pattern matching - `Plus` wrongly applies `OneIdentity` to eradicate itself in `Plus[Power[

pattern matching - `Plus` wrongly applies `OneIdentity` to eradicate itself in `Plus[Power[_, 2] ..]`, unreproducible

I was trying to match some polynomials, but this is weird:

Plus[Power[x, 2], Power[y, 2]]~MatchQ~Plus[Power[_, 2] ..]
SetAttributes[f, Attributes@Plus]
f[Power[x, 2], Power[y, 2]]~MatchQ~f[Power[_, 2] ..]

Despite f having all of the same attributes as Plus, the expressions match only when it is used

False True

I found this is the root of the problem:

Plus[Power[_, 2] ..] // FullForm

gives Repeated[Power[Blank[],2]], the Plus entirely disappears, while

f[Power[_, 2] ..] // FullForm

gives f[Repeated[Power[Blank[],2]]] as I would expect.

I understand many built-in symbols escape the standard evaluation procedure anyways, so that not all of their behaviour is readily understandable from their Attributes etc. Obviously, Plus wrongly applies something like OneIdentity in this case, causing it to be removed. A user-defined symbol such as f doesn't do it here.

Is this a bug?

Answer

As pointed out in comments, this is caused by

Plus[x] is x

Here are some workarounds

Plus[Power[x, 2], Power[y, 2]]~MatchQ~Verbatim[Plus][Power[_, 2] ..]
Plus[Power[x, 2], Power[y, 2]]~MatchQ~HoldPattern[Plus][Power[_, 2] ..]
Plus[Power[x, 2], Power[y, 2]]~MatchQ~HoldPattern[Plus[Power[_, 2] ..]]

all giving True as expected.

Comments

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