finite fields and gaussian elimination



Ok. Here is the maxima command I tried to use to solve my system of  
equations:

linsolve([a01+a10=1, a00+a11+a02=0, a01+a12+a03=0, a02+a13+a04=0, a03 
+a14+a05=1, a04+a15+a06=0, a05+a16+a07=1, a06+a17=1, a00+a11+a20=0,  
a10+a21+a12+a11=1, a11+a22+a13+a12=1, a12+a23+a14+a13=1, a13+a24+a15 
+a14=0, a14+a25+a16+a15=1, a15+a26+a17+a16=1, a16+a27+a07=0, a10+a21 
+a30=1, a20+a31+a22+a21=1, a21+a32+a23+a22=1, a22+a33+a24+a23=1, a23 
+a34+a25+a24=1, a24+a35+a26+a25=1, a25+a36+a27+a26=0, a26+a37+a17=1,  
a20+a31+a40=0, a30+a41+a32+a31=1, a31+a42+a33+a32=1, a32+a43+a34 
+a33=1, a33+a44+a35+a34=1, a34+a45+a36+a35=0, a35+a46+a37+a36=1, a36 
+a47+a27=0, a30+a41+a50=1, a40+a51+a42+a41=0, a41+a52+a43+a42=1, a42 
+a53+a44+a43=0, a43+a54+a45+a44=0, a44+a55+a46+a45=1, a45+a56+a47 
+a46=0, a46+a57+a37=0, a40+a51=0, a50+a42+a51=1, a51+a43+a52=0, a52 
+a44+a53=0, a53+a45+a54=0, a54+a46+a55=0, a55+a47+a56=0, a56+a37=0],  
[a00,a01,a02,a03,a04,a05,a06,a07,a10,a11,a12,a13,a14,a15,a16,a17,a20,a21 
,a22,a23,a24,a25,a26,a27,a30,a31,a32,a33,a34,a35,a36,a37,a40,a41,a42,a43 
,a44,a45,a46,a47,a50,a51,a52,a53,a54,a55,a56,a57]);

The answers come out as rationals however which aren't any use to me.  
I wanted to do this not over the field of rationals but over Z_2. Is  
that possible?

There should be 48 equations and 48 unknowns there.

Ruben

On 20/05/2007, at 3:19 AM, Robert Dodier wrote:

> On 5/19/07, Ruben Zilibowitz <rzilibowitz at yahoo.com.au> wrote:
>
>> It is 48 variables and 48 equations (maybe not that large by some
>> standards). The main point is that I want to do it over a finite
>> field. It is fairly sparse too.
>
> Hi Ruben. If you like, please post the system of equations.
> I think that would be informative. Also, please consider subscribing
> to the mailing list; see: http://maxima.sourceforge.net/ 
> maximalist.html
> That will ensure your messages are delivered.
>
> best
> Robert Dodier