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SolveByCombiningRadicals(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
Several square roots of polynomials in the variable, written as one:
sqrt(1 + x^2) sqrt(1 - x^2) is sqrt(1 - x^4) , and a root below the bar
is a root above it over its own base,1/sqrt(B) = sqrt(B)/B .
is a root above it over its own base,
Remarks
to replace, Euler's rule wants one root of one quadratic, and each rule looked at
this integrand and saw two of what it takes one of. It is what by parts leaves from
and from every other pairing of an inverse function's radical with the one in
the power it stands over.
left is
For
so the rule asks whether there is a real
negative, and only rewrites when there is not. The bases are polynomials with
numeric coefficients; their real roots cut the line into intervals on each of which
every base keeps its sign, so the count at one point of each interval is the count
on the interval. Where the solver cannot give the roots, the rule declines.
it was given, and it is asked one level down more often than at the top, since the
two-radical shape is what a by-parts step produces.
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