How to find non zero elements of a list containing zeros and symbols

I have a list, obtained after differentiating a list of expressions, which contains zeros and symbols, say:

A = {x1^2, x2^2, x3^2, x4^2}
D[A,x3]


results in the list:

{0, 0, 2 x3, 0}


How do I get the position of the non-zero entry, mathematica cannot compare symbols to zero directly. I could convert the elements of the list to strings but is there a faster way?

• Have a look at === vs ==. Posting your code is also a good idea. Commented May 3, 2014 at 9:37
• Position[D[A, x3], x_ /; ! TrueQ[x == 0], {1}, Heads -> False]
– Kuba
Commented May 3, 2014 at 9:41
• Also Position[D[A, x3], Except[0], 1, Heads -> False] Commented May 3, 2014 at 9:55
• Also ArrayRules[D[A, x3]][[;; -2, 1, 1]] Commented May 3, 2014 at 9:59
• @YvesKlett, my code involves symbolic calculation with many subscripts, which does not look good when posted. Commented May 3, 2014 at 10:10

I've failed to find good topic to mark it a duplicate so this is the answer.

list = {0, 2 x3, 0.}


so we 0 is not 0. and missing this may cause troubles while pattern matching. Take a look here and there.

SparseArray[list]["NonzeroPositions"]

{{2}}


or alternatively:

Position[list, x_ /; ! TrueQ[x == 0], {1}, Heads -> False]

• The "NonzeroPositions" method should be the fastest available. It however does not work on a list that contains other lists, i.e. fails VectorQ but does not pass ArrayQ. One could replace List expressions first, e.g.: Replace[list, _List -> 1, {1}] Commented May 3, 2014 at 11:55
• @Mr.Wizard Thanks for the notes. General answer may be long, I'm no really interested in elaborating this subject, mainly because of lack of knowldge. But if you want to do this I will gladly upvote it and delete mine.
– Kuba
Commented May 3, 2014 at 12:17
• No need for that. :-) I think this has it covered now. Commented May 3, 2014 at 12:23
• In some use-cases, one might want Position[list, x_ /; ! PossibleZeroQ[x], {1}, Heads -> False] or other methods of checking sameness/zero/etc. Commented Oct 31, 2021 at 16:52