Oct 28, 2012
college football poll - week 9

Ohio State and Florida swap places as the Buckeyes beat Penn State and the Gators fall to Georgia.

An interesting phenomenon this season is the abundance of Pac-12 teams with medicore records in the top 25. Let’s take a closer look.

Stanford comes in at #8, just three spots behind national title contender Oregon. They have quality out-of-conference wins against San Jose State (giving them lots of WAC “wins”) and Duke (giving them lots of ACC “wins”), and of course they beat USC and Arizona. They also beat Cal, who beat UCLA, who beat Nebraska, giving them lots of distant Big Ten “wins”.

Oregon State, who was just handed their first loss last night against Washington, is no real surprise at #10. However, just three spots later, we have Arizona with three losses. They have wins over solid Toledo and Oklahoma State teams, giving them lots of “wins” in the MAC and Big 12. And their three losses happen to be the aforementioned Stanford and the two Oregon schools.

USC sits at 6-2 and #20. Nothing really very odd there.

Finally, the real head scratcher. The Huskies sitting at .500 landed in #21. They have a quality out-of-conference win against San Diego State, giving them lots of MWC “wins”. Their two conference wins include none other than Stanford and Oregon State, and their four losses are against some pretty great teams: LSU, Oregon, USC, and Arizona.

1 - Notre Dame (8-0) (34.2265625) (1)
2 - Ohio St. (9-0) (29.02734375) (6)
3 - Alabama (8-0) (28.328125) (3)
4 - LSU (7-1) (27.0625) (4)
5 - Oregon (8-0) (26.67578125) (8)
6 - Florida (7-1) (26.5546875) (2)
7 - Kansas St. (8-0) (25.41796875) (5)
8 - Stanford (6-2) (23.07421875) (9)
9 - Georgia (7-1) (23.0234375) (18)
10 - Oregon St. (6-1) (22.921875) (7)
11 - Louisville (8-0) (21.93359375) (11)
12 - South Carolina (7-2) (21.6796875) (14)
13 - Arizona (5-3) (20.28125) (22)
14 - Texas Tech (6-2) (18.80859375) (10)
15 - Mississippi St. (7-1) (17.32421875) (12)
16 - West Virginia (5-2) (17.15625) (15)
17 - Clemson (7-1) (17.1030578613281) (20)
18 - Nebraska (6-2) (16.54296875) (NR)
19 - Louisiana Tech (7-1) (16.51953125) (21)
20 - Southern California (6-2) (15.91015625) (19)
21 - Washington (4-4) (15.85546875) (NR)
22 - Texas (6-2) (15.8291015625) (23)
23 - Iowa St. (5-3) (15.724609375) (NR)
24 - Oklahoma (5-2) (15.505859375) (17)
25 - Texas A&M (6-2) (15.490234375) (NR)
dropped out: Rutgers, Florida St., Michigan, Ohio

Directed graph.
Oct 21, 2012
college football poll - week 8

Not much movement at the very top. ‘Bama moves up to #3 after pounding the Vols as the Fighting Irish and Gators hold on to the top two spots.

1 - Notre Dame (7-0) (27.71484375) (1)
2 - Florida (7-0) (26.59375) (2)
3 - Alabama (7-0) (25.25) (4)
4 - LSU (7-1) (24.421875) (7)
5 - Kansas St. (7-0) (23.529296875) (3)
6 - Ohio St. (8-0) (23.4755859375) (5)
7 - Oregon St. (6-0) (23.4453125) (6)
8 - Oregon (7-0) (22.66796875) (8)
9 - Stanford (5-2) (20.58984375) (11)
10 - Texas Tech (6-1) (19.146484375) (9)
11 - Louisville (7-0) (17.89453125) (16)
12 - Mississippi St. (7-0) (17.7900390625) (18)
13 - Rutgers (7-0) (17.37890625) (10)
14 - South Carolina (6-2) (16.5625) (13)
15 - West Virginia (5-2) (16.5546875) (12)
16 - Ohio (7-0) (16.416015625) (15)
17 - Oklahoma (5-1) (15.8076171875) (17)
18 - Georgia (6-1) (15.4140625) (22)
19 - Southern California (6-1) (15.099609375) (20)
20 - Clemson (6-1) (14.7895812988281) (24)
21 - Louisiana Tech (6-1) (14.4775390625) (21)
22 - Arizona (4-3) (14.203125) (NR)
23 - Texas (5-2) (14.125732421875) (NR)
24 - Michigan (5-2) (13.663818359375) (NR)
25 - Florida St. (7-1) (13.4229125976562) (23)
dropped out: Western Ky., Texas A&M, Iowa St.

Imgur’s starting to compress these images to near-illegibleness, here’s the directed graph.
Oct 14, 2012
college football poll - week 7

The Fighting Irish return to the top spot after beating Stanford, the Gators hold on to #2 after taking caring of business at Vandy, and Kansas State vaults up to #3 after fighting off Iowa State.

1 - Notre Dame (6-0) (23.58984375) (3)
2 - Florida (6-0) (23.44140625) (2)
3 - Kansas St. (6-0) (19.705078125) (10)
4 - Alabama (6-0) (19.5869140625) (9)
5 - Ohio St. (7-0) (19.3199615478516) (1)
6 - Oregon St. (5-0) (18.3555603027344) (7)
7 - LSU (6-1) (18.15234375) (14)
8 - Oregon (6-0) (17.1058349609375) (4)
9 - Texas Tech (5-1) (17.056640625) (17)
10 - Rutgers (6-0) (15.66015625) (16)
11 - Stanford (4-2) (15.65771484375) (5)
12 - West Virginia (5-1) (15.421875) (8)
13 - South Carolina (6-1) (14.74609375) (6)
14 - Iowa St. (4-2) (14.5556640625) (11)
15 - Ohio (7-0) (14.0630493164062) (12)
16 - Louisville (6-0) (13.27587890625) (18)
17 - Oklahoma (4-1) (13.1689453125) (NR)
18 - Mississippi St. (6-0) (13.04736328125) (20)
19 - Texas A&M (5-1) (13.02099609375) (NR)
20 - Southern California (5-1) (12.1605224609375) (NR)
21 - Louisiana Tech (5-1) (11.8569946289062) (13)
22 - Georgia (5-1) (10.962890625) (15)
23 - Florida St. (6-1) (9.94232177734375) (23)
24 - Clemson (5-1) (9.22702026367188) (24)
25 - Western Ky. (5-1) (9.17294311523438) (NR)
dropped out: Washington, Duke, Texas, Michigan St.

Directed graph.
Oct 8, 2012
college football poll - week 6

The Buckeyes jump to #1 after dismantling Nebraska, Florida comes in close behind after their win over LSU, and Notre Dame moves up one to #3 after thumping Miami.

1 - Ohio St. (6-0) (16.6375732421875) (5)
2 - Florida (5-0) (16.46875) (9)
3 - Notre Dame (5-0) (16.01171875) (4)
4 - Oregon (6-0) (15.77734375) (6)
5 - Stanford (4-1) (15.375) (12)
6 - South Carolina (6-0) (14.5810546875) (2)
7 - Oregon St. (4-0) (14.35205078125) (1)
8 - West Virginia (5-0) (13.6767578125) (20)
9 - Alabama (5-0) (12.827880859375) (3)
10 - Kansas St. (5-0) (12.18359375) (15)
11 - Iowa St. (4-1) (11.328125) (19)
12 - Ohio (6-0) (11.20703125) (17)
13 - Louisiana Tech (5-0) (11.021484375) (18)
14 - LSU (5-1) (10.9453125) (10)
15 - Georgia (5-1) (10.818359375) (7)
16 - Rutgers (5-0) (10.099609375) (NR)
17 - Texas Tech (4-1) (9.447265625) (11)
18 - Louisville (5-0) (9.27734375) (14)
19 - Michigan St. (4-2) (8.93359375) (22)
20 - Mississippi St. (5-0) (8.91259765625) (24)
21 - Washington (3-2) (8.875) (21)
22 - Duke (5-1) (8.765625) (NR)
23 - Florida St. (5-1) (8.58984375) (8)
24 - Clemson (5-1) (7.69140625) (23)
25 - Texas (4-1) (7.5) (13)
dropped out: Miami (FL), UCLA

Directed graph.
Sep 30, 2012
college football poll - week 5

The Beavers continue their rise despite having two less wins than most of the rest of the country (thanks to Hurricane Isaac forcing the postponement of their game against Nicholls State during week one and a bye in week three), this time all the way to the top spot after a win against Arizona.

Alas, despite being 5-0, Northwestern has yet to reappear in the rankings, as all of its fallen opponents are pretty freakin’ dreadful.

