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TrySplitOffRationalRoot​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity@,​AngouriMath.​Entity@,​AngouriMath.​Entity@)

 Method (no overloads)

Summary

One step of a partial fraction decomposition, at a rational root of the
denominator: N/D becomes A/(x - r) + R/Q, where D = (x - r)Q.

Remarks

One step, and not the whole decomposition, because a step is all that is needed:
what is left over is a smaller problem of the same kind, and by the time its
denominator is a quadratic there is already a rule for it. So
1/(x^3 + 1) splits into (1/3)/(x + 1) and (2 - x)/(3(x^2 - x + 1)),
and the second of those is a quotient the integrator can read as it stands.
 The coefficient is Heaviside's: at the root every other term of the
decomposition is finite, so A = N(r)/Q(r). What is left, N - A*Q,
then has r for a root by construction and divides exactly.
 Rational roots only, and simple ones: a repeated root needs a term over
(x - r)^2 as well, which this does not produce, so it declines instead.
Denominators of degree below three are left alone, since the rules for a linear
or quadratic denominator already answer those and answer them in one piece.

























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