Let A, B two matrices of size m x r and m x s over the ring R and consider the corresponding maps
r A m R -----> R ^ | | s R .
We want to compute the kernel of the map
r A m m R -----> R -----> R /Im(B) .
This can be done using the modulo
command:
r A m modulo(A,B)=ker(R -----> R /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; modulo(A,B); ==> _[1]=[yz2-x2,x2z-xz2] ==> _[2]=[xyz-y2,-x2z+y2z] ==> _[3]=[x2z-xy,xyz-yz2] ==> _[4]=[x3-y2z]