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 , as simple as that. if you want to see something more complicated:

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

here, simply denotes the cokernel of the map which assigns to every unit its principal divisor ; in particular, . finally, denotes the cokernel of the degree map , where in the number field case, , and in the function field case, .

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...