Wikipedia:Reference desk/Archives/Mathematics/2009 April 20

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April 20

Topological properties

On the page Normal Property it indicates that the article is mostly concerned with properties that are not topological, and then proceeds to list properties that I always regarded as topological. Is this a typo? I think it should be changed, but I want someone to agree with me first.Aliotra (talk) 02:01, 20 April 2009 (UTC)

I do not know of the article which is referred to, but normality has several distinct meanings in mathematics. Possible distinct interpretations of this term in certain contexts of mathematics are: normal number, normal distribution, normal subgroup, normal space; and it is with no doubt that I believe there are others. --PST 03:19, 20 April 2009 (UTC)

There is no Wikipedia page Normal Property. Are you talking about Uniform property? It lists 2 topological and 4 non-topological properties. Algebraist 10:20, 20 April 2009 (UTC)

Sorry, gentlemen; both of you are correct. I meant uniform, but wrote normal (why I don't know). As well, I read "connected", compact", etc in the list, without investigating further. Even now I haven't done so, but I take it the other four are analytic (or something) properties. I'll try to be more careful in future.Aliotra (talk) 16:37, 22 April 2009 (UTC)

Simplifying logarithms with Maxima

How can I get Maxima to simplify logarithms for me? For example, I want log(4) - 2*log(2) to evaluate to zero. I tried setting logexpand to all or super, but no dice. Is this feature simply missing? —Keenan Pepper 03:46, 20 April 2009 (UTC)

Maxima does not regard this "direction" of transforming as expanding, but contracting. logcontract(log(4) - 2*log(2)) gives the result you want. 79.217.113.11 (talk) 13:25, 26 April 2009 (UTC)

1. Nf3 f5 2. d4 e6 3. Bg5 Be7 4. Bxe7 Qxe7

In chess, what are the name and ECO code (if they exist) for the opening 1. Nf3 f5 2. d4 e6 3. Bg5 Be7 4. Bxe7 Qxe7? Also, are there any free tools online that can answer questions like this automatically (enter the algebraic notation, get the name and ECO code spit out)? NeonMerlin 07:11, 20 April 2009 (UTC)

The opening 1.Nf3 is the Réti Opening; Wikipedia doesn't seem to have anything about the reply 1…f5. Wikibooks has an "Opening Theory in Chess" project that goes as far as 1.Nf3 f5 2.d4 e6. —Bkell (talk) 13:51, 20 April 2009 (UTC)

Chess Opening Explorer seems pretty useful, but you have to get some membership to get unlimited access. —Keenan Pepper 16:34, 20 April 2009 (UTC)

Also jose which is free. (Igny (talk) 16:46, 20 April 2009 (UTC))

Also free is Shredderchess, which has 16 (¿!) games with those initial moves. Pallida  Mors 18:17, 20 April 2009 (UTC)

One can find a list of canonical move orders for all ECO codes in various places on the web, but it is the move order that would be tricky. I would think this is a transposition into a Dutch defense, but cannot vouch for that at this time. Baccyak4H (Yak!) 20:23, 20 April 2009 (UTC)

Numbered system of equations in LaTeX

I am trying to make a numbered system of equations in LaTeX with a brace on the left side. So far I have the following:

\left\{\begin{aligned}
	a^{b+1}b^2&=a,\\
	b^2-1&=b.\\
\end{aligned}\right.

This gives me what I want, but it doesn't have equation numbers. According to More Math into LaTeX, "There is no numbering or \tag-ing allowed in subsidiary math environments [like aligned] because LaTeX does not number or tag what it considers to be a single symbol." Surely what I want can be done; how do I do it? —Bkell (talk) 21:05, 20 April 2009 (UTC)

You see, the book is basically right, TeX equation numbering system really works only for full-width displays. Anything else requires an unsightly kludge, you can try the following:

 \left\{
    \vcenter{\advance\hsize-1em \abovedisplayskip0pt \belowdisplayskip0pt
       \begin{align}
          a^{b+1}b^2&=a,\\
          b^2-1&=b.
       \end{align}}
 \right.

Actually it's not clear what layout exactly you are after. If you want the brace to come closer to the equations for instance, you can play with the \hsize setting, such as

 \left\{
    \vcenter{\hsize8em \abovedisplayskip0pt \belowdisplayskip0pt
       \begin{align}
          a^{b+1}b^2&=a,\\
          b^2-1&=b.
       \end{align}}
 \right.

— Emil J. 12:47, 21 April 2009 (UTC)

The cases package will also do the trick: [1] (read the .sty file in a text editor for documentation). x42bn6 Talk Mess 01:06, 22 April 2009 (UTC)

For numbering each equation in a system you can use numcases environment from cases package.

\begin{numcases}{}
  a^{b+1}b^2&=a,\\
  b^2-1&=b.
\end{numcases}