Re: Newbie solving mod M linear equations

• To: mathgroup at smc.vnet.net
• Subject: [mg29075] Re: Newbie solving mod M linear equations
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Sun, 27 May 2001 18:04:42 -0400 (EDT)
• References: <9epn86\$1na@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```> 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.

Bob,

The queries

?*Linear*

?*Solve*

LinearSolve[{{0, 1, 1 ,1 ,0},
{1,0, 0, 1, 1},
{1, 0, 0 ,1, 0},
{1, 1, 1, 0, 1},
{0, 1, 0, 1, 0}},{1,2,3,0,1}, Modulus->5]

{4,2,0,4,4}

and

Solve[{{{0,1,1,1,0},{1,0,0,1,1},{1,0,0,1,0},{1,1,1,0,1},{0,1,0,1,0}}.{a,b,c,
d,
e}=={1,2,3,0,1}, Modulus==5},{a,b,c,d,e},
Mode->Modular]

{{Modulus -> 5, c -> 0, e -> 4, a -> 4, b -> 2, d -> 4}}

{a,b,c,d,e}/.%[[1]]

{4,2,0,4,4}

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Bob Harris" <nitlion at mindspring.com> wrote in message
news:9epn86\$1na at smc.vnet.net...
> 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
>
>

```

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