Suppose I have a lot of expressions multiplied by factors such as:
$$e^{-i\theta[1]-i\theta[2] - i\theta[3]-i\theta[4]-i\theta[5]}$$
I would like to separate this into a product of exponentials of the form
$$e^{-i\theta[1]}e^{-i\theta[2]}...$$
before employing the function ExpToTrig
and making substitutions to the result trigonometric functions.
However, since I plan to apply the tangent half angle substitution (cf. my previous question Simplifying Expressions for FindMinimum), I would like the arguments to involve only one variable at a time. In particular, I tried using ComplexExpand
on the function to express the trigonometric functions as functions of a single variable, but it expands the entire function out.
In short, I would like to keep the simplified form, but want to expand the exponential as per the above without having to expand the entire expression.
For reference, here is my function
(E^(-I θ[1] - I θ[2] - I θ[3] - I θ[4] - I (θ[5] - θ[6]))
Abs[Sin[ϕ[6]]]^2 (1 - E^(I (θ[1] - θ[6]))
Cot[ϕ[6]/2] Tan[ϕ[1]/2]) (Cos[θ[1]] + I Sin[θ[1]] + E^(I θ[2])
Tan[ϕ[1]/2] Tan[ϕ[2]/2]) (Cos[θ[2]] + I Sin[θ[2]] + E^(I θ[3])
Tan[ϕ[2]/2] Tan[ϕ[3]/2]) (Cos[θ[3]] + I Sin[θ[3]] + E^(I θ[4])
Tan[ϕ[3]/2] Tan[ϕ[4]/2]) (Cos[θ[5] - θ[6]] + I Sin[θ[5] - θ[6]] - Cot[ϕ[6]/2]
Tan[ϕ[5]/2]) (Cos[θ[4]] + I Sin[θ[4]] + E^(I θ[5])
Tan[ϕ[4]/2] Tan[ϕ[5]/2]))/
(2 Sqrt[(1 + Abs[Tan[ϕ[1]/2]]^2) (1 + Abs[Tan[ϕ[2]/2]]^2)]
Sqrt[(1 + Abs[Tan[ϕ[2]/2]]^2) (1 + Abs[Tan[ϕ[3]/2]]^2)]
Sqrt[(1 + Abs[Tan[ϕ[3]/2]]^2) (1 + Abs[Tan[ϕ[4]/2]]^2)]
Sqrt[(1 + Abs[Tan[ϕ[4]/2]]^2) (1 + Abs[Tan[ϕ[5]/2]]^2)]
Sqrt[(1 + Abs[Tan[ϕ[1]/2]]^2) (1 + Cos[ϕ[6]])]
Sqrt[(1 + Abs[Tan[ϕ[5]/2]]^2) (1 + Cos[ϕ[6]])])
TrigExpand[ExpToTrig[...]]
. $\endgroup$ – Daniel Lichtblau Aug 6 '15 at 23:22