AngouriMath
SolveByTheConjugateOfASumWithARootOfAQuadraticBelowTheBar(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A rational function of x and one square root of a quadratic Q , with the
root in a sum below the bar, written over a denominator free of it:
(A + B sqrt(Q))/(C + D sqrt(Q)) is (A + B sqrt(Q)) (C - D sqrt(Q))/(C^2 - D^2 Q) ,
a rational function and one beside the root, each asked of the chain.
root in a sum below the bar, written over a denominator free of it:
a rational function and one beside the root, each asked of the chain.
Remarks
Rubi's 1/(a c + b c x^2 + d sqrt(a + b x^2)) : Euler's substitution takes the
generic first substitution for a symbolic leading coefficient, withsqrt(b) in
every coefficient, and was declined. Over the conjugate it is
(c Q - d sqrt(Q))/(c^2 Q^2 - d^2 Q) , and both pieces are answered. It runs after
every rule that answers the numeric spellings. Only a sum: a root alone below the bar,
C = 0 , is the root moved above it, which the chain writes back, and D = 0 has nothing to clear.
https://github.com/asc-community/AngouriMath/issues/718
generic first substitution for a symbolic leading coefficient, with
every coefficient, and was declined. Over the conjugate it is
every rule that answers the numeric spellings. Only a sum: a root alone below the bar,
https://github.com/asc-community/AngouriMath/issues/718
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