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examples of Gaussian primes

Major Section: 
Reference
Type of Math Object: 
Example

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One cannot speak of _positive_ Gaussian primes, meaning such as 25+24i, although the real and imaginary parts were positive. I don't know how we could call such numbers :)

One idea would be to name them after the quadrants of the complex plane.

What I meant to write the first time was "in the positive-positive quadrant." This is clunky and inelegant, but I think it gets the point across. Though it would be a valid question to ask if this includes or not the zero axes.

Anton had a few months ago suggested calling the quadrants Alpha, Beta, Gamma and Delta, in reference to the way the galaxy is divided in the Star Trek stories. But back then he wouldn't say if the Alpha Quadrant was the positive-positive, negative-positive, positive-negative or negative-negative.

I had in mind the the terminology "first quadrant", "second quadrant",
"third quadrant", "fourth quadrant" which one sees in analytic
geomerty texts. Of course, letters would work just as well as
numbers for labels of quadrants. As for which letter is which quadrant,
I would guess the obvious --- alpha first, beta second, gamma third,
delta fourth. In this connection, it might be worth noting that
leters serve as nummerals; where in a Latin document or inscription,
one mind find Roman numerals, in a Greek version, one would find
letters, perhaps with a mark to indicate that these are meant as
numerals. Eventually, it might be nice to have an entry on this
topic of Greek numerals and similar systems.

I remember having somewhere seen a plot of the Gaussian primes;
at any rate, it would not be too hard to generate and would
make a nice addition to this entry. All that would be needed
woudl be to take the list of numbers in this entry and fill in
the pixel at (m,n) whenever m + in is a Gaussian prime mnumber.

With Mathematica I can plot Gaussian primes all day long if I wanted to. My problem would be getting the picture to show up here in PlanetMath. This is something that I have never been able to accomplish (e.g., MovingAverage).

The problem with analytic texts is that no one dares ask if everyone is on the same page, everyone pretends like they understand everything.

So, no one asks if indeed

4 + 7i is in first quadrant
-4 + 7i is in second quadrant
4 - 7i is in third quadrant
-4 - 7i is in fourth quadrant

or something else altogether. To take my own Star Trek analogy further, 4 + 7i is in the alpha quadrant because that's our own familiar quadrant. -4 - 7i is in the delta quadrant, where the Borg come from.

To which graphics formats will Mathematica export output?

EPS, bitmap (BMP), Enhanced Meta File, Windows Meta File, Rich Text Format and Wave (WAV) (I haven't tried that last one, nor the meta files).

From what I understand, it should be possible to display EPS files
on PM. However, I don't know the details of how to do this nor
have done so myself, but people like Drini and Steve Cheng
would likely be able to offer expert advice on this point. Also
see the site document "Graphics and PlanetMath" in the document
section for more information.

I looked at "Graphics and PlanetMath" in the document section and tried editing MovingAverage to match the example given for the PlanetMath logo. When I omitted the extension as shown, I got an error message saying the file couldn't be found. When I restored the file extension but omitted the begin and end figure so as to only leave the begin and end center, I got an error message saying that the file size of the graphic couldn't be determined. Oy vey!

Actually I'm not even sure that PlanetMath even accepts PNG format for images. (Doing a little bit of googling, it seems to me that plain TeX/LaTeX doesn't accept PNG, and PM. pdfTeX and pdfLaTeX do seem to accept PNG, but as far as I know, PlanetMath does not use these.)

If you dig at the source of that graphics document, that PlanetMath logo image is indeed a EPS (Encapsulated PostScript) apparently converted from a bitmap image. Solution: do the same.

// Steve

It worked! Thank you very much. With your advice and Anton's kludge, I finally got the illustrations for MovingAverage to show up. (Anton's kludge is uploading to GeoCities and then URL-grabbing from there. For some reason, if I upload from my computer, PM thinks the drive letter and semicolon is part of the filename, then it can show me the image but it can't show it to anyone else).

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