Add docstrings; minor edits

lucas.py

@@ -33,6 +33,15 @@ def Dsequence():
         val = val + 2
 
 def Legendre(a, p):
+    """Function for calculating Legendre symbol.
+
+    Note that this is only supposed to be defined if p is an odd prime, but we
+    don't know in advance if that is true - will therefore only throw and error
+    if p is even.
+
+    Uses original power definition from
+    <https://en.wikipedia.org/wiki/Legendre_symbol>
+    """
     if (p % 2 == 0):
         raise ValueError("p must be odd, is {}".format(p))
     lv =  pow(a, (p-1)//2, p)
@@ -41,8 +50,17 @@ def Legendre(a, p):
     return lv
 
 def Jacobi(a, n):
+    """Function for calculating Jacobi symbol.
+
+    Note that this is only defined for positive odd integers n.
+
+    Uses algorithm from
+    <https://en.wikipedia.org/wiki/Jacobi_symbol#Calculating_the_Jacobi_symbol>
+    """
+    if n < 1:
+        raise ValueError("n must be positive")
     if (n % 2 == 0):
-        raise ValueError("n must be odd, is {}".format(n))
+        raise ValueError("n must be odd")
     if a % n != a:
         return Jacobi(a%n, n)
     if a != 0 and a % 2 == 0:
@@ -77,5 +95,3 @@ for n in range(1, 21, 2):
 
 
 
-
-