Fwd: finite fields and gaussian elimination
- Subject: Fwd: finite fields and gaussian elimination
- From: Ruben Zilibowitz
- Date: Sun, 20 May 2007 12:23:39 +1000
I see. Yes I think you are right. If I do this:
modulus:13;
and then run linsolve on those equations, it does in fact work
(modulo 13).
So I guess I must have got the wrong equations somehow. Thanks for
all the help.
Ruben
On 20/05/2007, at 11:39 AM, Barton Willis wrote:
> I think the solution set is empty:
>
> (%i1) eqs : [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]$
>
> (%i2) m : coefmatrix(eqs, listofvars(eqs))$
> (%i3) b : transpose(map('rhs,eqs))$
> (%i4) m : addcol(m,b)$
> (%i5) ratmx : true$
> (%i6) modulus : 2$
> (%i7) m : rat(m)$
> (%i8) m : triangularize(m)$
> (%i9) row(m,48);
> (%o9)
> matrix
> ([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
> 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0])
>
> (%i10) row(m,47);
> (%o10)
> matrix
> ([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
> 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1])
>
>
>
> Barton
>