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GCD in $ \mathbb {Z}$/p$ \mathbb {Z}$[x] : gcd

gcd takes as arguments two polynomials with coefficients in $ \mathbb {Z}$/p$ \mathbb {Z}$ (p must be prime).
gcd returns the GCD of these polynomials computed in $ \mathbb {Z}$/p$ \mathbb {Z}$[x] (see also 1.25.7 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 $ \mathbb {Z}$[X] followed by a reduction modulo 5, input:
gcd(x^2+2*x+1,x^2-1) mod 5
Output :
1



giac documentation written by Renée De Graeve and Bernard Parisse