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Applications: Finding A Maximal Two-sided Ideal In A Given Left Ideal - Computations
The preliminary settings:
ring r=0,(e,f,h,a),Dp;
matrix d[4][4];
d[1,2]=-h; d[1,3]=2e; d[2,3]=-2f;
system("PLURAL",1,d);
int i;int j;int s;
ideal A,B;
poly p;
module U,W;
A=e,h-a;
A=std(A);
The iteration cycle:
s=size(A);
for(i=1;i<=s;i++)
{ W[i]=A[i]*gen(1)+gen(i+1);
p=NF(A[i]*f,A);
W[s+i]=p*gen(1)+gen(i+s+1); }
U=transpose(std(W));
B=0;
for (i=1;i<=nrows(U);i++)
{ if (U[1][i]==0)
{ p=0;
for(j=s+2;j<=ncols(U);j++)
{ if (U[j][i]!=0) { p=p + U[j][i]*A[j-s-1]; }}
if (p!=0)
{ if (B==0) { B=B,p; B=std(B); }
else { B=std(B,p); }}}}
B;
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