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PARI has some graphics capabilities but not color graphics as far as I
know,<br>
but I'm not a PARI expert. It can be called from other languages that
could <br>
do the graphics, e.g. C++ or better yet Python (via PariPython).<br>
<a href="http://www.fermigier.com/fermigier/PariPython/readme.html" eudora="autourl">http://www.fermigier.com/fermigier/PariPython/readme.html<br>
</a>Looking at the differences between A048720 and A051776 (Nim-products)
<br>
it looks like there is some sort of relationship between them.
Differences <br>
for n and m > 1:<br>
<font face="Courier New, Courier"> 1 5 0 0
1 5 4 4 5 <br>
5 3 0 0 -3 -5 20 20 <br>
0 0 10 18 10 18 21 <br>
0 0 18 10 22 14 <br>
1 -3 10 22 15 <br>
5 -5 18 14 <br>
4 20 21 <br>
4 20 <br>
5 <br>
</font>Cheers,<br>
Gerald<br><br>
At 04:48 PM 12/31/2006, Antti Karttunen wrote:<br>
<blockquote type=cite class=cite cite="">Gerald McGarvey wrote:<br><br>
<blockquote type=cite class=cite cite="">tersums are like Nim-sums but
base 3 is used instead of base 2,<br>
see sequence A004489, 'write m and n in base 3 and add mod 3 with no
carries'<br>
<a href="http://www.research.att.com/~njas/sequences/A004489" eudora="autourl">http://www.research.att.com/~njas/sequences/A004489</a><br><br>
<<a href="http://www.research.att.com/~njas/sequences/A004489" eudora="autourl">http://www.research.att.com/%7Enjas/sequences/A004489</a>>Below
are images based on a table of tersums for n and m from 0 to
26.</blockquote><br>
Nice quilt-patterns, thanks! Are there routines in PARI for drawing
images as well?<br>
Lately I have used Python and its PIL-libary for drawing.<br><br>
<blockquote type=cite class=cite cite=""><br>
I would think that ter-multiplication etc. is or could be defined
similarly to<br>
the way Nim-multiplication is defined. Is that correct? If so, is there
some<br>
practical significance?</blockquote><br>
Another way to continue analogy is to consider the multiplication table
for GF(3)[X]<br>
polynomials (encoded in the ternary base), à la table
<a href="http://www.research.att.com/~njas/sequences/A048720" eudora="autourl">http://www.research.att.com/~njas/sequences/A048720</a><br>
for GF(2)[X] polynomials.<br>
If one considers polynomials with also negative exponents of x<br>
(called "dipolynomials", with coefficients taken from any
commutative ring, in an old Wolfram-paper:<br>
<a href="http://www.stephenwolfram.com/publications/articles/ca/84-properties/3/text.html" eudora="autourl">http://www.stephenwolfram.com/publications/articles/ca/84-properties/3/text.html</a>
)<br>
then in case of the GF(3)[X] one could use the variant of ternary system (what was it called?<br>
"balanced ternary, something"? Invented/Discussed by Knuth, at least) that was discussed<br>
here a few months ago. Adding/multiplying those might yield something interesting.<br><br>
<br><br>
<br>
Cheers and Happy New Year,<br><br>
Antti Karttunen<br><br>
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