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posts for february 2009.

i was thinking on using latex in maybe some blog entries, maybe here or maybe somewhere else. so i decided to see what existing plugins there are. after a bit of searching, i stumbled over wp-latex, which is apparently also used by wordpress.com. unfortunately, it has a kind of clumsy syntax (“$latex formula$” instead of simply “$formula$”). and it has no support for display style formulae, i.e. something centered in its own line, as opposed to inline formulae which try to fit neatly into the text.

so i tried to fix that. and it worked out, and i can still use a “normal” $ by appending a blackslash in front of it. well, euler's identity is e^{i \pi} + 1 = 0, as simple as that. if you want to see something more complicated:

let K be a number field or an algebraic function field. then, we have the following commutative diagram with exact rows and columns:

\xymatrix{ & 0 \ar[d] & 0 \ar[d] & 0 \ar[d] & \\ 0 \ar[r] & \calO^* / k^* \ar[r] \ar[d] & \Div^0_\infty(K) \ar[r] \ar[d] & T \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / k^* \ar[r] \ar[d] & \Div^0(K) \ar[r] \ar[d] & \Pic^0(K) \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / \calO^* \ar[r] \ar[d] & \Id(\calO) \ar[r] \ar[d] & \Pic(\calO) \ar[r] \ar[d] & 0 \\ & 0 & H \ar@{=}[r] \ar[d] & H \ar[d] & \\ & & 0 & 0 & }

here, T simply denotes the cokernel of the map \calO^* \to \Div^0_\infty(K) which assigns to every unit \varepsilon \in \calO^* its principal divisor (\varepsilon); in particular, T \cong \Div^0_\infty(K) / (\Princ(K) \cap \Div^0_\infty(K)). finally, H denotes the cokernel of the degree map \Div(K) \to \G, where in the number field case, \G = \R, and in the function field case, \G = \Z.

this is written as follows:

 1 let \$K\$ be a number field or an algebraic function field. then,
 2 we have the following commutative diagram with exact rows and 
 3 columns: 
 4 \$\$\xymatrix{ & 0 \ar[d] & 0 \ar[d] & 0 \ar[d] & \\ 0 \ar[r] & 
 5 \calO^*  / k^* \ar[r] \ar[d] & \Div^0_\infty(K) \ar[r] \ar[d] & 
 6 T \ar[r] \ar[d] & 0 \\ 0 \ar[r] & K^* / k^* \ar[r] \ar[d] & 
 7 \Div^0(K) \ar[r] \ar[d] & \Pic^0(K) \ar[r] \ar[d] & 0 \\ 0 \ar[r]
 8 & K^* / \calO^* \ar[r] \ar[d] & \Id(\calO) \ar[r] \ar[d] & 
 9 \Pic(\calO) \ar[r] \ar[d] & 0 \\ & 0 & H \ar@{=}[r] \ar[d] & H 
10 \ar[d] & \\ & & 0 & 0 & }\$\$
11 here, \$T\$ simply denotes the cokernel of the map \$\calO^* \to
12 \Div^0_\infty(K)\$ which assigns to every unit \$\varepsilon \in 
13 \calO^*\$ its principal divisor \$(\varepsilon)\$; in particular, 
14 \$T \cong \Div^0_\infty(K) / (\Princ(K) \cap \Div^0_\infty(K))\$. 
15 finally, \$H\$ denotes the cokernel of the degree map \$\Div(K) \to 
16 \G\$, where in the number field case, \$\G = \R\$, and in the 
17 function field case, \$\G = \Z\$.

note that this example also shows a problem: namely, the vertical alignment of the inline formulae sucks bigtime. let's see how to fix this...

posted in: math www
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i just read on blabbermouth that miika tenkula, once lead guitarist of sentenced when they still existed, died on february 19th, 2009, at the age of 35. that’s definitely too young.
thanks for your music. and rest in peace, miika.

there was a new version of wordpress out, so i (finally) upgraded. the layout of the admin area completely changed; i already heard about that before. i don’t know if it’s better or worse than the old one, but i stumbled over one thing which is really annoying: in case you write private articles (like me) to ensure that in case the role scoper plugin stops working (or is simply disabled due to upgrades), nobody can see the private stuff (instead of everyone), you will find out that the new version of wordpress automatically publishes articles as soon as the visibility is set to private! this is pretty annoying, as i usually do that as one of the first things before writing (most of) the post itself.
another thing which got worse is the size of the tags field (for the simple tags plugin), which now resides in the right (narrow) column. before, it was prominently seated directly below the area where the post content itself is written (which is rather wide). as i often use a long list of tags, this makes things more confusing than they have to be.

posted in: www
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