julian-upc / discrete-geometry Goto Github PK

74f4d46#diff-8bfbb63f03040c1840d060bcc7db478f

https://github.com/julian-upc/discrete-geometry/blob/d6d662cef6dcbb6ee14f17d42f5c3d559bb8e92c/2014/exercises/sheet1/sheet1_quentin_pergeline.gpg
... has some problems. It appears to be an ascii hex dump but not a gpg encrypted file.

Hi Cassandra,

... the point being that if you encrypt your code, we can't use github's comment facilities to discuss it.

Thanks!

Hi Elisabet,

Just some nits to pick in your solutions on Sheet 2:

1. In problem (1), a face is actually the set of points where the linear form in question achieves equality, given that it is valid for P. So if ax<=b is valid for P, the face defined by (b,a) in homogeneous coordinates would be { x in P : ax = b }. In your notation,
   F_a(P) = P cap { x in R^d : (a,x) = min {(a,y) : y in P } }.
2. Being Sl_2(Z)-equivalent actually means that P = AQ for some A in Sl_2(Z), so it's a linear transform, not an affine one. The latter would be expressed as saying that P and Q are Aff_2(Z)-equivalent.
3. You didn't catch the part about metadata being unencrypted.

Best,
Julian

... at 6e78ca4

Let's talk about some details in your c++ code.

Re Problem 2: Compare your list to http://arxiv.org/pdf/math/0406224 . Which one are you missing?

Congratulations! You wrote some excellent code, and kudos for using c++11. Some minor comments are at 93a1f59 .

However, there are some comments on the larger picture I'd like to make. Above all, I think you should reconsider your choice of programming language for this assignment. You spent an inordinate amount of time reinventing the wheel (Rational class, explicit determinants, etc), when in fact all computations in sight are constant-time (because the size of the matrices is fixed), and so the choice of an efficiency monster like c++ isn't really justified.

So I'd suggest that the next time you find yourself in such a situation, you reach for a higher-level language that allows for type-checking, like the sage framework. I think you'll save yourself a huge amount of development time, when ultimately the performance difference (and thus, sadly, the benefit of using c++) is going to be negligible.

Problem 1

You actually don't prove that the edges of the permutahedron correspond to adjacent transpositions! So you don't really know that the polytope is simple. But otherwise, the exposition is very nice and detailed. Thanks!

Problem 2

Congratulations! You solved the problem. Here is a prize for you:
http://arxiv.org/pdf/math/0406224
However, I missed where you use Pick's Theorem.

Problem 3

Thanks for the nice research! You missed the issue with the unencrypted metadata, though.

Hi Ainize,
just some comments on your latex: the scalar product is best written \langle x,y\rangle (and if you want you can define a macro so that you don't have to type that every time).
Moreover, general math operators are defined using, e.g., \DeclareMathOperator{\skel}{skel}. This will give you the correct font and the correct spacing of the symbols around it. In your case, the operator \min is already predefined in latex.

In the part about email with gpg, you missed the issue with unencrypted metadata.

Finally, see the comments on your code in
74f4d46

29165b3

7fb0845#diff-74462e9b21f6b0715e5805cc17618faf

5e06dd5#diff-8d1e016ee7d26fbe9d2c303aee6aaaac

It would be better to not encrypt your code, because that way we can use github's commenting features to talk about it..