The following references would seem relevant for what a "typical"
mathematician might think coming to Sage who isn't directly involved
in either kind of lattice on a daily basis, though it's not clear that
it resolves this discussion, since the authors below are self-
selecting.  The idea that a "point" lattice (and hence Euclidean
lattice) is a special case of a "poset" lattice is interesting, though
I don't see how would that work for the cocompact definition or for
unordered fields...

- kcrisman

http://mathworld.wolfram.com/PointLattice.html
http://mathworld.wolfram.com/Lattice.html
http://en.wikipedia.org/wiki/Lattice_%28group%29
http://en.wikipedia.org/wiki/Lattice_%28order%29

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