### 2.25.7 GCD of two polynomials with Euclide algorithm: `gcd`

`gcd` denotes the gcd (greatest common divisor) of two polynomials
(or of a list of polynomials or of a sequence of polynomials)
(see also 2.6.2 for GCD of integers).

**Examples**

Input :

`gcd(x``^`

`2+2*x+1,x``^`

`2-1)`

Output :

`x+1 `

Input :

`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])`

Output :

`x-1`

For polynomials with modular coefficients, input e.g. :

`gcd((x``^`

`2+2*x+1) mod 5,(x``^`

`2-1) mod 5)`

Output :

`x % 5`

Note that :

`gcd(x``^`

`2+2*x+1,x``^`

`2-1) mod 5`

will output :

`1`

since the mod operation is done after the GCD is computed in ℤ[*X*].