padic.py

@@ -0,0 +1,81 @@
+from fractions import Fraction
+from sys import maxint
+
+class PAdic:
+    p = 2
+    def __init__(self):
+        self.val  = '' # current known value
+        self.prec = 0 # current known precision
+        self.order = 0 # order/valuation of number
+        pass # initialize object as subclass perhaps
+    
+    def get(self, prec):
+        'Return value of number with given precision.'
+        raise NotImplementedError
+    
+    # return value with precision up to 32 bits
+    def __int__(self):
+        return int(self.get(32), p)
+    def __str__(self):
+        return self.get(32)
+    def __repr__(self):
+        pass
+    
+    # arithmetic operations
+    def __add__(self, other):
+        return PAdicAdd(self, other)
+    def __radd__(self, other):
+        return PAdicAdd(other, self)
+    def __sub__(self, other):
+        return PAdicAdd(self, PAdicInv(other))
+    def __rsub__(self, other):
+        return PAdicAdd(other, PAdicInv(self))
+    def __smul__(self, other):
+        return PAdicMul(self, other)
+    def __rsub__(self, other):
+        return PAdicMul(other, self)
+    
+    # p-adic norm
+    def __abs__(self):
+        if self.order == maxint:
+            return 0
+        norm = Fraction(1)
+        if self.order > 0:
+            norm.numerator = p ** self.order
+        if self.order < 0:
+            norm.denominator = p ** self.order
+        return norm
+
+class PAdicConst(PAdic):
+    def __init__(self, value):
+        PAdic.__init__(self)
+        value = Fraction(value)
+        
+        # calculate valuation
+        if value == 0:
+            self.value = value
+            self.val = '0'
+            return
+        
+        self.norm = Fraction(1)
+        self.order = 0
+        while not value.numerator % p:
+            self.norm /= p
+            self.order += 1
+            value.numerator /= p
+        while not value.denominator % p:
+            self.norm *= p
+            valuation -= 1
+            value.denominator /= p
+        self.value = value
+    
+    def get(self, prec):
+        'Return value of constant with given precision.'
+        if self.value == 0:
+            return self.val
+        
+        while self.prec < prec:
+            # update val based on value
+            
+            self.prec += 1
+        return self.val # TODO add decimal point or trailing zeros