Greatest common divisor of polynomials
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q, …) gcd(
gcd(p, q, ...) returns the greatest common
divisor of the polynomials p, q,
… The coefficient
ring of the polynomials may either be the integers or the rational
Expr, a residue class ring
a prime number
n, or a domain.
All polynomials must have the same indeterminates and the same coefficient ring.
Polynomial expressions are converted to polynomials. See
poly for details.
The return value is of the same type as the input polynomials,
i.e., either a polynomial of type
DOM_POLY or a polynomial
gcd returns 0 if
all arguments are 0, or if
no argument is given. If at least one of the arguments is -
1 or 1,
gcd returns 1.
all arguments are known to be integers, since it is much faster than
The greatest common divisor of two polynomial expressions can be computed as follows:
gcd(6*x^3 + 9*x^2*y^2, 2*x + 2*x*y + 3*y^2 + 3*y^3)
f := (x - sqrt(2))*(x^2 + sqrt(3)*x-1): g := (x - sqrt(2))*(x - sqrt(3)): gcd(f, g)
One may also choose polynomials as arguments:
p := poly(2*x^2 - 4*x*y - 2*x + 4*y, [x, y], IntMod(17)): q := poly(x^2*y - 2*x*y^2, [x, y], IntMod(17)): gcd(p, q)
delete f, g, p, q:
Polynomial or a polynomial expression.
If the arguments are polynomials with coefficients from a domain,
then the domain must have the methods
"gcd" must return the greatest common
divisor of any number of domain elements. The method
divide two domain elements. If domain elements cannot be divided,
this method must return