This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

PolynomialGCD

PolynomialGCD
gives 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:
In[1]:=
Click for copyable input
Out[1]=
The GCD of univariate polynomials:
The GCD of multivariate polynomials:
The GCD of more than two polynomials:
The GCD of rational functions:
By default, algebraic numbers are treated as independent variables:
With Extension->Automatic, 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:
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:
New in 2 | Last modified in 3