# InnerTrigonometricManipulations(R, F, FG)ΒΆ

- 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.