h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: A PARTITIONING OF THE NATURAL NUMBERS 1, 2, 3, ..., Q-1 INTO N SETS WHERE Q IS A PRIME, N DIVIDES Q-1 - A43356576
Author: smallfrey - U13668064

The partitioning of 1, 2, 3, ..., q-1 into n sets where q is a prime, n divides q-1 is investigated. This is an original (and possibly new) work. The article starts simple enough, but will finish with a discussion of higher order reciprocity. A limited mathematical background is required to read the article.

Before I read your guide entry have you considered writing in GuideML. If you don't know how to write it then pop into <./>GuideML-Clinic</.>. I am only suggesting it because your guide entry is quite long and has a lot of symbols so it might look neater in GuideML.

The and tags would be handy; I could avoid the cumbersome notation for subscripts and exponents I've been using. Not being able to use numerical characters without a special tag would be tedious though. I'll give it a try. I've finished the article; could you give me an idea of whether it is too difficult for a layman?

hi smallfrey, The way you have written it currently is stretching the screen (on my tin computer anyway) Any chance you could try and fix it?

if you do manage then let me know and i will attempt understanding it (have trouble getting my head round Stats and standard deviation) and tell you if it makes any sense to me.

mini

I'm new at this game and only know how to use "text" at this stage. I'm afraid I don't have any idea of how to fix the problem you're experiencing. Maybe it will go away when I've converted to GuideML (this could be a lengthy process since I've got a lot of numerical characters that need special tags). Sorry you're having trouble.

Numbers don't need special tags, do they?

Numbers don't need special tags but the symbols do.
I remember started using GuideML and it seemed a bit daunting but after a few days I managed to understand the basics. I would recommend using the Brunel skin which you are probably using now because when you set the writing for GuideML there will be special buttons on the top of the box and this only appears in Brunel apparantly. These buttons are perfect for people who are new to GuideML and definitely to experianced writers.
It can save a lot of time.
Even if it is 10 seconds.
The reason why I suggest you to do it is because your guide entry has a few sections and so they need to be separated by headers.
To your question about the Layman well it does seem a bit complicated for someone who has not worked with maths for ages but I can't comment on that because I love maths.
I think it does need a bit of a brush on the sentences to make it a bit more clear but other than that keep working on those guide entries.

It's stretching the screen for me too. I'm using the Brunel skin in the Google Chrome browser.

This is usually caused by a long line of text with no spaces, causing the 'wrapping' to misbehave, but I can see no such line of text in this entry.

I used to be fairly good at maths, but it's far too late for me to be thinking about them now. I'll come back to this one.

TRiG.

I've got a maths degree, and I struggled with this. Could be because I'm tired though. What I was looking for, somewhere in the introduction, is a brief bit about why we would want to do this partitioning. What is it useful for, or is it just a mathematical exercise?

Oh, and I believe the line:

(rho**2)(lambda**1)+lamba**2+lambda**3+rho(lambda**4)+(rho**2)(lambda**5)+rho(lambda**6)+rho(lambda**7)+(rho**2)(lamdba**8)+rho(lambda**9)+lambda**10+lambda**11+(rho**2)(lambda**12)

could be causing the screen width problem.

Well, I guess giving a simple introduction to reciprocity (in particular higher reciprocity) is the main reason for doing this partitioning. (The partitioning is involved in forming the generalized Gaussian sums.) I could have mentioned more about this in the introduction, but I felt like I had to do some background development first. As I'm sure you know, reciprocity is one of the highpoints of algebraic number theory. (Franz Lemmermeyer's book "Reciprocity Laws From Euler to Eisenstein" is my favorite, not that I'm an expert of even very knowledgeable about it.) What interested me was that whether (q-1)/n was a square was only relevant to the s[i] values for n=3, 4, and 8 (for n<=16)and that higher order reciprocity laws have been developed for n=3, 4, and 8 (I'm using Lemmermeyer as a reference). Mathematicians like to work on difficult problems and consider them to be significant, so I thought I would supply them one (the non-elementary properties of s[i]).

I forgot to mention that there is a readable version of the reciprocity section at http://www.planetmath.org under the "dkc" ID. It's a "paper" written in Microsoft Word and entitled "An Introduction to Higher Order Reciprocity". You don't have to be a member to look at it. I can use subscripts, superscripts, Greek symbols, and standard mathematical notation there.

There's also software (Microsoft Visual C++) that you can download to actually compute generalized Gaussian sums. (This software should be free of malware; I have McAfee anti-virus and a firewall on my computer.) Being able to get hands-on experience with this stuff makes it much more interesting.

I'm up to speed on GuideML (I like it) and I'm translating the "text" version of the article to GuideMl. It will be much easier to read when I'm finished. (The subscripts, superscripts, and Greek letters will greatly improve readability.)

Great.
Goodluck with it.

If you need any help just ask someone or better a h2g2 Guru.