### 5.34.7 Euclidean quotient and euclidean remainder : quorem

quorem 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.
quorem returns the list of the quotient and remainder of the euclidean division of A by B in ℤ/pℤ[x] (see also 5.6.12 and 5.28.6).
Input :

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

or :

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

Output:

[(-6%13)*x+-6%13,(-2%13)*x+-1%13]

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