Add a note on scimath.sqrt for the definition of square root as the principal square root.

1 files changed, 16 insertions, 0 deletions

diff --git a/numpy/lib/scimath.py b/numpy/lib/scimath.py
index d601cbd14..ed04d1ce5 100644
--- a/numpy/lib/scimath.py
+++ b/numpy/lib/scimath.py
@@ -192,6 +192,22 @@ def sqrt(x):
 
     >>> np.lib.scimath.sqrt([-1,4])
     array([ 0.+1.j,  2.+0.j])
+
+    Notes
+    -----
+
+    As the numpy.sqrt, this returns the principal square root of x, which is
+    what most people mean when they use square root; the principal square root
+    of x is not any number z such as z^2 = x. 
+
+    For positive numbers, the principal square root is defined as the positive
+    number z such as z^2 = x. 
+
+    The principal square root of -1 is i, the principal square root of any
+    negative number -x is defined a i * sqrt(x). For any non zero complex
+    number, it is defined by using the following branch cut: x = r e^(i t) with
+    r > 0 and -pi < t <= pi. The principal square root is then 
+    sqrt(r) e^(i t/2).
     """
     x = _fix_real_lt_zero(x)
     return nx.sqrt(x)