Selecting terms containing some expression

Question

Imagine I have an expression like

a*k + (a^2)*b*c + b*e

and I would like to obtain the term containing, for example, some power of a. In that case I would extract the two first terms. If I wanted to obtain the term b*e, I would extract the last.

How can I do it? I guess I should use Cases or something similar, but I don't understand its syntax.

Answer 1

You can use pattern matching. For instance to match a which is multiplied by something else you use

Cases[a*k + (a^2)*b*c + b*e, a*_]

or

Cases[a*k + (a^2)*b*c + b*e, a^_, 2]

The 2 is necessary because a^2 appears deeper in you expression. Furthermore, to prevent trouble, you should be aware of FullForm which shows you the full underlying representation of your structure.

If something does not work, check the FullForm of you pattern and the thing you want to match first. You should start by

Introduction to Patterns

Update

The first part of my answer was not a ready to use solution. It assumed, that you do some work for yourself: Finding the patterns which help you to extract the parts you want.

Now, it seems you are asking something different: When you look at your expression as a polynomial in a, then it's worth looking at functions like CoefficientList (as already mentioned by Daniel in the comment), Coefficient, ... Please look here to have an overview

Polynomial algebra

With this you get the expression containing some power (even the one with a^0) easily

CoefficientList[a*k + (a^2)*b*c + b*e, a]

Or you can pick one special power, like the second one

Coefficient[a*k + (a^2)*b*c + b*e, a, 2]

Answer 2

I think this is what you want:

Cases[
 a*k + (a^2)*b*c + b*e,
 term_ /; ! FreeQ[term, a],
 {1}
]

{a^2 b c, a k}

Note that the terms are not in the explicit order given as Plus is Orderless. I am assuming this does not matter in practice but other measures can be taken of needed.

As a function:

selectTerms[expr_, pat_] := Cases[expr, term_ /; ! FreeQ[term, pat], {1}]

Answer 3

Maybe:

 Select[a*k + (a^2)*b*c + b*e, MemberQ[#, a | a^_] &]

=> a^2 b c + a k

Select[a*k + (a^2)*b*c + b*e, MemberQ[#, b] && FreeQ[#, a] &]

=> b e

Select[a*k + (a^2)*b*c + b*e, MemberQ[#, e] &]

=> b e