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GatherPowersOfOneBase(AngouriMath.Entity)

Method (no overloads)

Summary

Gathers the factors of a product that are powers of one base, wherever they sit
in it: a^n * c * a^m becomes a^(n+m) * c.

Remarks

PowerRules(AngouriMath.Entity) already has {}^n * {}^m = {}^(n+m), but it pairs
two sibling nodes, and a product is a tree rather than a list -- in
sin(x)^4 * (-6) * sin(x)^2 the constant sits between the two powers, so
they are never siblings and the rule never fires. Full Simplify(System.Int32) gets these because it reassociates and sorts the factors first; nothing that
normalises without sorting does.
a^n * a^m = a^(n+m) needs no condition: with a^n read as
e^(n Log a) on the principal branch, the two sides are
e^(n Log a) * e^(m Log a) and e^((n+m) Log a), which are equal for
every complex n and m. This is what makes it unlike
(a^b)^c = a^(b*c), which moves the branch and is guarded above.
The one point it does not cover is a = 0 with a negative exponent, where
0^2 * 0^(-1) is undefined and 0^1 is 0 -- so this is applied to
integrands, where an antiderivative may differ on a measure-zero set, and not in
PowerRules(AngouriMath.Entity). https://github.com/asc-community/AngouriMath/issues/781

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AngouriMath

GatherPowersOfOneBase​(AngouriMath.​Entity)

GatherPowersOfOneBase(AngouriMath.Entity)