I am looking for the function equivalent of Sympy's function: as_independent (*deps, **hint) in Mathematica. The function naively separates an expression into arguments that are not dependent on deps. This operation does not work for non-commutative terms, since they cannot always be separated out.
For example, let us consider the expression
F[x_,t_,a_] = Cos[2*t] Sin[5 x] Exp[-2 t] t^3 a
We observe that $f(x,t,a) = T(t)*X(x)*A(a)$ and thus the equation is separable in its arguments $x,t,a$. Suppose I would like to separate the equation in its arguments x and t. For argument t, this operation should return $X(x)*A(a)$ and $T(t)$
Cos[2*t] Exp[-2t] t^3
For argument x the operation should return $T(t)*A(a)$ and $X(x)$
Cos[2*t] Exp[-2t] t^3 a
Is this possible in Mathematica?