Singular 2-0-4 Manual: A.24 Kernel of module homomorphisms

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A.24 Kernel of module homomorphisms

Let , be two matrices of size $m\times r$ and $m\times s$ over the ring 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

User manual for Singular version 2-0-4, October 2002, generated by texi2html.