gives the greatest common divisor of the polynomials polyi.
Details and Options
- In PolynomialGCD[poly1,poly2,…], all symbolic parameters are treated as variables.
- PolynomialGCD[poly1,poly2,…] will by default treat algebraic numbers that appear in the polyi as independent variables.
- PolynomialGCD[poly1,poly2,…,Extension->Automatic] extends the coefficient field to include algebraic numbers that appear in the polyi.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (4)
Advanced Uses (6)
Properties & Relations (3)
The GCD of polynomials divides the polynomials; use PolynomialMod to prove it:
Cancel divides the numerator and the denominator of a rational function by their GCD:
PolynomialLCM finds the least common multiple of polynomials:
Resultant of two polynomials is zero if and only if their GCD has a nonzero degree:
Discriminant of a polynomial f is zero if and only if the polynomial has multiple roots:
Wolfram Research (1991), PolynomialGCD, Wolfram Language function, https://reference.wolfram.com/language/ref/PolynomialGCD.html (updated 2023).
Wolfram Language. 1991. "PolynomialGCD." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/PolynomialGCD.html.
Wolfram Language. (1991). PolynomialGCD. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolynomialGCD.html