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6.34.7  Euclidean quotient and euclidean remainder: quorem

The quorem command finds the quotient and remainder of the Euclidean division of two polynomials (see also Section 6.5.10 and Section 6.28.4).


Example.
Input:

quorem((x^3+x^2+1)%13,(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.


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