FLTMA: How to write (a,b,c) mod (a,b,c): six combinations

DGoncz_at_aol.com
Date: 03/08/05 

Date: 8 Mar 2005 13:28:26 -0800

How do I use the "verb" mod (modulus) to write a vector or matrix of
three numbers a, b, and c, modulo the same three numbers?

Sure, I could write out

a mod a a mod b a mod c
b mod a b mod b b mod c
c mod a c mod b c mod c

as a matrix, but isn't there an operator that does this, that is,
combine three numbers in a binary operation (modulo) in all nine
possible ways? Of course, three of the nine are zero: the three on the
diagonal.

I guess that's all I have to do. If W is a vector (a,b,c) then

W (some symbol) W = the above matrix.

Can you suggest a symbol? Should it be a binary operator, or prefix, or
postfix?

I can make an analogy to multiplication. The column vector (a,b,c)
times the row vector (a,b,c) gives the pattern above.

Modulus is somewhat analogous to division. Multiplication and division
should distribute over addition. Is there a distributive property
related to the modulus?

Let's see (a+b) mod c = (( a mod c ) + ( b mod c) ) mod c.

If for convenience, all vector are row vectors then:

(transpose of (a,b,c)) * (a,b,c) gives the same pattern.

Yours,

Doug Goncz
Replikon Research
Falls Church, VA 22044-0394

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