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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

\begin{displaymath}
R^r \buildrel{A}\over{\longrightarrow}
R^m \buildrel{B}\over{\longleftarrow} R^s\;.
\end{displaymath}

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:

\begin{displaymath}
\hbox{\tt modulo}(A,B)=\hbox{ker}(R^r
\buildrel{A}\over{\longrightarrow}R^m/\hbox{Im}(B)) \; .
\end{displaymath}

 
  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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