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update padic.py

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Ata Deniz Aydin 2017-05-15 10:48:33 +03:00
parent 0b694c22e8
commit 058b45976f
1 changed files with 41 additions and 26 deletions
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padic.py
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@ -6,17 +6,19 @@ class PAdic:
def __init__(self, p): def __init__(self, p):
self.p = p self.p = p
self.val = '' # current known value self.val = '' # current known value
self.prec = 0 # current known precision, also containing leading zeros self.prec = 0 # current known precision, not containing trailing zeros
self.order = 0 # order/valuation of number self.order = 0 # order/valuation of number
pass # initialize object as subclass perhaps pass # initialize object as subclass perhaps
def get(self, prec): def get(self, prec, decimal = True):
'Return value of number with given precision.' 'Return value of number with given precision.'
while self.prec < prec: while self.prec < prec:
# update val based on value # update val based on value
self.val = self._nextdigit() + self.val self.val = str(int(self._nextdigit())) + self.val
self.prec += 1 self.prec += 1
return self.val # TODO add decimal point or trailing zeros if self.order < 0:
return (self.val[:self.order] + ('.' if decimal else '') + self.val[self.order:])[-prec-1:]
return (self.val + self.order * '0')[-prec:]
def _nextdigit(self): def _nextdigit(self):
'Calculate next digit of p-adic number.' 'Calculate next digit of p-adic number.'
@ -24,15 +26,17 @@ class PAdic:
def getdigit(self, index): def getdigit(self, index):
'Return digit at given index.' 'Return digit at given index.'
return int(self.get(index+1)[0]) 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 # return value with precision up to 32 bits
def __int__(self): def __int__(self):
return int(self.get(32), p) return int(self.get(32), self.p)
def __str__(self): def __str__(self):
return self.get(32) return self.get(32)
# arithmetic operations # arithmetic operations
def __neg__(self):
return PAdicNeg(self.p, self)
def __add__(self, other): def __add__(self, other):
return PAdicAdd(self.p, self, other) return PAdicAdd(self.p, self, other)
def __radd__(self, other): def __radd__(self, other):
@ -41,21 +45,21 @@ class PAdic:
return PAdicAdd(self.p, self, PAdicNeg(self.p, other)) return PAdicAdd(self.p, self, PAdicNeg(self.p, other))
def __rsub__(self, other): def __rsub__(self, other):
return PAdicAdd(self.p, other, PAdicNeg(self.p, self)) return PAdicAdd(self.p, other, PAdicNeg(self.p, self))
def __smul__(self, other): def __mul__(self, other):
return PAdicMul(self.p, self, other) return PAdicMul(self.p, self, other)
def __rsub__(self, other): def __rmul__(self, other):
return PAdicMul(self.p, other, self) return PAdicMul(self.p, other, self)
# p-adic norm # p-adic norm
def __abs__(self): def __abs__(self):
if self.order == maxint: if self.order == maxint:
return 0 return 0
norm = Fraction(1) numer = denom = 1
if self.order > 0: if self.order > 0:
norm.numerator = self.p ** self.order numer = self.p ** self.order
if self.order < 0: if self.order < 0:
norm.denominator = self.p ** self.order denom = self.p ** self.order
return norm return Fraction(numer, denom)
class PAdicConst(PAdic): class PAdicConst(PAdic):
def __init__(self, p, value): def __init__(self, p, value):
@ -72,22 +76,23 @@ class PAdicConst(PAdic):
self.order = 0 self.order = 0
while not value.numerator % self.p: while not value.numerator % self.p:
self.order += 1 self.order += 1
self.prec += 1 value /= self.p
value.numerator /= self.p
while not value.denominator % self.p: while not value.denominator % self.p:
valuation -= 1 self.order -= 1
value.denominator /= self.p value *= self.p
self.value = value self.value = value
self.zero = not value
def get(self, prec): def get(self, prec, decimal = True):
if self.value == 0: if self.zero:
return '0' # * prec return '0' * prec
return PAdic.get(self, prec) return PAdic.get(self, prec, decimal)
def _nextdigit(self): def _nextdigit(self):
'Calculate next digit of p-adic number.' '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 -= rem self.value -= int(rem)
self.value /= self.p self.value /= self.p
return rem return rem
@ -98,17 +103,23 @@ class PAdicAdd(PAdic):
self.carry = 0 self.carry = 0
self.arg1 = arg1 self.arg1 = arg1
self.arg2 = arg2 self.arg2 = arg2
self.order = min(arg1.order, arg2.order) # might be larger than this self.order = self.prec = min(arg1.order, arg2.order) # might be larger than this
arg1.order -= self.order
arg2.order -= self.order
# loop until first nonzero digit is found # loop until first nonzero digit is found
self.index = 0
digit = self._nextdigit() digit = self._nextdigit()
while digit == 0: while digit == 0:
self.index += 1
self.order += 1 self.order += 1
self.prec += 1
digit = self._nextdigit() digit = self._nextdigit()
self.val += str(int(digit))
self.prec = 1
def _nextdigit(self): def _nextdigit(self):
s = self.arg1.getdigit(self.prec) + self.arg2.getdigit(self.prec) + self.carry s = self.arg1.getdigit(self.index) + self.arg2.getdigit(self.index) + self.carry
self.carry = s // self.p self.carry = s // self.p
self.index += 1
return s % self.p return s % self.p
class PAdicNeg(PAdic): class PAdicNeg(PAdic):
@ -121,7 +132,7 @@ class PAdicNeg(PAdic):
def _nextdigit(self): def _nextdigit(self):
if self.prec == 0: if self.prec == 0:
return self.p - self.arg.getdigit(0) # cannot be p, 0th digit of arg must be nonzero return self.p - self.arg.getdigit(0) # cannot be p, 0th digit of arg must be nonzero
return self.p - 1 - self.arg.getdigit(0) return self.p - 1 - self.arg.getdigit(self.prec)
class PAdicMul(PAdic): class PAdicMul(PAdic):
'Product of two p-adic numbers.' 'Product of two p-adic numbers.'
@ -130,8 +141,12 @@ class PAdicMul(PAdic):
self.carry = 0 self.carry = 0
self.arg1 = arg1 self.arg1 = arg1
self.arg2 = arg2 self.arg2 = arg2
self.order = arg1.order + arg2.order
self.arg1.order = self.arg2.order = 0 # TODO requires copy
self.index = 0
def _nextdigit(self): def _nextdigit(self):
s = sum(self.arg1.getdigit(i) * self.arg2.getdigit(self.prec - i) for i in xrange(self.prec + 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.carry = s // self.p
self.index += 1
return s % self.p return s % self.p