# IntegrationTools(R, F)ΒΆ

Tools for the integrator Author: Manuel Bronstein Date Created: 25 April 1990 Keywords: elementary, function, integration.

intPatternMatch: (F, Symbol, (F, Symbol) -> IntegrationResult F, (F, Symbol) -> Union(Record(special: F, integrand: F), failed)) -> IntegrationResult F if R has GcdDomain and F has LiouvillianFunctionCategory and F has ElementaryFunctionCategory and R has PatternMatchable Integer and R has ConvertibleTo Pattern Integer
intPatternMatch(f, x, int, pmint) tries to integrate f first by using the integration function int, and then by using the pattern match intetgration function pmint on any remaining unintegrable part.
kmax: List Kernel F -> Kernel F
kmax([k1, ..., kn]) returns the top-level ki for integration.
ksec: (Kernel F, List Kernel F, Symbol) -> Kernel F
ksec(k, [k1, ..., kn], x) returns the second top-level ki after k involving x.
mkPrim: (F, Symbol) -> F if R has GcdDomain and F has ElementaryFunctionCategory
mkPrim(f, x) makes the logs in f which are linear in x primitive with respect to x.
removeConstantTerm: (F, Symbol) -> F if R has IntegralDomain
removeConstantTerm(f, x) returns f minus any additive constant with respect to x.
union: (List Kernel F, List Kernel F) -> List Kernel F
union(l1, l2) returns set-theoretic union of l1 and l2.
vark: (List F, Symbol) -> List Kernel F
vark([f1, ..., fn], x) returns the set-theoretic union of (varselect(f1, x), ..., varselect(fn, x)).
varselect: (List Kernel F, Symbol) -> List Kernel F
varselect([k1, ..., kn], x) returns the ki which involve x.