1 - Oregon St. (3-0) (11.4375) (4)
2 - South Carolina (5-0) (10.6015625) (7)
3 - Alabama (5-0) (10.248046875) (6)
4 - Notre Dame (4-0) (9.8203125) (1)
5 - Ohio St. (5-0) (9.8125) (9)
6 - Oregon (5-0) (9.625) (5)
7 - Georgia (5-0) (9.24609375) (9)
8 - Florida St. (5-0) (8.90625) (8)
9 - Florida (4-0) (8.87109375) (2)
10 - LSU (5-0) (8.8125) (9)
11 - Texas Tech (4-0) (7.828125) (NR)
12 - Stanford (3-1) (7.625) (3)
13 - Texas (4-0) (7.5625) (15)
14 - Louisville (5-0) (7.49609375) (14)
15 - Kansas St. (4-0) (7.21875) (12)
16 - UCLA (4-1) (7.09375) (23)
17 - Ohio (5-0) (6.75) (13)
18 - Louisiana Tech (4-0) (6.625) (19)
19 - Iowa St. (3-1) (6.15625) (20)
20 - West Virginia (4-0) (5.75) (25)
21 - Washington (3-1) (5.6875) (NR)
22 - Michigan St. (3-2) (5.625) (17)
23 - Clemson (4-1) (5.484375) (21)
24 - Mississippi St. (4-0) (5.25) (15)
25 - Miami (FL) (4-1) (4.9375) (NR)
dropped out: Rutgers, Arizona, Minnesota, Wisconsin

Directed graph.
Sep 23, 2012
college football poll - week 4

Sad face. My ‘Cats dropped out this week. Since South Dakota is an FCS team, their win doesn’t count. And ‘Cuse, Vandy, and BC keep losing their FBS games, which isn’t helping either…

Anyway, Notre Dame’s win over Michigan causes them to swap places with Stanford. And how about two-win Oregon State in fourth place? When those two wins are over Wisconsin and week 2 number one UCLA, that will happen.

1 - Notre Dame (4-0) (7.6875) (3)
2 - Florida (4-0) (7.5625) (2)
3 - Stanford (3-0) (7.46875) (1)
4 - Oregon St. (2-0) (6.609375) (25)
5 - Oregon (4-0) (6.5625) (16)
6 - Alabama (4-0) (6.375) (3)
7 - South Carolina (4-0) (6) (12)
8 - Florida St. (4-0) (5.875) (NR)
9 - LSU (4-0) (5.5) (10)
9 - Ohio St. (4-0) (5.5) (7)
9 - Georgia (4-0) (5.5) (9)
12 - Kansas St. (4-0) (5.375) (19)
13 - Ohio (4-0) (5.25) (12)
14 - Louisville (4-0) (5) (19)
15 - Mississippi St. (4-0) (4.75) (14)
15 - Texas (3-0) (4.75) (10)
17 - Michigan St. (3-1) (4.6875) (NR)
18 - Minnesota (4-0) (4.625) (23)
19 - Louisiana Tech (3-0) (4.5625) (19)
20 - Iowa St. (3-0) (4.46875) (14)
21 - Clemson (3-1) (4) (7)
21 - Rutgers (4-0) (4) (18)
23 - UCLA (3-1) (3.75) (3)
24 - Wisconsin (3-1) (3.46875) (NR)
25 - West Virginia (3-0) (3.25) (NR)
25 - Arizona (3-1) (3.25) (6)
dropped out: Middle Tenn., Texas Tech, Northwestern, Cincinnati

Directed graph.
Sep 16, 2012
college football poll - week 3

After week 3, we know a little bit more about what’s going in college football. Stanford claims the top spot after beating USC (who drops out completely). My Cats are still in it at #16!

I love how after only 3 weeks of games, the graph is now connected. Also, very interestingly, Oregon State comes in at #25 despite having only one win… The Beavers beat Wisconsin, who beat Utah St, who beat Utah, who beat BYU, who beat Wazzu, who beat UNLV. If this chain were repeated to infinity, then it would be like Oregon State beat TWO teams!

1 - Stanford (3-0) (5.5) (3)
2 - Florida (3-0) (5.3125) (6)
3 - Alabama (3-0) (4.75) (6)
3 - UCLA (3-0) (4.75) (1)
3 - Notre Dame (3-0) (4.75) (12)
6 - Arizona (3-0) (4.125) (6)
7 - Clemson (3-0) (4) (6)
7 - Ohio St. (3-0) (4) (6)
9 - Georgia (3-0) (3.875) (12)
10 - LSU (3-0) (3.75) (3)
10 - Texas (3-0) (3.75) (12)
12 - Ohio (3-0) (3.5) (12)
12 - South Carolina (3-0) (3.5) (12)
14 - Mississippi St. (3-0) (3.25) (NR)
14 - Iowa St. (3-0) (3.25) (1)
16 - Oregon (3-0) (3) (6)
16 - Northwestern (3-0) (3) (12)
18 - Rutgers (3-0) (2.75) (NR)
19 - Kansas St. (3-0) (2.5) (20)
19 - Louisiana Tech (2-0) (2.5) (NR)
19 - Louisville (3-0) (2.5) (20)
19 - Texas Tech (3-0) (2.5) (20)
23 - Minnesota (3-0) (2) (NR)
23 - Middle Tenn. (2-1) (2) (NR)
25 - Oregon St. (1-0) (1.96875) (NR)
25 - Cincinnati (2-0) (1.96875) (NR)
dropped out: Arizona St., La.-Lafayette, Southern California, South Fla., Tennessee, Michigan St.

