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*
will each lead to
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
>
>