AngouriMath
SolveByTheConjugateOfARadicalSumBelowTheBar(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A quotient by A + B sqrt(R) whose conjugate product A^2 - B^2 R is a constant
c , written over the conjugate: N/(A + B sqrt(R)) = N (A - B sqrt(R))/c , a sum
of terms without the quotient.e^asech(a x) arrives as
1/(a x) + sqrt(1/(a x)^2 - 1) , whose conjugate product is 1, so x^m/e^asech(a x) is x^m (1/(a x) - sqrt(1/(a x)^2 - 1)) . Rubi's 7.5.2.
https://github.com/asc-community/AngouriMath/issues/233
of terms without the quotient.
https://github.com/asc-community/AngouriMath/issues/233
Remarks
The search took the quotient as written, a root below the bar beside a pole, and ran past
the budget. The rewrite is the identity(A + B sqrt(R))(A - B sqrt(R)) = A^2 - B^2 R ,
withsqrt(R)^2 = R on every branch, so it holds wherever the quotient is defined.
Only for a constant product: otherwise the quotient by it is the harder question.
the budget. The rewrite is the identity
with
Only for a constant product: otherwise the quotient by it is the harder question.
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