AngouriMath
SolveAPolynomialOverASymbolicQuarticThatSplitsIntoTwoQuadratics(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A polynomial over a quartic with symbols in it that splits into two quadratics in a hidden
variable: a palindromic one,c x^4 + b x^3 + e x^2 + b x + c , is
c (x^2 - p x + 1)(x^2 - q x + 1) with p and q the roots of
c w^2 + b w + e - 2 c , since it is x^2 times a quadratic in w = x + 1/x ;
and one whose odd terms vanish undery = x + c3/(4 c4) is c4 (y^2 - p)(y^2 - q) .
The integral over the factored quartic is asked withp and q named, and they are
written back.
variable: a palindromic one,
and one whose odd terms vanish under
The integral over the factored quartic is asked with
written back.
Remarks
The integral over two real quadratics splits on the signs of their discriminants, which mean
nothing for roots that may be complex; the first arm differentiates back for any of them, and
the answer is checked. A quartic already even is the biquadratic rule's. Rubi's 1.3.1
(A + B x + C x^2 + D x^3)/(a + b x + c x^2 + b x^3 + a x^4) and
1/(4 a c + 4 c^2 x^2 + 4 c d x^3 + d^2 x^4) were declined.
https://github.com/asc-community/AngouriMath/issues/718
nothing for roots that may be complex; the first arm differentiates back for any of them, and
the answer is checked. A quartic already even is the biquadratic rule's. Rubi's 1.3.1
https://github.com/asc-community/AngouriMath/issues/718
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