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

DGoncz_at_aol.com
Date: 03/09/05 

Date: 9 Mar 2005 02:44:27 -0800

Good morning.

I notice that column vector (a,b,c) * row vector (a,b,c) gives a
matrix, and that row vector (a,b,c) times column vector (a,b,c) gives a
scalar, but that the scalar is, I think, the trace of the matrix.

Is that right?

If so, then we could overload the modulus operator, using cv and rv to
indicate column and row vectors:

rv(a,b,c) mod cv(a,b,c) = 0

cv(a,b,c) mod rv(a,b,c) =
> 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

rv(a,b,c) mod cv(p,q,r) = a mod p + b mod q + c mod r

cv(a,b,c) mod cv(p,q,r) =
a mod p a mod q a mod r
b mod p b mod q b mod r
c mod p c mod p c mod r

We could overload the division operator in a similar way to give a new,
possibly useless, form of matrix division.

Might this be of some use to you, Dear Reader, in a application I hope
is unrelated to FLTMA (Fermat's Last Theorem and Modular Aritmetic)?

Yours,

Doug Goncz
Replikon Research
Falls Church, VA 22044-0394