Fwd: finite fields and gaussian elimination
- Subject: Fwd: finite fields and gaussian elimination
- From: Barton Willis
- Date: Sat, 19 May 2007 20:39:00 -0500
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