I'm not sure which grammatical number to use in the following sentence from a mathematical text:

The points of S whose Galois conjugate lies in the same sub-interval have the same prototile.

The points of S whose Galois conjugates lie in the same sub-interval have the same prototile.

The problem is that each point has exactly one Galois conjugate, therefore the plural sounds strange to me.

  • It might not be obvious that Galois conjugate(s) is a noun and lie(s) is a verb. (It didn't appear so the first round I tried to understand the sentence.) This sentence, which has a similar pattern, might be helpful, "(I have read that, on the shores of the Adriatic sea,) the wives of fishermen whose husbands are far out at sea are in the habit of going down to the seashore at night and sweetly singing the first verse of some beautiful hymn". – Damkerng T. Jul 28 '14 at 13:27

Because most of us aren't familiar with Galois conjugates, we may as well substitute a more common term which would be syntactically identical...

"Disregard those circles whose centres fall outside the shaded area"

From which it should be obvious the "plurality" of both nouns must agree. To underline the point,...

"Disregard any circle whose centre falls outside the shaded area"
"Disregard any circles whose centres fall outside the shaded area"

  • @tohecz: I realise it's not always easy to think of an analogous usage when you're already having a problem with the original - particularly when it's not even your native language. So I imply no criticism of you for the "obscure" reference in your question as phrased, but I'm glad you see the advantage of presenting any questionable/confusing syntax using more familiar nouns, verbs, adjectives, etc. Sometimes (as I hope is the case here) the problem simply goes away when you're not struggling with semantics/meaning at the same time as syntax/grammar. – FumbleFingers Reinstate Monica Jul 28 '14 at 15:06

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