RationalFunctionLimitPackage(R)

sign.spad line 174 [edit on github]

• R : GcdDomain

Computation of limits for rational functions.

complexLimit : (Fraction(Polynomial(R)), Equation(Fraction(Polynomial(R)))) -> OnePointCompletion(Fraction(Polynomial(R)))

complexLimit(f(x), x = a) computes the complex limit of f as its argument x approaches a.

complexLimit : (Fraction(Polynomial(R)), Equation(OnePointCompletion(Polynomial(R)))) -> OnePointCompletion(Fraction(Polynomial(R)))

complexLimit(f(x), x = a) computes the complex limit of f as its argument x approaches a.

limit : (Fraction(Polynomial(R)), Equation(Fraction(Polynomial(R))), String) -> Union(OrderedCompletion(Fraction(Polynomial(R))), "failed")

limit(f(x),x,a,"left") computes the real limit of f as its argument x approaches a from the left; limit(f(x),x,a,"right") computes the corresponding limit as x approaches a from the right.

limit : (Fraction(Polynomial(R)), Equation(Fraction(Polynomial(R)))) -> Union(OrderedCompletion(Fraction(Polynomial(R))), Record(leftHandLimit : Union(OrderedCompletion(Fraction(Polynomial(R))), "failed"), rightHandLimit : Union(OrderedCompletion(Fraction(Polynomial(R))), "failed")), "failed")

limit(f(x), x = a) computes the real two-sided limit of f as its argument x approaches a.

limit : (Fraction(Polynomial(R)), Equation(OrderedCompletion(Polynomial(R)))) -> Union(OrderedCompletion(Fraction(Polynomial(R))), Record(leftHandLimit : Union(OrderedCompletion(Fraction(Polynomial(R))), "failed"), rightHandLimit : Union(OrderedCompletion(Fraction(Polynomial(R))), "failed")), "failed")

limit(f(x), x = a) computes the real two-sided limit of f as its argument x approaches a.