simplification in maxima : removing terms with "small" contributions from an expression

Question

Often in applied situations there are simplifications for small x.

For example $x<<1$ and $x/(1+x) \approx x$ or $(x + x^2)/c \approx x/c$.

Is there a way in Maxima to carry out these sorts of expression simplifications? If there's no way to do this sort of operation in Maxima, do other CAS programs have support for something like this?

Answer 1

I am assuming, you want to automatically generate the approximation and use it in other calculations. One trick I have found to be useful is

factor(f,x,0,1)

This will just keep the first order terms of $f$. You could also use expand

Noticed a typo: It should be factor(taylor(f,x,0,1))

Answer 2

Since you gave the Magma CAS, there you can comfortably calculate with truncated power resp. Taylor series, for instance to compute Sin(X+O(X^60)). I'd think that Taylor series arithmetics is established long enough so that it also can be found in or for maxima.