Determine if a polygon is convex

J, 105

echo>('concave';'convex'){~1=#=(o.1)([:>-.~)(o.2)|3([:-/12 o.-@-/@}.,-/@}:)\(,2&{.)j./"1}.0&".;._2(1!:1)3

Passes all three tests above.

Edit: (111->115) Handle co-linear points by eliminating angles of pi. Gained a few characters elsewhere.

Edit: (115->105) Less dumb.

Explanation for the J-impaired:

(1!:1)3 read STDIN to EOF. (I think.)
0&".;._2 is a nice idiom for parsing this kind of input.
j./"1}. lop off first line of input (N 0) and convert pairs to complexes.
(,2&{.) tack first two points onto the end of the list.
3(f)\ applies f to sliding window of length 3 (3 points for an angle)
[:-/12 o.-@-/@}.,-/@}: is a verb that transforms each 3 points into an angle between -pi and pi.
- -@-/@}.,-/@}: produces (p1 - p2),(p3 - p2). (Recall that these are complexes.)
- 12 o. gives an angle for each complex.
- [:-/(...) gives the difference of the two angles.
(o.1)([:>-.~)(o.2)| mod 2 pi, eliminate angles of pi (straight segments), and compare to pi (greater than, less than, doesn't matter unless the points are supposed to be wound in one direction).
1=#= if all those comparison result 1 or 0 (With self-classify. This seems dumb.)
echo>('concave';'convex'){~ print convex.

p=[map(int,raw_input().split())for i in[0]*input()]*2
print'ccoonncvaevxe'[all((a-c)*(d-f)<=(b-d)*(c-e)for(a,b),(c,d),(e,f)in zip(p,p[1:],p[2:]))::2]

gets
puts ($<.map{|s|s.split.map &:to_i}*2).each_cons(3).any?{|(a,b),(c,d),(e,f)|(e-c)*(d-b)<(d-f)*(a-c)}?:concave: :convex