Merge pull request #2 from RobinZ16/master

add Morton section
reformat Robin's code

Tabs are evil. Better not indent code with tabs. Also apply fill-column
70 so that code is more readable on a wider range of text editors.

Robin: if you have any objection, feel free to discuss with me. We can
easily revert the changes by running 'git revert'.
use 'n' instead of 'N' for dimension of...

projective space.

N is later used for the length of cycles. Must be renamed to avoid name
clash.
add Zhiming's comments regarding the N=4 section

To summarize, I think we need more precise definitions (since there are
crucial paradigm shifts) and a little bit more math about the rational
points (due to their central role).
Merge pull request #4 from zmwangx/master

Presentation 1: improve section 1 and 2, and comment on section 2
presentation 1: section 2 (N=5) preliminary ver.

Here and there the prose is more formal then what should be given in the
talk.
add *.fmt to .gitignore

Found another preview-latex junk that I previously never noticed.
presentation 1: rewrite section 2 (N=4 case)

Fix #3.

I've given more details than could be included in the talk.
improve presentation 1

Fixed problems found in the rehearsal.

Section 1 is not affected.
add a template to kick start all future tex files

Custom definitions subject to additions.
introducing dump

A dumping field for ideas, observations, conjectures, and preliminary
results!
add presentation-0.tex

This is the TeX source file of my (Zhiming's) first quick
presentation. I'm now adding it for the completeness of the repo.
rename dump/ directory to misc/
initial commit for the search program using FLINT

Added:
* Makefile;
* search.cpp, with the rational and irrational parts of f(x)
  implemented (f is the polynomial in x, where y^2 = f(x) gives a
  projective model for C_0(5));
* local .gitignore.
finish search with FLINT!

Got a great speed boost!
search: print slightly more information
quadratic-5-cycle.nb

Search for quadratic five cycles (with quadratic c). This is not at all
fruitful, though, since factoring over Q(y) is extremely expensive for y
with large height -- and y always has large height even for x with small
height -- especially when y is complex (i.e., the extension is
Q(sqrt(d)) with d < 0).
discriminant.sage: failed attempt

Failed attempt to calculate the relative discriminant of the field
extension Q(x)[y]/(y^2 - f(x)) over Q(c). Sage can only handle relative
discriminants of relative number fields, not function fields.
add another idea
move template.tex to preamble.tex...

to be included by all tex source files in the repo.

Greatly reduce redundancy.