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2.31.6  Euclidian remainder : rem

rem 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 optionnal third argument.
rem returns the remainder of the euclidian division of A by B in ℤ/pℤ[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)(x+1/2)+5x−4/4 and −3*4=−6*2=1 mod13.


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