% file  2lat1-5.tex   (has a .fr)
\magnification=1200
\pageno=153
\hfuzz=2.5pt
\input ../louis.sty
\input ../l.sty
\input lattice.sty
\headline{Geometry of lattices I\s5 \hfill\er file 2lat1-5.tex.\qquad\today}

\entete {I \s5 }{The classification of two dimensional lattices}

\proclaim I\s5-1. Reduction of two variable quadratic forms. 

We can always choose an arbitrary visible vector to be a vector basis. 
For the 2-dimensional lattice $L$ we choose a shortest vector $\vec s\in 
S$. Then the other basis vector must be in one the two $\Sigma_\pm$ the 
nearest paralleles to $\lambda\vec s$ which contain lattice points 
