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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.


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