Euclidean quotient : quo

### 5.36.5 Euclidean quotient : quo

quo takes as arguments two polynomials A and B with coefficients in ℤ/pℤ, where A and B are list polynomials or symbolic polynomials with respect to x or to an optional third argument.
quo returns the quotient of the euclidean division of A by B in ℤ/pℤ[x].
Input :

quo((x`^`3+x`^`2+1)%13,(2*x`^`2+4)%13)

or :

quo((x`^`3+x`^`2+1,2*x`^`2+4)%13)

Output:

(-6%13)*x+-6%13

Indeed x3+x2+1=(2x2+4)(x+1/2)+5x−4/4 and −3*4=−6*2=1 mod13.