Euclidian remainder : rem

rem takes as arguments two polynomials A and B with coefficients in $\mathbb {Z}$/p$\mathbb {Z}$, where A and B are list polynomials or symbolic polynomials with respect to x or to an optionnal third argument.
rem returns the remainder of the euclidian division of A by B in $\mathbb {Z}$/p$\mathbb {Z}$[x].
Input :

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

Or :

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

Output:

(-2%13)*x+-1%13

Indeed x³ + x² +1 = (2x² +4)($${\frac{{x+1}}{{2}}}$$) + $${\frac{{5x-4}}{{4}}}$$ and -3*4 = - 6*2 = 1  mod 13.