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I've tried Googling first but I didn't really find a clear answer. I am looking at the definition of "Graded Lex Order" where it says

Let $\alpha$,$\beta \in \mathbb{Z}^n$. We say $\alpha >_{grlex} \beta$ if $|\alpha|= \sum{\alpha_i}>|\beta|=\sum{\beta_i}$ or $|\alpha|=|\beta|$ and $\alpha >_{lex} \beta$

Well, I understand $\alpha$ and $\beta$ are $n$-tuples but is the modulus of an $n$-tuple defined to be the sum of all the entries? For a second I confused it with the modulus of a vector... but yes, I might have learned it somewhere but I forgot, so I just want to check.

Can someone confirm it? Thank you!

Kydo
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Yes, $|\alpha|$ is just the sum of the entries. You can look this up in e.g. Ideals, Varieties, and Algorithms by Cox, Little, O'Shea.

  • Cheers, that's exactly the book I am working on. Just didn't really see the definition of the modulus of $n$-tuples there...thanks for the help! – Kydo Oct 18 '15 at 15:55