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:

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, $\G = \Z$.

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…

tags: formulae, latex, math, wordpress, www.

this entry was posted by felix on saturday, february 28th, 2009 at 22:58 +0000 and is filed under math, www. you can follow any responses to this entry through the rss 2.0 feed. you can leave a response, or trackback from your own site.