This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

PolynomialGCD

 PolynomialGCDgives the greatest common divisor of the polynomials . PolynomialGCD[poly1, poly2, ..., Modulus->p]evaluates the GCD modulo the prime p.
• In PolynomialGCD, all symbolic parameters are treated as variables.
• PolynomialGCD will by default treat algebraic numbers that appear in the as independent variables.
The greatest common divisor of polynomials:
The greatest common divisor of polynomials:
 Out[1]=
 Scope   (3)
The GCD of univariate polynomials:
The GCD of multivariate polynomials:
The GCD of more than two polynomials:
The GCD of rational functions:
 Options   (3)
By default, algebraic numbers are treated as independent variables:
With Extension, PolynomialGCD detects algebraically dependent coefficients:
Compute the GCD over the integers modulo 2:
By default, PolynomialGCD treats trigonometric functions as independent variables:
With Trig->True, PolynomialGCD recognizes dependencies between trigonometric functions:
 Applications   (2)
Find common roots of univariate polynomials:
Find multiple roots of univariate polynomials:
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 degree of GCD is nonzero:
Discriminant of a polynomial f is zero if and only if the polynomial has multiple roots: