Mauro_Braunstein: Sloppy but interesting. Numerous typos, but nothing that bad. Skipped many details, but that's OK. Not enough about connections and open problems and misleading last sentence. No bibliography. Nothing about how to actually compute fundamental unit. Grade: 78% Steven Byrnes: Nice paper, but one gets the sense he really doesn't have a feeling at all for how the algorithm actually works. There's not a single example. Grade: 93% William Fithian: Very nice. Not too deep, but a noice choice of topics; follows through and very clear. Good examples. Grade: 93% Francis Kelly: Awkward wording in last paragraph. Awkward typesetting. Catchy intro and good choice of topic. No overview of contents or hint as to upcoming structure of paper. * Very frustrating to read. * Not well researched. * Ugly weird notation. * No examples. GRADE: 80% Alison Miller: Almost nothing there. I don't know what to do. Grade: 75%? Nizameddin Ordulu: Very nicely systematic. Clear Complete Many typos and confusing notation No real examples Grade: 89% Corina Patrascu: Seems like she just copied some stuff. But she did a great job copying, and I learned something. Reminds me of the "learn something if you don't know much already." Annoying lack of examples or connection with real world. Too abstract. Grade: 89% Anatoly Preygel: Huge paper; proves a very hard theorem completely. wow. Grade: 99% Emily Riehl: Very very well written up and clean. Could probably be published. I found no typos, and the writing is clear. I really like the clean coherence of the paper overall. But it didn't push or really have anything super interesting or original in it. Grade: 91% Gary Sivek: Good motivation. On page 1: "the free abelian subgroup" (meaningless!) Nice applications. Grade: 90% Steven Sivek: Very nice discussion of Bernoulli polynomials. Clear. Nice complexity analyssis and really felt reasonably deep and original. Grade: 95% Kaloyan Slavov: Solid and competent. He clearly totally understands it. Not really that "original" or deep, but very clean. Grade: 93% Gregory Valiant: Really good examples, though; well researched and honest. Grade: 95% Yan Zhang: Awkward phrasing. Typos (e.g., "texst" in theorem 2). I couldn't understand the math on page 1, since the index form is defined in a very confusing way. Very good and interesting choice of problem. What is n in the proof of prop 2? (anything -- but unclear.) "Sp" --> "So". In alternative proof of prop 2, you can't use MAGMA, since you're making a claim for general x,y! In thm 8, f and g have to be over Z_{(p)} or the mod-p condition doesn't make sense. Word "nonic" ??? What's that? It was well researched, I learned much, and someone could find this paper *very* useful when doing research. I can't give it higher because of typos and lack of clarity. Grade: 92%