AngouriMath
TrySplitOverWrittenFactors(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity@)
Method (no overloads)
Summary
where the denominator is written as a product of distinct linear and quadratic
factors whose coefficients may be symbols, or
or the decomposition cannot be settled.
Remarks
do, and a symbol is not a rational:
hand and each of them is a shape the integrator reads, and it was declined because
nothing here could read the factors. This is the textbook method for it -- undetermined
coefficients -- and it is the one that survives a symbol, because it solves a linear
system in the unknown numerators rather than dividing polynomials whose coefficients
have to be compared to zero.
and a row reduction has to decide whether a pivot is zero. A number is decided by
looking; a symbolic pivot is taken only when it does not simplify to zero, which is a
judgement and not a proof, and that is why the decomposition is checked before it
is returned: the identity
points with every symbol pinned, and a split that fails it is declined rather than
handed on. A wrong pivot can cost an answer here and cannot produce a wrong one.
one value of a parameter are coprime for every other, and the answer is the one for
those. See the note on
power. A repeated symbolic quadratic has no rule to land on and is declined.
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