# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/K^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="img4.gif"
 ALT="$ K^3$">|; 

$key = q/:x',y',z':;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$ \:x', y', z' \: $">|; 

$key = q/:mathcal{M}inGL_3(K);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$ \:\mathcal{M} \in GL_3(K) $">|; 

$key = q/,v_1,v_2,v_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$ \,v_1,v_2,v_3
\,$">|; 

$key = q/:v_1,v_2,v_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$ \:
v_1,v_2,v_3 $">|; 

$key = q/,widetilde{mathcal{M}}inGL_4(K);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$ \, \widetilde{\mathcal{M}} \in GL_4(K)$">|; 

$key = q/:x,y,z:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$ \: x, y, z
\: $">|; 

$key = q/:M_{e,(v_1,v_2,v_3)}(id_{K^3}):;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ \:
M_{e,(v_1,v_2,v_3)}(id_{K^3}) \:$">|; 

$key = q/c=hspace{2mm}^t(c_1,c_2,c_3):;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$ \\\\ c = \hspace{2mm} ^t(c_1, c_2,c_3) \: $">|; 

$key = q/:c,v_1,v_2,v_3inK^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$ \:c,v_1,v_2,v_3 \in K^3$">|; 

$key = q/{displaymath}left(array{{c}x<row_mark>y<row_mark>z<row_mark>array{right)=M_{e,(v<row_mark>c_2<row_mark>c_3<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="367" HEIGHT="90" BORDER="0"
 SRC="img11.gif"
 ALT="\begin{displaymath}
\left(
\begin{array}{c}
x\\\\  y\\\\  z\\\\
\end{array}
\ri...
...\begin{array}{c}
c_1\\\\  c_2\\\\  c_3\\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/,mathcal{Q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$ \, \mathcal{Q} \,$">|; 

$key = q/:f(x,y,z)=0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \: f(x,y,z) = 0 \:$">|; 

1;

