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, Symbol) -> F

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

complexElementary: F -> F

complexElementary(f) rewrites f 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, Symbol) -> F

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

complexNormalize: F -> F

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

imag: F -> F

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

real?: F -> Boolean

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

real: F -> F

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

trigs: F -> F

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