I need to simplify big symbolic solution of equations system by truncating terms that are orders of magnitude less then others in subexpressions like a + b. The solution is big fraction with sum of terms in numerator and denominator like
a b + c ( d - f + g + ...
where every symbol has value (real number). Is it possible to apply rule like this to solution:
replace a + b by a, if Abs[a] >> Abs[b] (say, 1000 times more), by b, if Abs[a] << Abs[b], or leave it as a + b in other cases.
Repeated application of such a rule should result in symbolic expression that is much simpler then exact solution, but is good enough approximation for concrete values of symbols. I am new to Mathematica, searched for similar questions but didn't find any.
Minimal working example: solving eq gives solution that should be simplified by truncating terms basing on parameters alpha and beta below:
v1 = α1 a - β1 b;
v2 = α2 a;
v3 = α3 c;
eq = {-v1 - v2 == 0, v1 + v3 == 0, a + b + c == p};
Solve[eq, {a, b, c}]
α1 = 1000; β1 = 1000; α2 = 1; α3 = 1;
{a, b, c ,d, ...}
? $\endgroup$