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 Documentation / Mathematica / Built-in Functions / Algebraic Computation / Polynomial Functions  /
PolynomialGCD

  • PolynomialGCD[ , , ... ] gives the greatest common divisor of the polynomials .
  • PolynomialGCD[ , , ... , Modulus-> p ] evaluates the GCD modulo the prime p.
  • Example: PolynomialGCD[1 + x y, x + x^2 y].
  • In PolynomialGCD[ , , ... ], all symbolic parameters are treated as variables.
  • PolynomialGCD[ , , ... ] will by default treat algebraic numbers that appear in the as independent variables.
  • PolynomialGCD[ , , ... , 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`.

    Further Examples

    This gives the greatest common divisor of a pair of polynomials.

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    Here is the greatest common divisor of another pair.

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    We can take the gcd of polynomials involving Gaussian rationals, and this can even be done modulo a real Gaussian prime.

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    To find the gcd of trigonometric polynomials, use the option setting Trig -> True.

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    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.

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    PolynomialGCD finds a nontrivial gcd with Extension -> Automatic.

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