ElementaryFunctionSign(R, F)

limitps.spad line 673 [edit on github]

• R : Join(IntegralDomain, Comparable, RetractableTo(Integer), LinearlyExplicitOver(Integer), GcdDomain)
• F : Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, FunctionSpace(R))

This package provides functions to determine the sign of an elementary function around a point or infinity.

sign : F -> Union(Integer, "failed")

sign(f) returns 1 if f is always non-negative; returns -1 is f is always non-positive; returns 0 if f is always 0; returns "failed" if the sign of f varies or can't be determined.

sign : (F, Symbol, F, String) -> Union(Integer, "failed")

sign(f, x, a, s) returns the sign of f as x nears a from below if s is "left", or above if s is "right".

sign : (F, Symbol, OrderedCompletion(F)) -> Union(Integer, "failed")

sign(f, x, a) returns the sign of f as x nears a, from both sides if a is finite.