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I was playing with pattern matching and I ran into something I didn't expect. I imagine the following line would return True, but it returns False:

MatchQ[x, (+1 | -1) a_]

This will return True:

MatchQ[-x, (+1 | -1) a_]

Digging slightly deeper with FullForm I find the reason for this; FullForm[-a] returns Times[-1, a] whereas FullForm[a], of course, returns a. What's the best way to return True for both cases? Does Mathematica have an equivalent to the ? symbol in regular expressions which matches a group zero or one times?

I've also tried

MatchQ[x, (Nothing | -1) a_]

which again returns False.

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    $\begingroup$ This would work: MatchQ[x, fact_. a_Symbol /; Abs[fact] == 1] It matches only if the factor in front of a symbol is +1 or -1. Nothing is not meant to be used in pattern matching. $\endgroup$
    – Szabolcs
    Sep 6, 2016 at 18:57
  • $\begingroup$ What would be an example of a match failure you would hope to see with the pattern you are searching for? $\endgroup$
    – Alan
    Sep 6, 2016 at 20:12
  • $\begingroup$ @Szabolcs Thank you, _. was just what I needed to know about. @Alan 2x would fail to match. $\endgroup$
    – alessandro
    Sep 6, 2016 at 23:32

1 Answer 1

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FullForm (and Head) is useful in seeing what lies under the hood.

FullForm@x

x

Head@x

Symbol

and

FullForm@-x

Times[-1,x]

Head@-x

Times

Now

(+1 | -1) a_ // FullForm

Times[Alternatives[1,-1],Pattern[a,Blank[]]]

That's why -x matches the pattern and x does not. For a fix:

MatchQ[x, -1 a_ | _Symbol]

True

MatchQ[-x, -1 a_ | _Symbol]

True

MatchQ[2 x, -1 a_ | _Symbol]

False

MatchQ[-2 x, -1 a_ | _Symbol]

False

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