InnerTrigonometricManipulations(R, F, FG)¶

R: Join(IntegralDomain, Comparable)
F: Join(FunctionSpace R, RadicalCategory, TranscendentalFunctionCategory)
FG: Join(FunctionSpace Complex R, RadicalCategory, TranscendentalFunctionCategory)

This package provides transformations from trigonometric functions to exponentials and logarithms, and back. F and FG should be the same type of function space.

do_liou: (BasicOperator, List Complex F) -> Complex F: do_liou(op, lf) should be local but conditional.

explogs2trigs: FG -> Complex F: explogs2trigs(f) rewrites all the complex logs and exponentials appearing in f in terms of trigonometric functions.

F2FG: F -> FG: F2FG(a + sqrt(-1) b) returns a + i b.

FG2F: FG -> F: FG2F(a + i b) returns a + sqrt(-1) b.

GF2FG: Complex F -> FG: GF2FG(a + i b) returns a + i b viewed as a function with the i pushed down into the coefficient domain.

trigs2explogs: (FG, List Kernel FG) -> FG: trigs2explogs(f, [k1, ..., kn]) rewrites all the trigonometric functions appearing in f in terms of complex logarithms and exponentials. A kernel of the form tan(u) is expressed using exp(u)^2 if it is one of the ki's, in terms of exp(2*u) otherwise.