GCD in ℤ/pℤ[x] : gcd

### 4.31.13 GCD in ℤ/pℤ[x] : gcd

gcd takes as arguments two polynomials with coefficients in ℤ/pℤ (p must be prime).
gcd returns the GCD of these polynomials computed in ℤ/pℤ[x] (see also 4.25.7 for polynomials with non modular coefficients).
Input :

gcd((2*x`^`2+5)%13,(5*x`^`2+2*x-3)%13)

Output :

(-4%13)*x+5%13

Input :

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

Output :

x%5

Note the difference with a gcd computation in ℤ[X] followed by a reduction modulo 5, input:

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

Output :

1