GCD of two polynomials with the Euclidean algorithm

### 11.2.5 GCD of two polynomials with the Euclidean algorithm

The gcd command computes the gcd (greatest common divisor) of polynomials. (See also Section 7.1.1 for GCD of integers.)

- gcd takes an arbitrary number or arguments: polys, a sequence or list of polynomials.
- gcd(polys) returns the greatest common divisor of the polynomials in polys.

Gcd is the inert form of gcd; namely, it evaluates to gcd for later evaluation. It is used when Xcas is in Maple mode (see Section 2.5.2) to compute the gcd of polynomials with coefficients in ℤ/pℤ using Maple-like syntax.

#### Examples

gcd(x^2+2*x+1,x^2-1)

x+1 |  |  |  |  |  |  |  |  |  |

gcd(x^2-2*x+1,x^3-1,x^2-1,x^2+x-2)

or:

gcd([x^2-2*x+1,x^3-1,x^2-1,x^2+x-2])

x−1 |  |  |  |  |  |  |  |  |  |

For polynomials with modular coefficients:

gcd((x^2+2*x+1) mod 5,(x^2-1) mod 5)

| ⎛ ⎝ | 1%5 | ⎞ ⎠ | x+1%5

Input in Xcas mode:

Gcd(x^3-1,x^2-1)

gcd | ⎛ ⎝ | x3−1,x2−1 | ⎞ ⎠

Input in Maple mode:

Gcd(x^2+2*x,x^2+6*x+5) mod 5

1 |  |  |  |  |  |  |  |  |  |