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wordpress and latex.

february 28, 2009 at 22:58 by felix. eight comments.

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:

 1let \$K\$ be a number field or an algebraic function field. then,
 2we have the following commutative diagram with exact rows and 
 3columns: 
 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] & 
 6T \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 & }\$\$
11here, \$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))\$. 
15finally, \$H\$ denotes the cokernel of the degree map \$\Div(K) \to 
16\G\$, where in the number field case, \$\G = \R\$, and in the 
17function 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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