proc det_minor(matrix a,int n){

	int c,ones;
	int small,new_small;
	int sig0,sig0s,s,u,v,b1,b2;
	int l,j,k,m,r;
	matrix x[1][n];
	matrix y[1][n];
	matrix q[1][n];   
	matrix ct[n][n+1];

	if(n==1){
		return a[1,1];
	}

	ct[1,1]=1;
	ct[1,2]=1;
	for(l=2;l<=n;l++){
 	   ct[l,1]=1;
	   for(j=2;j<=l;j++){
	      ct[l,j]=ct[l-1,j-1]+ct[l-1,j];		
	   }
           ct[l,l+1]=1;
	}

	matrix p[1][n];

	for(l=1;l<=n;l++){
		p[1,n-l+1]=a[1,l];
	}

        sig0s=-1;

	for(l=2;l<=n;l++){

		for(k=1;k<=l;k++){
			x[1,k]=1;
		}

		for(k=l+1;k<=n;k++){
			x[1,k]=0;
		}

		for(k=1;k<=n;k++){
			y[1,k]=0;
		}

		r=int(ct[n,l+1]);
		matrix p0[1][r];

		k=l;

		m=1;
		while(k!=0){

			k=1;
			for(j=1;j<=n;j++){
				if(x[1,j]==1){
					q[1,k]=j;
					k=k+1;				
				}
			}

			sig0=sig0s;

			s=r-m+1;
			p0[1,s]=0;
			for(j=1;j<=l;j++){

				u=1;
				v=l-1;
				b1=n-1;

				for(k=l;k>j;k--){
					for(b2=b1;b2>=q[1,k];b2--){
						u=u+int(ct[b2,v]);	
					}
					b1=b2-1;
					v--;
				}

				for(k=j-1;k>0;k--){
					for(b2=b1;b2>=q[1,k];b2--){
						u=u+int(ct[b2,v]);	
					}
					b1=b2-1;
					v--;
				}
				
				p0[1,s]=p0[1,s]+(sig0*a[l,int(q[1,j])])*p[1,u];
				sig0=-sig0;
	
			}
		
			m=m+1;
		
			for(k=1;k<=n;k++){
				if(x[1,k]!=0){
					break;
				}
			}
			small=k;

			c=1;
			for(k=small;(c!=0) && (k<=n);k++){
				if(x[1,k]==1 && c==1){
					x[1,k]=0;
				}
				else{
			 		if(x[1,k]==0 && c==1){
						x[1,k]=1;
						c=0;	
					}
				}
			}

			for(k=1;k<=n;k++){
				if(x[1,k]!=0){
					break;
				}
			}
			new_small=k;

			if(new_small<=n){
				ones=new_small-small-1;

				for(k=1;k<=ones;k++){
					x[1,k]=int(x[1,k]) || 1;
				}
	
			}

			for(k=n;k>=1;k--){
				if(x[1,k]!=y[1,k]){
					break;
				}	
			}	

		}
		
		p=p0;
                sig0s=-sig0s;

	}

	return(p[1,1]);
}

proc user_srem(poly a,poly x,int l){

   int i,s;
   matrix a0;
   poly p;

   a0=coeffs(a,x);
   s=size(a0);

   p=0;

   for(i=1;i<=l;i++){
     if(s>=i){
       p=p+a0[i,1]*x^(i-1);
     }
   }

   return(p);
}

proc user_coef(poly a,poly x,int l){

   int i;
   matrix a0;

   a0=coeffs(a,x);

   if(size(a0)<l+1){
      return(0);
   }
   else{ 
      return(a0[l+1,1]);
   }
}

proc user_resultant(poly a,poly b,poly x,list v){

  int i,j;
  int m,n,l,s;
  intvec u;
  poly t;
  poly f,g,h;

  for(i=1;i<=size(v);i++){
    if(v[i]==x){
       u[i]=1;
    }
    else{
       u[i]=0;
    }
  }  
   
  m=deg(a,u);
  n=deg(b,u);
   
  if(m>=n){
    l=m;
    s=n;
  }
  else{
    l=n;
    s=m;
    t=a;
    a=b;
    b=t;
  }

  matrix mat[l][l];

  for(i=0;i<(l-s);i++){
    for(j=0;j<=s;j++){
      mat[i+1,j+i+1]=user_coef(b,x,j);
    }
  }

  b=x^(l-s)*b;

  f=user_srem(a,x,l);
  g=user_srem(b,x,l);

  h=user_coef(a,x,l)*g-user_coef(b,x,l)*f;
  for(j=0;j<l;j++){
     mat[2*l-s-l+1,j+1]=user_coef(h,x,j);
  }

  for(i=l-1;i>(l-s);i--){
    h=x*user_srem(h,x,l-1)+user_coef(a,x,i)*g-user_coef(b,x,i)*f;
    for(j=0;j<l;j++){
      mat[2*l-s-i+1,j+1]=user_coef(h,x,j);
    }
  }

  return(mat);
}

timer=1;
ring r=(0),(a0,a1,a2,a3,a4,a5,a6,a7,x),lp;
poly p1=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5+a6*x^6+a7*x^7+x^8+x^9;
poly p2=diff(p1,x);
list l=a0,a1,a2,a3,a4,a5,a6,a7,x;
matrix m=user_resultant(p1,p2,x,l);
ring r0=(0),(a0,a1,a2,a3,a4,a5,a6,a7),lp;
matrix m0=imap(r,m);
poly b=det_minor(m0,9);
quit;