started work on field class:

GF.py

@@ -0,0 +1,44 @@
+from math import log
+
+#defines the field itself
+#responsible for creating elements and performing operations
+#all elements contain a pointer to the field that created them
+#elements from different fields can't interact, even if they're equivalent
+
+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:
+                if a%i == 0:
+                    b = log(a, i)
+                    if b != int(b):
+                        raise ValueError('%i is not a prime power' % a)
+                    return i, int(b)
+                i += 2
+        
+        if len(args) == 1:
+            p, n = characteristic(args[0])
+        elif len(args) > 2:
+            raise TypeError('too many arguments')
+        else:
+            p, n = args
+        self.characteristic = p
+        self.order = p**n
+        self.degree = n
+        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]
+        if p == 2:
+            self.poly[0] = 1
+        for i in pol