This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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. In[1]:= Out[1]= Here is the greatest common divisor of another pair. In[2]:= In[3]:= Out[3]= In[4]:= We can take the gcd of polynomials involving Gaussian rationals, and this can even be done modulo a real Gaussian prime. In[5]:= In[6]:= In[7]:= Out[7]= In[8]:= Out[8]= In[9]:= To find the gcd of trigonometric polynomials, use the option setting Trig -> True. In[10]:= Out[10]= 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. In[11]:= Out[11]= PolynomialGCD finds a nontrivial gcd with Extension -> Automatic. In[12]:= Out[12]= In[13]:= Out[13]=