PowerSeriesLimitPackage(R, FE)

limitps.spad line 1 [edit on github]

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

PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits, left- and right- hand limits, and limits at plus or minus infinity.

complexLimit : (FE, Equation(OnePointCompletion(FE))) -> Union(OnePointCompletion(FE), "failed")

complexLimit(f(x), x = a) computes the complex limit lim(x -> a, f(x)).

limit : (FE, Equation(FE), String) -> Union(OrderedCompletion(FE), "failed")

limit(f(x),x=a,"left") computes the left hand real limit lim(x -> a-, f(x)); limit(f(x),x=a,"right") computes the right hand real limit lim(x -> a+, f(x)).

limit : (FE, Equation(OrderedCompletion(FE))) -> Union(OrderedCompletion(FE), Record(leftHandLimit : Union(OrderedCompletion(FE), "failed"), rightHandLimit : Union(OrderedCompletion(FE), "failed")), "failed")

limit(f(x), x = a) computes the real limit lim(x -> a, f(x)).