[CAES] (x^4-4*x^3+2*x^2+4*x+4) Exact factorization of Quartic Polynomial

[compsystems]

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I also be agree, when the EXACT mode is fixed and internally the CAES has not algorithm to calculate exactly, should display a numerical solution. It is uncomfortable to be changing flags manually, much even would know and think that it can at least throw the approximate response

HPPRIME

cfactor(x^4-4*x^3+2*x^2+4*x+4) & EXACT MODE ON [ENTER]->
x^4-4*x^3+2*x^2+4*x+4 =( ALGORITHM INTERNAL NOT DEFINED YET


cfactor(x^4-4*x^3+2*x^2+4*x+4) & EXACT MODE OFF (APPROX CALCULATION)[ENTER]->
(x-2.52409830...+0.568221484...*i)*(x-2.52409830...-0.568221484...*i)*(x+0.524098309...+0.568221484...*i)*(x+0.524098309...-0.568221484...*i)

or one QPIROOT exact algorithm is required
exact(ANS)
(x+(-740017*(i)/1302339)-(1185781/469784))*(x+(-740017*(i)/1302339)+(490784/936435))*(x+(740017*(i)/1302339)-(1185781/469784))*(x+(740017*(i)/1302339)+(490784/936435))
=(


(1+sqrt(2-i *sqrt(3))-X) * (1+sqrt(2+i *sqrt(3))-X) * (-1+sqrt(2-i *sqrt(3))+X) * (-1+sqrt(2+i *sqrt(3))+X)
the most important answers are real and exact, there is no loss of information.

Numerical answers are acceptable when there is not human power or algorithm to calculate.

on the internet there are formulas to calculate exactly one factorization of a quartic, that should be BUILT-IN in the CAES as it does WOLFRAM