Question on slack: wonder if any symbolic package can perform the completing the square in the Gaussian density
f(x,F,Γ) = exp(((-x^2) /2)*(Γ)+ x*F)
Yes:
using Mitosis
using Symbolics
@variables F,Γ
p = convert(Mitosis.Gaussian{(:μ,:Σ)}, Mitosis.Gaussian{(:F,:Γ)}(F, Γ))
There it is
julia> p
Gaussian{(:μ, :Σ)}((μ = F*(Γ^-1), Σ = Γ^-1))