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numbertheory.py: factor out invert().

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I'm about to want to reuse it.
This commit is contained in:
Simon Tatham 2020-02-28 20:13:06 +00:00
parent 122d785283
commit 3ee9b92935
1 changed files with 12 additions and 14 deletions
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26
test/numbertheory.py
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@ -1,6 +1,16 @@
import numbers import numbers
import itertools import itertools
def invert(a, b):
"Multiplicative inverse of a mod b. a,b must be coprime."
A = (a, 1, 0)
B = (b, 0, 1)
while B[0]:
q = A[0] // B[0]
A, B = B, tuple(Ai - q*Bi for Ai, Bi in zip(A, B))
assert abs(A[0]) == 1
return A[1]*A[0] % b
def jacobi(n,m): def jacobi(n,m):
"""Compute the Jacobi symbol. """Compute the Jacobi symbol.
@ -103,18 +113,6 @@ class ModP(object):
else: else:
self.check(other) self.check(other)
return other return other
def invert(self):
"Internal routine which returns the bare inverse."
if self.n % self.p == 0:
raise ZeroDivisionError("division by {!r}".format(self))
a = self.n, 1, 0
b = self.p, 0, 1
while b[0]:
q = a[0] // b[0]
a = a[0] - q*b[0], a[1] - q*b[1], a[2] - q*b[2]
b, a = a, b
assert abs(a[0]) == 1
return a[1]*a[0]
def __int__(self): def __int__(self):
return self.n return self.n
def __add__(self, rhs): def __add__(self, rhs):
@ -139,10 +137,10 @@ class ModP(object):
return type(self)(self.p, (self.n * rhs.n) % self.p) return type(self)(self.p, (self.n * rhs.n) % self.p)
def __div__(self, rhs): def __div__(self, rhs):
rhs = self.coerce_to(rhs) rhs = self.coerce_to(rhs)
return type(self)(self.p, (self.n * rhs.invert()) % self.p) return type(self)(self.p, (self.n * invert(rhs.n, self.p)) % self.p)
def __rdiv__(self, rhs): def __rdiv__(self, rhs):
rhs = self.coerce_to(rhs) rhs = self.coerce_to(rhs)
return type(self)(self.p, (rhs.n * self.invert()) % self.p) return type(self)(self.p, (rhs.n * invert(self.n, self.p)) % self.p)
def __truediv__(self, rhs): return self.__div__(rhs) def __truediv__(self, rhs): return self.__div__(rhs)
def __rtruediv__(self, rhs): return self.__rdiv__(rhs) def __rtruediv__(self, rhs): return self.__rdiv__(rhs)
def __pow__(self, exponent): def __pow__(self, exponent):