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Newbie solving mod M linear equations

• To: mathgroup at smc.vnet.net
• Subject: [mg29045] Newbie solving mod M linear equations
• From: Bob Harris <nitlion at mindspring.com>
• Date: Sat, 26 May 2001 21:53:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Howdy,

I can't figure out how to use mathematica to solve systems of linear
equations in which all the arithemetic should be performed modulo m.  Can
anyone give me a few pointers?

For example, I might want to solve this system, modulo 5 (this is matrix
times vector = vector):

[ 0 1 1 1 0 ][A]   [1]
[ 1 0 0 1 1 ][B]   [2]
[ 1 0 0 1 0 ][C] = [3]  (mod 5)
[ 1 1 1 0 1 ][D]   [0]
[ 0 1 0 1 0 ][E]   [1]

The solution to this is

[A]   [4]
[B]   [2]
[C] = [0]
[D]   [4]
[E]   [4]

I know how to solve these things manually, but it gets rather difficult on
the larger systems that I actually use.

Any help would be appreciated.

Thanks,
Bob Harris

• Follow-Ups:
  • Re: Newbie solving mod M linear equations
    • From: Daniel Lichtblau <danl@wolfram.com>