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jake-doliskani / divpoly_pit

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Give an explicit formula for η #16

Closed defeo closed 6 years ago

defeo commented 6 years ago

Here:

https://github.com/javad-doliskani/divpoly_pit/blob/98734cc4aff5acd423f0d10277c6f9d0162e0eb5/divpoly_pit.tex#L624-L628

Without a precise definition for η, the reader can not:

Please give more details on the proofs of Theorems 7-8, and on the definition of η.

jake-doliskani commented 6 years ago

I added a simplified estimate for \eta as a function of \epsilon for explicit parameters and implementation. But do I really need to reiterate the proofs of Theorems 7-8. It is basically a copy and past and I'm a bit reluctant to do that.

defeo commented 6 years ago

Well, you say in the paper that the proof must be modified to make it work for your case (switching the roles of the curve and the projective line). It's not the reader's job to play the modification for you.

You can leave out the proof of the lemmas, if there are any, pointing to Voloch's paper for it. But you should not abuse the reader's "diffing algorithm" by writing an incremental proof.

Anyway your paper is quite short, so I do not understand why you are reluctant (other than being lazy, which I can totally understand :)

jake-doliskani commented 6 years ago

Ok, details are added. I think it is rather self-contained now.

defeo commented 6 years ago

Much better!