AngouriMath
GatherSignsAndModuli(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
The signs and moduli of one real-valued argument among the factors of a product
gathered into a power of the argument and at most one sign:|a|^k is
sgn(a)^k a^k for a real a , so sgn(a)^m |a|^k is
sgn(a)^((m + k) mod 2) a^k , and sgn(a)^2 is 1 -- away from
a = 0 , which is the generic case every rule answers in.
gathered into a power of the argument and at most one sign:
Remarks
The secant substitution answers 1/(x^2 (x^2 - 1)^(5/2)) in |x| and
sgn(x) , and a step of parts against it -- Timofeev's
arccsc(x)/(x^2 (x^2 - 1)^(5/2)) -- leaves a remainder with |x|^4 ,
|x|^2 and sgn(x)/|x| in it that no rule reads, where it is
x^4 , x^2 and 1/x . Applied with the gathering of powers on every
entry to the chain, for the same reason: the shape is the integrator's own.
entry to the chain, for the same reason: the shape is the integrator's own.
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