DefiniteIntegrationTools(R, F)

defintrf.spad line 1 [edit on github]

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

DefiniteIntegrationTools provides common tools used by the definite integration of both rational and elementary functions.

checkForZero : (Polynomial(R), Symbol, OrderedCompletion(F), OrderedCompletion(F), Boolean) -> Union(Boolean, "failed")

checkForZero(p, x, a, b, incl?) is true if p has a zero for x between a and b, false otherwise, "failed" if this cannot be determined. Check for a and b inclusive if incl? is true, exclusive otherwise.

checkForZero : (SparseUnivariatePolynomial(F), OrderedCompletion(F), OrderedCompletion(F), Boolean) -> Union(Boolean, "failed")

checkForZero(p, a, b, incl?) is true if p has a zero between a and b, false otherwise, "failed" if this cannot be determined. Check for a and b inclusive if incl? is true, exclusive otherwise.

computeInt : (Kernel(F), F, OrderedCompletion(F), OrderedCompletion(F), Boolean) -> Union(OrderedCompletion(F), "failed")

computeInt(x, g, a, b, eval?) returns the integral of f for x between a and b, assuming that g is an indefinite integral of f and f has no pole between a and b. If eval? is true, then g can be evaluated safely at a and b, provided that they are finite values. Otherwise, limits must be computed.

ignore? : String -> Boolean

ignore?(s) is true if s is the string that tells the integrator to assume that the function has no pole in the integration interval.