# [Maxima] [Newbie:] How to discard higher orders of variables?

Stavros Macrakis macrakis at alum.mit.edu
Wed Jul 11 13:34:34 CDT 2007

```On 7/11/07, Schirmacher, Rolf <Rolf.Schirmacher at muellerbbm.de> wrote:

> ...My problem is that I want to discard higher order terms within an
> expression
> as it is often done when simplifying analytical equations in
> engineering....
>
> beta is a small quantity, so terms with an order higher than beta^2 (e.g.
> beta^4) should be omitted....
>

So, the remaining solution coming to my mind was to go to the taylor series:

Yes, this is probably the best approach.

(%i15) taylor(term,beta,0,2);
>
> (%o15) c+sqrt(2)*d+sqrt(2)*e+2*f+((4*f+sqrt(2)*d+2*c+4*a)*beta^2)/4+...
>
> As a second step, one would have to sort out all terms (manually?) from
> the
> beta^2 term, which occur in the part independent of beta (as they
> represent
> the beta^2 << 1 - issue). While this seems to be reasonable for the terms
> given here, it shows up to be rather involved for "real world" equations.
>

If I understand the question, the following will work:

ratcoeff(%o15,beta,i)
for i=0,1,2

for example

makelist( ratcoeff(%o15,beta,i), i, 0, 2)

-s
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