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IsAQuotientOfDistinctSumsOfSymbolsInLowestTerms​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

 Method (no overloads)

Summary

Whether expr is a quotient of products of positive whole powers of
sums in u of the first or second degree with a constant term, each
term of a sum one, a symbol, or one of them times u or u^2, the symbols of
a sum distinct and some sum holding one, no sum written twice, and no two neighbours
to one power above the bar.

Remarks

Such a quotient is in lowest terms and its factors coprime: no sum has a content or a
power of u to take out, two sums are proportional only where they are the same
sum, a quadratic is irreducible, and a linear divides none, since
q0 c1^2 - q1 c0 c1 + q2 c0^2 is one or two monomials with a plus sign and at most
one with a minus, which cannot cancel. Nothing is left for the simplifier, which hands
it back as it came: ten of the eleven integrands of Rubi's 4.3.4.2 with whole powers,
which the tangent substitution makes such quotients, came back from it unchanged after
6.5 to 13.4 s each with the seven symbols in them, and the eleventh after 3.7 s with
its two neighbours to one power below the bar gathered, which
WithNeighboursToOnePowerGathered(AngouriMath.Entity) does as it does. The answer is the one
the simplified integrand had.
Neighbours to one power above the bar are excluded: there the simplifier gathers them
and writes a lone 1 + u^2 below as u^2 + 1 as well, and the integral is
asked of that spelling -- 4.3.2.1's (a + b tan)^2 (c + d tan)^2 answered with
ln(tan^2 + 1) where ln(1 + tan^2) was written. A difference, a numeric
coefficient other than one, a root or a factor that is not a sum is excluded too, as
nothing measured.
https://github.com/asc-community/AngouriMath/issues/233

























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