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A.24 Kernel of module homomorphisms

Let A , B be two matrices of size m × r and m × s over the ring R and consider the corresponding maps

Rr −A→  Rm ←B− Rs .
We want to compute the kernel of the map Rr A Rm RmIm(B) . This can be done using the modulo command:
modulo(A,B ) = ker(Rr −A→ Rm ∕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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