Greatest common divisor

Functions
void	fmpq_poly_gcd (fmpq_poly_ptr rop, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_xgcd (fmpq_poly_ptr rop, fmpq_poly_ptr s, fmpq_poly_ptr t, const fmpq_poly_ptr a, const fmpq_poly_ptr b)
void	fmpq_poly_lcm (fmpq_poly_ptr rop, const fmpq_poly_ptr a, const fmpq_poly_ptr b)

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Function Documentation

void fmpq_poly_gcd	(	fmpq_poly_ptr	rop,
		const fmpq_poly_ptr	a,
		const fmpq_poly_ptr	b
	)

Returns the (monic) greatest common divisor res of a and b.

Corner cases: If a and b are both zero, returns zero. If only one of them is zero, returns the other polynomial, up to normalisation.

void fmpq_poly_lcm	(	fmpq_poly_ptr	rop,
		const fmpq_poly_ptr	a,
		const fmpq_poly_ptr	b
	)

Computes the monic (or zero) least common multiple of a and b.

If either of a and b is zero, returns zero. This behaviour ensures that the relation

holds, where denotes equality up to units.

void fmpq_poly_xgcd	(	fmpq_poly_ptr	rop,
		fmpq_poly_ptr	s,
		fmpq_poly_ptr	t,
		const fmpq_poly_ptr	a,
		const fmpq_poly_ptr	b
	)

Returns polynomials s, t and rop such that rop is (monic) greatest common divisor of a and b, and such that rop = s a + t b.

Corner cases: If a and b are zero, returns zero polynomials. Otherwise, if only a is zero, returns (res, s, t) = (b, 0, 1) up to normalisation, and similarly if only b is zero.

Assumes that the output parameters rop, s, and t refer to distinct objects in memory. Otherwise, an exception is raised in the form of an abort statement.