, ... ] gives the greatest common divisor of the polynomials .
, ... ,
] evaluates the GCD modulo the prime p.
Example: PolynomialGCD[1 + x y, x + x^2 y].
, ... ], all symbolic parameters are treated as variables.
, ... ] will by default treat algebraic numbers that appear in the as independent variables.
, ... ,
Extension->Automatic] extends the coefficient field to include algebraic numbers that appear in the .
See the Mathematica book: Section 3.3.4.
See also: PolynomialLCM, PolynomialQuotient, GCD, Cancel, Together, PolynomialMod.
Related package: Algebra`PolynomialExtendedGCD`.
This gives the greatest common divisor of a pair of polynomials.
Here is the greatest common divisor of another pair.
We can take the gcd of polynomials involving Gaussian rationals, and this can even be done modulo a real Gaussian prime.
To find the gcd of trigonometric polynomials, use the option setting Trig
This pair of polynomials is over an extension of the rational numbers. With the default setting of Extension
None, PolynomialGCD cannot find a nontrivial gcd.
PolynomialGCD finds a nontrivial gcd with Extension
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