AngouriMath
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PowerOfAPower(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom)
Method (no overloads)
Summary
A power of a power to constant real exponents, (g^a)^b, as g^(a b) where g is positive near the point on each
side approached.
side approached.
Remarks
For g positive and a, b real, g^a is positive and (g^a)^b is g^(a b). Where g is negative it is not:
sqrt(x^3) is i |x|^(3/2) for x < 0, and x^(3/2) is -i |x|^(3/2). Read as written, sqrt(x^3) / x at 0 from the
right was 0 only after four seconds of l'Hopital's rule, each step another root over a power, where x^(3/2) / x
is sqrt(x) at once; floor(sqrt(x^3)) and sgn(sqrt(x^3)) asked it for the sign of sqrt(x^3). An integer outer
exponent is left to the normalisation, which takes (g^a)^n apart whatever the sign of g. Found by limitcheck;
no issue was filed.
sqrt(x^3) is i |x|^(3/2) for x < 0, and x^(3/2) is -i |x|^(3/2). Read as written, sqrt(x^3) / x at 0 from the
right was 0 only after four seconds of l'Hopital's rule, each step another root over a power, where x^(3/2) / x
is sqrt(x) at once; floor(sqrt(x^3)) and sgn(sqrt(x^3)) asked it for the sign of sqrt(x^3). An integer outer
exponent is left to the normalisation, which takes (g^a)^n apart whatever the sign of g. Found by limitcheck;
no issue was filed.
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