### 2.31.7 Euclidian quotient and euclidian remainder : `quorem`

`quorem` takes as arguments
two polynomials *A* and *B* with coefficients in ℤ/*p*ℤ, where
*A* and *B* are list polynomials or symbolic polynomials with
respect to *x* or to an optionnal third argument.

`quorem` returns the list of the quotient and remainder of the
euclidian division of *A* by *B* in ℤ/*p*ℤ[*x*]
(see also 2.6.12 and 2.25.6).

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
*x*^{3}+*x*^{2}+1=(2*x*^{2}+4)(*x*+1/2)+5*x*−4/4

and −3*4=−6*2=1 mod13.