Reducing powers by x^2=x-a gives remainder r0(a)+r1(a)x. The concrete remainder arrays are r0=[90,-1,10,-36,56,-35,6] and r1=[2,-11,45,-84,70,-21,1]. Their monic gcd over Q[a] is gcd=[-2,1], namely a-2 with unique root a=2, so simultaneous vanishing occurs only at a=2. At a=2 the ascending quotient is quotient=[45,23,-11,-17,-3,7,5,-1,-3,-1,1,1]; the product from multiplying it by x^2-x+2 recovers x^13+x+90.
RESULT_JSON: {"common_gcd":[-2,1],"parameter":2,"quotient":[45,23,-11,-17,-3,7,5,-1,-3,-1,1,1],"remainder_constant":[90,-1,10,-36,56,-35,6],"remainder_x":[2,-11,45,-84,70,-21,1]}
