40 lines
No EOL
1.3 KiB
Python
40 lines
No EOL
1.3 KiB
Python
class ModP(int):
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'Integers mod p, p a prime power.'
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def __new__(cls, p, num):
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self.p = p
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return int.__new__(cls, int(num) % p)
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# arithmetic
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def __add__(self, other):
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return ModP(self.p, int(self) + int(other))
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def __radd__(self, other):
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return ModP(self.p, int(other) + int(self))
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def __sub__(self, other):
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return ModP(self.p, int(self) - int(other))
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def __rsub__(self, other):
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return ModP(self.p, int(other) - int(self))
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def __mul__(self, other):
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return ModP(self.p, int(self) * int(other))
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def __rmul__(self, other):
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return ModP(self.p, int(other) * int(self))
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def __div__(self, other):
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return self * other._inv()
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def __rdiv__(self, other):
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return other * self._inv()
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def _inv(self):
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'Find multiplicative inverse of self in Z mod p.'
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# extended Euclidean algorithm
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rcurr = self.p
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rnext = int(self)
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tcurr = 0
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tnext = 1
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while rnext:
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q = rcurr // rnext
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rcurr, rnext = rnext, rcurr - q * rnext
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tcurr, tnext = tnext, tcurr - q * tnext
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if rcurr != 1:
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raise ValueError("%d not a unit modulo %d" % (self, self.p))
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return ModP(self.p, tcurr) |