A.24 Kernel of module homomorphisms
===================================
Let 
$A$
, 
$B$
 be two matrices of size
$m\times r$ and $m\times s$
over the ring 
$R$
 and consider the corresponding maps
$$
R^r \buildrel{A}\over{\longrightarrow}
R^m \buildrel{B}\over{\longleftarrow} R^s\;.
$$
We want to compute the kernel of the map
$R^r \buildrel{A}\over{\longrightarrow}
R^m\longrightarrow
R^m/\hbox{Im}(B) \;.$
This can be done using the modulo command:
$$
\hbox{\tt modulo}(A,B)=\hbox{ker}(R^r
\buildrel{A}\over{\longrightarrow}R^m/\hbox{Im}(B)) \; .
$$

  ring r=0,(x,y,z),(c,dp);
  matrix A[2][2]=x,y,z,1;
  matrix B[2][2]=x2,y2,z2,xz;
  print(modulo(A,B));
==> yz2-x2, xyz-y2,  x2z-xy, x3-y2z,
==> x2z-xz2,-x2z+y2z,xyz-yz2,0      

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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