more work on field class

GF.py

@@ -1,4 +1,4 @@
-from math import log
+import math
 
 #defines the field itself
 #responsible for creating elements and performing operations
@@ -8,23 +8,16 @@ from math import log
 class GF:
     def __init__(self, *args):
         
-        def characteristic(a):
-            if a%2 == 0:
-                b = log(a, 2)
-                if b != int(b):
-                    raise ValueError('%i is not a prime power' % a)
-                return 2, int(b)
-            i = 3
-            while i <= 23:
+        def getcharacteristic(a):
+            for i in (2, 3, 5, 7, 11, 13, 17, 19, 23):
                 if a%i == 0:
-                    b = log(a, i)
-                    if b != int(b):
+                    b = math.log(a, i)
+                    if not math.isclose(b, int(b+1e-6), abs_tol=1e-6) :
                         raise ValueError('%i is not a prime power' % a)
-                    return i, int(b)
-                i += 2
+                    return i, int(b+1e-6)
         
         if len(args) == 1:
-            p, n = characteristic(args[0])
+            p, n = getcharacteristic(args[0])
         elif len(args) > 2:
             raise TypeError('too many arguments')
         else:
@@ -35,10 +28,57 @@ class GF:
         file = open('gf' + str(p) + '.txt', 'r')
         pol = file.readlines()[n-2]
         file.close()
-        pol = pol.split(',')
-        #integer coefficients of defining polynomial
-        #index is the exponent 
-        self.poly = [None]*n + [1]
+        #removes newline then splits into individual terms
+        pol = pol[:-1].split(',')
+        #(exponent, coefficient) for each term of the polynomial
+        self.poly = []
+        for i in pol:
+            if '(' in i:
+                a, b = i.split('(')
+                #constant term isn't given an exponent in the txt file
+                a = a if a else 0
+                self.poly.append((int(a), int(b[:-1])))
+            else:
+                self.poly.append((int(i),1))
         if p == 2:
-            self.poly[0] = 1
-        for i in pol
+            self.poly.append((0,1))
+        
+    
+    #creates a new element with the given value
+    def new(val):
+        
+        #splits integers into their binary components
+        def bisplit(bal):
+            pass
+        
+        if isisntance(val, int):
+            if self.characteristic != 2:
+                raise TypeError('integer definition of field elements is only allowed in fields of characteristic 2')
+        #covers the case that the value is an iterable of individual terms
+        #first term is for exponent zero, etc.
+        #accepts integers or strings
+        else:
+            pol = [0] * self.degree
+            for i in range(len(val)):
+                if isinstance(val[i], int):
+                    pol[i] = val[i]
+                else:
+                    #TODO for christs sake refactor this
+                    try:
+                        pol[i] = val[i]
+                    except ValueError:
+                        try:
+                            pol[i] = int(val[i])
+                        except ValueError:
+                            a = ord(val[i].tolower())
+                            if 97 <= a <= 122:
+                                pol[i] = a - 87
+                            else:
+                                raise ValueError('polynomial coefficient is uninterprettable')
+            
+                    
+            
+
+class GFElement:
+    def __init_(self, value, field):
+        self.field = field