     """
-    if len(roots) == 0:
-        return np.ones(1)
-    else:
-        [roots] = pu.as_series([roots], trim=False)
-        roots.sort()
-        p = [legline(-r, 1) for r in roots]
-        n = len(p)
-        while n > 1:
-            m, r = divmod(n, 2)
-            tmp = [legmul(p[i], p[i+m]) for i in range(m)]
-            if r:
-                tmp[0] = legmul(tmp[0], p[-1])
-            p = tmp
-            n = m
-        return p[0]
+    return pu._fromroots(legline, legmul, roots)
 
 
 def legadd(c1, c2):
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py
index 3cb6765da..2b6c9fd0a 100644
--- a/numpy/polynomial/polynomial.py
+++ b/numpy/polynomial/polynomial.py
@@ -188,21 +188,7 @@ def polyfromroots(roots):
     array([1.+0.j,  0.+0.j,  1.+0.j])
 
     """
-    if len(roots) == 0:
-        return np.ones(1)
-    else:
-        [roots] = pu.as_series([roots], trim=False)
-        roots.sort()
-        p = [polyline(-r, 1) for r in roots]
-        n = len(p)
-        while n > 1:
-            m, r = divmod(n, 2)
-            tmp = [polymul(p[i], p[i+m]) for i in range(m)]
-            if r:
-                tmp[0] = polymul(tmp[0], p[-1])
-            p = tmp
-            n = m
-        return p[0]
+    return pu._fromroots(polyline, polymul, roots)
 
 
 def polyadd(c1, c2):
diff --git a/numpy/polynomial/polyutils.py b/numpy/polynomial/polyutils.py
index 4054d77ff..9482ed89f 100644
--- a/numpy/polynomial/polyutils.py
+++ b/numpy/polynomial/polyutils.py
@@ -459,3 +459,33 @@ def _vander3d(vander_f, x, y, z, deg):
     vz = vander_f(z, degz)
     v = vx[..., None, None]*vy[..., None,:, None]*vz[..., None, None,:]
     return v.reshape(v.shape[:-3] + (-1,))
+
+
+def _fromroots(line_f, mul_f, roots):
+    """
+    Helper function used to implement the ``<type>fromroots`` functions.
+
+    Parameters
+    ----------
+    line_f : function(float, float) -> ndarray
+        The ``<type>line`` function, such as ``polyline``
+    mul_f : function(array_like, array_like) -> ndarray
+        The ``<type>mul`` function, such as ``polymul``
+    roots :
+        See the ``<type>fromroots`` functions for more detail
+    """
+    if len(roots) == 0:
+        return np.ones(1)
+    else:
+        [roots] = as_series([roots], trim=False)
+        roots.sort()
+        p = [line_f(-r, 1) for r in roots]
+        n = len(p)
+        while n > 1:
+            m, r = divmod(n, 2)
+            tmp = [mul_f(p[i], p[i+m]) for i in range(m)]
+            if r:
+                tmp[0] = mul_f(tmp[0], p[-1])
+            p = tmp
+            n = m
+        return p[0]