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Euclidian quotient and euclidian remainder : quorem

quorem 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.
quorem returns the list of the quotient and remainder of the euclidian division of A by B in $ \mathbb {Z}$/p$ \mathbb {Z}$[x] (see also 1.6.12 and 1.25.6).
Input :
quorem((x^3+x^2+1)%13,(2*x^2+4)%13)
Or :
quorem((x^3+x^2+1,2*x^2+4)%13)
Output:
[(-6%13)*x+-6%13,(-2%13)*x+-1%13]
Indeed x3 + x2 +1 = (2x2 +4)($\displaystyle {\frac{{x+1}}{{2}}}$) + $\displaystyle {\frac{{5x-4}}{{4}}}$
and -3*4 = - 6*2 = 1  mod 13.



giac documentation written by Renée De Graeve and Bernard Parisse