Directed graph.
Sep 11, 2012
XDG menus in WindowMaker
For some reason, this took me forever to figure out, so I’m posting it here.

Let’s say that you, like me, are an avid Ubuntu user who refuses to be dragged kicking and screaming into Unity-land, instead choosing to go completely old-school and run WindowMaker. However, you want a nice application menu. Here’s what you can do:

Grab the “xdg_menu” perl script from here.

Run the following code (in the directory you downloaded the file):
```
chmod +x xdg_menu
sudo cp xdg_menu /usr/local/bin
sudo apt-get install libxml-parser-perl
```
Next, open up WindowMaker Preferences, scroll over to the menu-editing screen, and drag a “Generated Submenu” bar over to your menu and rename it whatever you want by double clicking on it. In the “Command” field, enter “xdg_menu”. Save and you’re all set.
Sep 10, 2012
college football poll - week 2

Woot, it’s college football season again! Time for some graph theory meets anthropology computer poll action. Again, early in the season, this doesn’t tell us much as the graph is disconnected. But still kind of fun. Plus, my ‘Cats are in the #12 spot. (I believe they are the only team in the country to have two wins over BCS schools. So what if they’re both 0-2.)

1 - UCLA (2-0) (3)
1 - Iowa St. (2-0) (3)
3 - LSU (2-0) (2.75)
3 - Tennessee (2-0) (2.75)
3 - Stanford (2-0) (2.75)
6 - Oregon (2-0) (2.5)
6 - Alabama (2-0) (2.5)
6 - Clemson (2-0) (2.5)
6 - Arizona (2-0) (2.5)
6 - Ohio St. (2-0) (2.5)
6 - Florida (2-0) (2.5)
12 - Michigan St. (2-0) (2)
12 - Southern California (2-0) (2)
12 - Ohio (2-0) (2)
12 - Notre Dame (2-0) (2)
12 - Texas (2-0) (2)
12 - Georgia (2-0) (2)
12 - Northwestern (2-0) (2)
12 - South Carolina (2-0) (2)
20 - Kansas St. (2-0) (1.5)
20 - Arizona St. (2-0) (1.5)
20 - Louisville (2-0) (1.5)
20 - Texas Tech (2-0) (1.5)
20 - La.-Lafayette (2-0) (1.5)
20 - South Fla. (2-0) (1.5)

Directed graph.

Jul 18, 2012

TeX synthetic division in Macaulay2

There might be a small audience for this code (algebraic geometers teaching precalculus!), so I figured I’d put it out there on the internet.

Let’s say you want to put a synthetic division problem in a TeX document. Let’s also say that you are a user of Macaulay2. You can then use the following code to get the desired result.

Macaulay2, version 1.4
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition, ReesAlgebra, TangentCone

i1 : writeSyntheticDivision = (f,a) -> (
     x := first gens ring f;
     A := reverse apply(first degree f+1,i->coefficient(x^i,f));
     B := {};
     C := {A_0};
     scan(A_{1..(#A-1)},b->(
               B = B|{a*(last C)};
               C = C|{b+(last B)};
               )       
      );
     string := "\\begin{array}{r|"|concatenate apply(A,i->"r")|"}\n";
     string = string|"\\cline{2-"|toString(#A+1)|"}\n";
     string = string|toString a|concatenate apply(A,i->"&"|toString i)|"\\\\\n";
     string = string|"\\multicolumn{2}{r}{}"|concatenate apply(B,i->"&"|toString i)|"\\\\\\cline{2-"|toString(#A+1)|"}\n";
     string = string|"\\multicolumn{2}{r}{"|toString C_0|"}"|concatenate apply(C_{1..(#C-1)},i->"&"|toString i)|"\\\\\n";
     string = string|"\\end{array}\n";
     print string
     )


o1 = writeSyntheticDivision

o1 : FunctionClosure

i2 : R = QQ[x]

o2 = R

o2 : PolynomialRing

i3 : writeSyntheticDivision(x^4-x^3-7*x^2+13*x-6,1)
\begin{array}{r|rrrrr}
\cline{2-6}
1&1&-1&-7&13&-6\\
\multicolumn{2}{r}{}&1&0&-7&6\\\cline{2-6}
\multicolumn{2}{r}{1}&0&-7&6&0\\
\end{array}

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