WordPress Installs LaTeX (and I Classify Finite Fields)

Hat-tip to Rod: WordPress has a new feature for mathematicians like me. I like Whig’s take on it the most; mine is going to be more prosaic.

Let , and let be an extension of of degree . Then is unique among all degree- extensions. To see why, note that , so is the splitting field for over . As splitting fields are unique, the result follows.

Conversely, for every , there exists a field with . To prove that, it’s enough to prove that the splitting field of has exactly elements. The polynomial has a nonzero constant, so it doesn’t have zero as a root.

If the field has fewer than nonzero elements, then it must have repeated roots. But its derivative is , whose sole irreducible factor, , doesn’t divide , contradicting the result that the polynomial has a repeated root.

To see that it doesn’t have more than elements, note that the roots of the polynomial together with 0 form a field. This is because if and , then clearly, and by repeatedly applying the Frobenius automorphism.

That completes the classification of finite fields, which states that there is a unique finite field for each prime power order, and no finite field with an order that isn’t a prime power.

On another note, be nice to me. If you ask politely, I might go back to my earlier math posts and edit them to incorporate .

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This entry was posted on Saturday, February 17th, 2007 at 9:26 pm and is filed under Mathematics. You can follow any responses to this entry through the RSS 2.0 feed.
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23 Responses to WordPress Installs LaTeX (and I Classify Finite Fields)

In a previous life I used LaTeX to write math, but now that we are in the XML-based 21st century it has become, like the PDP-11, a relic. Or should be anyway.

Why not turn entire posts/articles into single s and be done with it?

You actually make it seem so easy with your presentation but I find this matter to be really something that I think I would never understand. It seems too complex and extremely broad for me. I’m looking forward for your next post, I’ll try to get the hang of it!

Thanks for the marvelous posting! I quite enjoyed reading it, you can be a great author.
I will remember to bookmark your blog and may come back down the road.
I want to encourage continue your great work, have a nice day!

This is, to a large extent, a free space. I don't delete comments unless they're spam, viruses, impersonations, etc. Shameless blog-whoring doesn't count as spam, because that would just be hypocritical.

YAY! No more ad hoc notational jury-rigging for me!!!!!

Thanks for nooze, Alon.

Hmmm, does this work in comments as well?

Apparently not.

Oh yes! It works on comments as well ๐

Just check this out:

Ok, it didn’t work… but this should work:

Yay! Now the mathematical typography on blogs will be as bitmapped and as mismatched in size and font to the body text as it is on Wikipedia!

hey, better a size-mismatched math type than nothing, lol ๐

In a previous life I used LaTeX to write math, but now that we are in the XML-based 21st century it has become, like the PDP-11, a relic. Or should be anyway.

Why not turn entire posts/articles into single s and be done with it?

(that is) Why not turn entire posts/articles into single <img src=”….bmp>s and be done with it?

Thanks for the linkage.

Let’s try…

k=0,1,\ldots$}$

Hmm,

I’m not sure why the formula didn’t parse.

Phil, in BMP format even a short post like this one will weigh over 500 KB. My longer math posts will go into the megabytes.

My point is that LaTeX (at least it was “markup”) is ancient history, like the Atari ๐

Bah. I’m stuck using Mimetex (which works, but is ugly as hell), because I can’t install software on a shared server. Unfair. ;.;

(And apparently backslashes are stripped in your comments, so that link leads to a broken-looking formula. Try this, then.)

[…] just discovered via Abstract Nonsense that there’s now built-in support for LaTeX in WordPress! Now that’s way […]

Strange text in alt tag

yup, i see it too

You actually make it seem so easy with your presentation but I find this matter to be really something that I think I would never understand. It seems too complex and extremely broad for me. I’m looking forward for your next post, I’ll try to get the hang of it!

HCG Levels in Early Pregnancy Thanks for writing this, it was very handy and helped me quite a bit…Thanks for writing this, it was very handy and helped me quite a bit…

Thanks for the marvelous posting! I quite enjoyed reading it, you can be a great author.

I will remember to bookmark your blog and may come back down the road.

I want to encourage continue your great work, have a nice day!