AngouriMath
SolveAnEvenPolynomialOverASymbolicBiquadratic(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A polynomial in x^2 over a + b x^2 + c x^4 with a symbol in it, by the
two roots inx^2 : with q = sqrt(b^2 - 4 a c) and
r = (-b ± q)/(2c) , (d + e x^2)/(a + b x^2 + c x^4) is
(d + e r_1)/(q (x^2 - r_1)) - (d + e r_2)/(q (x^2 - r_2)) , and
1/(x^2 - r) is atan(x/sqrt(-r))/sqrt(-r) for any complex r . A
higher even degree is divided down first, and an odd numerator is left to the
substitutionu = x^2 .
two roots in
higher even degree is divided down first, and an odd numerator is left to the
substitution
Remarks
as one; over the rationals it is factored, over symbols it was declined, and Rubi's
quartic files --
even numerators to it:
that is zero as written declines, the square of a quadratic being another shape.
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