WithTheAtomsAsSymbols​(AngouriMath.​Entity[][],​AngouriMath.​Entity[],​System.​Boolean,​AngouriMath.​Entity[]@)

The system with every entry written as a polynomial over Q in symbols, each
atom that is not one -- a function of the parameters, ln(F); a root of one,
sqrt(b); a constant that is not exact, ln(2) or pi -- standing
as a symbol of its own, solved as such, and the atoms written back. The polynomial
elimination declines an entry that is not a polynomial in symbols, and the one on
entities that follows does not collect terms, so its zero test is numeric: an
inexact number is never a pivot and never decidably zero once a pivot has been
through its row, and a function of a symbol is neither. So the ansatz for
2^(x + c x^3)(1 + 3 c x^2), whose identity has ln(2) in every
coefficient, and Rubi's F^(a + b x + c x^3)(b + 3 c x^2) with ln(F) in every one, were declined where e^(k (x + c x^3))(1 + 3 c x^2) is answered.
The innermost atoms, so that 3 ln(2) is three times the symbol for ln(2),
and an atom holding another is written in that one's symbol; false where there is
no atom, and the callers go on to the elimination on entities.