ring R = 307,x(0..5),dp;

proc Ideale (intvec #)
{
 int i;
 intmat m;
 ideal I = 1;
 ideal I(1) = x(0),x(1),x(2),x(3),x(4);
 ideal I(2) = x(0),x(1),x(2),x(3),x(5);
 ideal I(3) = x(0),x(1),x(2),x(4),x(5);
 ideal I(4) = x(0),x(1),x(3),x(4),x(5);
 ideal I(5) = x(0),x(2),x(3),x(4),x(5);
 ideal I(6) = x(1),x(2),x(3),x(4),x(5);
 ideal I(7) = x(1)-x(0),x(2)-x(0),x(3)-x(0),x(4)-x(0),x(5)-x(0);

 if ( size(#) > 7 ) 
 {
  for (i=1;i<=7;i=i+1) { I = std(intersect(I,I(i)^#[i])); }
  for (i=8;i<=size(#);i=i+1)
  {
   m = random(306,1,5);
   ideal I(i) = 
   x(1)-m[1,1]*x(0),
   x(2)-m[1,2]*x(0),
   x(3)-m[1,3]*x(0),
   x(4)-m[1,4]*x(0),
   x(5)-m[1,5]*x(0);
   I = std(intersect(I,I(i)^#[i]));
  }
 }
 else
 {
  for (i=1;i<=size(#);i=i+1) { I = std(intersect(I,I(i)^#[i])); }
 }
 return(I);
}

LIB "general.lib";
int i,s,n,vir,dg,si,r;
bigint dimL;
intmat m;
ideal I,P;
intvec d,ll,hi;

r = 5;

d = 1,1,1,1,1;

for (d[5]=1;d[5]<=5;d[5]=d[5]+1)
{
 ll = 0;
 dg = sum(d);
 n = product(d+1) div (r+1);
 vir = (product(d+1) mod (r+1)) - 1;
 ll = -d + dg;
 for (s=1;s<=n;s=s+1) { ll = ll,2; }
 
 printf("Analyzing L_(%s,%s,%s,%s,%s)(2^%s)",d[1],d[2],d[3],d[4],d[5],n); 
  I = Ideale(ll);
 hi = hilb(I,2);
 si = size(hi); if ( dg < si ) { si = dg+1; }
 dimL = binomial(dg+r,r) - sum(hi,1..si) - 1;
 
 if ( dimL > vir ) 
 {
  printf("L_(%s,%s,%s,%s,%s)(2^%s) 
  might be special with dim(L) = %s 
  and vdim(L) = %s",d[1],d[2],d[3],d[4],d[5],n,dimL,vir); 
 }
 m = random(306,1,r);
 P = x(1)-m[1,1]*x(0),x(2)-m[1,2]*x(0),x(3)-m[1,3]*x(0),x(4)-m[1,4]*x(0),x(5)-m[1,5]*x(0);
 I = std(intersect(I,P^2));
 si = size(hilb(I,2)); if ( dg < si ) { si = dg+1; }
 dimL = binomial(dg+r,r) - sum(hilb(I,2),1..si);
 if ( dimL > 0 ) 
 {
  printf("L_(%s,%s,%s,%s,%s)(2^%s) 
  might be special with dim(L) = %s 
  and vdim(L) = %s",d[1],d[2],d[3],d[4],d[5],n+1,dimL,vir-r); 
 }
}