TrigonometricManipulations(R, F)

efstruc.spad line 1029 [edit on github]

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

TrigonometricManipulations provides transformations from trigonometric functions to complex exponentials and logarithms, and back.

complexElementary : F -> F

complexElementary(f) rewrites f in terms of the 2 fundamental complex transcendental elementary functions: log, exp.

complexElementary : (F, Symbol) -> F

complexElementary(f, x) rewrites the kernels of f involving x in terms of the 2 fundamental complex transcendental elementary functions: log, exp.

complexForm : F -> Complex(F)

complexForm(f) returns [real f, imag f].

complexNormalize : F -> F

complexNormalize(f) rewrites f using the least possible number of complex independent kernels.

complexNormalize : (F, Symbol) -> F

complexNormalize(f, x) rewrites f using the least possible number of complex independent kernels involving x.

imag : F -> F

imag(f) returns the imaginary part of f where f is a complex function.

real : F -> F

real(f) returns the real part of f where f is a complex function.

real? : F -> Boolean

real?(f) returns true if f = real f.

trigs : F -> F

trigs(f) rewrites all the complex logs and exponentials appearing in f in terms of trigonometric functions.