How to get every term of a sum thats not multiplied by a convergent exponential function?

Hey, I need every term of a sum thats not multiplied by a convergent exponential function. In my case:

syms t
G = exp(-t)*cos(t) + 3*exp(-2*t)*sin(2*t) + 1/2*cos(4*t) + 1/5

G = 

What I need is stored in a variable. Is there any MATLAB function that fits my purpose?

Answer 1

[Walter Roberson]

Not exactly what you asked, but

syms t
G = exp(-t)*cos(t) + 3*exp(-2*t)*sin(2*t) + 1/2*cos(4*t) + 1/5

G = 

mapSymType(G, 'exp', @(varargin) 0)

ans = 

The reason it is not exactly what you asked is that you specified "not multipled by a convergent exponential function", implying that you would want a term with exp(5*t) [for example] to be retained as that is not convergent. So the parameter to the exp() needs to be examined to determine whether the exp() would be convergent or not.

[Walter Roberson]

syms t
G = exp(-t)*cos(t) + 3*exp(-2*t)*sin(2*t) + 1/2*cos(4*t) + 1/5 + 5*exp(7*t)

G = 

H = mapSymType(G, 'exp', @(EXPR) piecewise(LimitIsInf(children(EXPR,1)), EXPR, sym(0)))

H = 

function tf = LimitIsInf(EXPR)
    var = symvar(EXPR,1);
    if ~isempty(var)
    tf = isAlways(limit(EXPR,var,inf)==inf, 'unknown', "true");
    else
      tf = isAlways(~isfinite(EXPR), 'unknown', "true");
    end
    tf = tf == symtrue;
end