diff --git a/padic.py b/padic.py index 198111f..90d680d 100644 --- a/padic.py +++ b/padic.py @@ -1,58 +1,71 @@ from fractions import Fraction -from sys import maxint -from modp import * +from sys import maxsize +from modp import ModP + class PAdic: def __init__(self, p): self.p = p - self.val = '' # current known value - self.prec = 0 # current known precision, not containing trailing zeros - self.order = 0 # order/valuation of number - pass # initialize object as subclass perhaps - - def get(self, prec, decimal = True): + self.val = '' # current known value + self.prec = 0 # current known precision, not containing trailing zeros + self.order = 0 # order/valuation of number + pass # initialize object as subclass perhaps + + def get(self, prec, decimal=True): 'Return value of number with given precision.' while self.prec < prec: # update val based on value self.val = str(int(self._nextdigit())) + self.val self.prec += 1 if self.order < 0: - return (self.val[:self.order] + ('.' if decimal else '') + self.val[self.order:])[-prec-1:] + return ( + self.val[:self.order] + ('.' if decimal else '') + + self.val[self.order:])[-prec-1:] return (self.val + self.order * '0')[-prec:] - + def _nextdigit(self): 'Calculate next digit of p-adic number.' raise NotImplementedError - + def getdigit(self, index): 'Return digit at given index.' - return int(self.get(index + 1, False)[0]) #int(self.get(index+1+int(index < -self.order))[-int(index < -self.order)]) - + return int(self.get(index + 1, False)[0]) + # int( + # self.get(index+1+int(index < -self.order) + # )[-int(index < -self.order)]) + # return value with precision up to 32 bits def __int__(self): return int(self.get(32), self.p) + def __str__(self): return self.get(32) - + # arithmetic operations def __neg__(self): return PAdicNeg(self.p, self) + def __add__(self, other): return PAdicAdd(self.p, self, other) + def __radd__(self, other): return PAdicAdd(self.p, other, self) + def __sub__(self, other): return PAdicAdd(self.p, self, PAdicNeg(self.p, other)) + def __rsub__(self, other): return PAdicAdd(self.p, other, PAdicNeg(self.p, self)) + def __mul__(self, other): return PAdicMul(self.p, self, other) + def __rmul__(self, other): return PAdicMul(self.p, other, self) - + # p-adic norm def __abs__(self): - if self.order == maxint: + if self.order == maxsize: return 0 numer = denom = 1 if self.order > 0: @@ -61,18 +74,19 @@ class PAdic: denom = self.p ** self.order return Fraction(numer, denom) + class PAdicConst(PAdic): def __init__(self, p, value): PAdic.__init__(self, p) value = Fraction(value) - + # calculate valuation if value == 0: self.value = value self.val = '0' - self.order = maxint + self.order = maxsize return - + self.order = 0 while not value.numerator % self.p: self.order += 1 @@ -81,21 +95,23 @@ class PAdicConst(PAdic): self.order -= 1 value *= self.p self.value = value - + self.zero = not value - - def get(self, prec, decimal = True): + + def get(self, prec, decimal=True): if self.zero: return '0' * prec return PAdic.get(self, prec, decimal) - + def _nextdigit(self): 'Calculate next digit of p-adic number.' - rem = ModP(self.p, self.value.numerator) / ModP(self.p, self.value.denominator) + rem = ModP(self.p, self.value.numerator) /\ + ModP(self.p, self.value.denominator) self.value -= int(rem) self.value /= self.p return rem + class PAdicAdd(PAdic): 'Sum of two p-adic numbers.' def __init__(self, p, arg1, arg2): @@ -103,7 +119,8 @@ class PAdicAdd(PAdic): self.carry = 0 self.arg1 = arg1 self.arg2 = arg2 - self.order = self.prec = min(arg1.order, arg2.order) # might be larger than this + # might be larger than this + self.order = self.prec = min(arg1.order, arg2.order) arg1.order -= self.order arg2.order -= self.order # loop until first nonzero digit is found @@ -115,12 +132,14 @@ class PAdicAdd(PAdic): digit = self._nextdigit() self.val += str(int(digit)) self.prec = 1 - + def _nextdigit(self): - s = self.arg1.getdigit(self.index) + self.arg2.getdigit(self.index) + self.carry + s = self.arg1.getdigit(self.index) + \ + self.arg2.getdigit(self.index) + self.carry self.carry = s // self.p self.index += 1 - return s % self.p + return s % self.p + class PAdicNeg(PAdic): 'Negation of a p-adic number.' @@ -128,12 +147,14 @@ class PAdicNeg(PAdic): PAdic.__init__(self, p) self.arg = arg self.order = arg.order - + def _nextdigit(self): if self.prec == 0: - return self.p - self.arg.getdigit(0) # cannot be p, 0th digit of arg must be nonzero + # cannot be p, 0th digit of arg must be nonzero + return self.p - self.arg.getdigit(0) return self.p - 1 - self.arg.getdigit(self.prec) + class PAdicMul(PAdic): 'Product of two p-adic numbers.' def __init__(self, p, arg1, arg2): @@ -142,11 +163,14 @@ class PAdicMul(PAdic): self.arg1 = arg1 self.arg2 = arg2 self.order = arg1.order + arg2.order - self.arg1.order = self.arg2.order = 0 # TODO requires copy + self.arg1.order = self.arg2.order = 0 # TODO requires copy self.index = 0 - + def _nextdigit(self): - s = sum(self.arg1.getdigit(i) * self.arg2.getdigit(self.index - i) for i in xrange(self.index + 1)) + self.carry + s = sum( + self.arg1.getdigit(i) * self.arg2.getdigit(self.index - i) + for i in xrange(self.index + 1) + ) + self.carry self.carry = s // self.p self.index += 1 - return s % self.p \ No newline at end of file + return s % self.p