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- factor_prime_power(x)
- Return p and d for a prime power x = p**d.
- gcdext(...)
- gcdext(a, b, /) -> tuple[mpz, mpz, mpz]
Return a 3-element tuple (g,s,t) such that g == gcd(a,b)
and g == a*s + b*t.
- invert(...)
- invert(x, m, /) -> mpz
Return y such that x*y == 1 modulo m. Raises `ZeroDivisionError` if no
inverse exists.
- iroot(...)
- iroot(x,n,/) -> tuple[mpz, bool]
Return the integer n-th root of x and boolean value that is `True`
iff the root is exact. x >= 0. n > 0.
- is_prime(...)
- is_prime(x, n=25, /) -> bool
Return `True` if x is *probably* prime, else `False` if x is
definitely composite. x is checked for small divisors and up
to n Miller-Rabin tests are performed.
- is_square(object, /)
- is_square(x, /) -> bool
Returns `True` if x is a perfect square, else return `False`.
- isqrt(object, /)
- isqrt(x, /) -> mpz
Return the integer square root of a non-negative integer x.
- jacobi(...)
- jacobi(x, y, /) -> mpz
Return the Jacobi symbol (x|y). y must be odd and >0.
- kronecker(...)
- kronecker(x, y, /) -> mpz
Return the Kronecker-Jacobi symbol (x|y).
- legendre(...)
- legendre(x, y, /) -> mpz
Return the Legendre symbol (x|y). y is assumed to be an odd prime.
- next_prime(object, /)
- next_prime(x, /) -> mpz
Return the next *probable* prime number > x.
- powmod(...)
- powmod(x, y, m, /) -> mpz
Return (x**y) mod m. Same as the three argument version of Python's
built-in `pow`, but converts all three arguments to `mpz`.
- prev_prime(object, /)
- prev_prime(x, /) -> mpz
Return the previous *probable* prime number < x.
Only present when compiled with GMP 6.3.0 or later.
- ratrec(x, y, N=None, D=None)
- Return rational reconstruction (n, d) of x modulo y.
That is, n/d = x (mod y) with -N <= n <= N and 0 < d <= D,
provided 2*N*D < y.
Default N=D=None will set both N and D to sqrt(y/2) approximately.
- version()
- version() -> str
Return string giving current GMPY2 version.
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