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If someone could make a rudimentary diagram of a Newton Polygon that would be really useful. I guess there's a question about what field we're using - I would say the p-adic numbers but then I'm studying them. Even without an explicit field, a diagram would help make things clearer. Owen Jones 19:18, 15 January 2006 (UTC) reply

Suggest making a request at Wikipedia:Requested pictures, mathematics section. Charles Matthews 19:32, 15 January 2006 (UTC) reply

To make this more accessible, it would be nice to start with polynomials in two variables over a field (or even over C), and only then pass to valuation fields. There are a few words about this in the beginning, but it is not at all clear (for a non-algebraist) how is this special case connected to the general definition. Sodin 13:45, 3 August 2007 (UTC) reply

I agree, the statement should be given for C, it would make this article much more accessible. Superhiggs ( talk) 06:10, 24 October 2017 (UTC) reply

The lead of this article is terrible. I've read it several times over, and even though I have an above average background in mathematics, I couldn't make heads or tails of it. Shinobu ( talk) 09:15, 25 December 2008 (UTC) reply