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English heroes.

I recently learn math in English. However, what I found is the words "where" and "with" are both used to describe something.

e.g

  • where
    Graph G where every node has degree 1
    Polynomial P where all the coefficients are zero.

  • with
    Graph G with (V, E)
    Polynomial P with P(1) = 0

The part that confuses me is, can I use them interchangeably? Like, can I say "Polynomial P where P(1) = 0"?

I know that "where" means "in which or to which" and "with" means "in relation to" but by the similarity between these two situations that the words are used, I'm confused when to used one of those. When should I use either "where" or "with" in math writing?

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The word with has various meanings. The one relevant for your question is having: a polynomial P having P(1) = 0 etc.

I think where/with/such that/having can be used more or less interchangeably (with necessary changes).

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