\\ 1175 Perfect Laihem lattices (dimension 8, contain some  P_7^k) 
\\ p7lh: file of LLL-reduced GRAM matrices for the P_7^k 
\\ LAIHEM1175 is a vector with 10 components: 
\\   First 8 = last line of the corresponding 8X8 (symmetric) GRAM matrix 
\\   9th (= b) = normalization factor for the inclusion P_7^k --> lh(k') 
\\  10th = number of the P7^k corner (1 <= k <= 33) 

\\============================================================

\\ v2m transforms a n(n+1)/2 vector into a symmetric n X n matrix 
{v2m(v,n,a,k)=
n=floor(sqrt(2*length(v)));a=matrix(n,n,k,l,1);
k=0;for(l=1,n,for(j=l,n,k=k+1;a[l,j]=v[k];a[j,l]=v[k]));a}

read("p7lh");
read("LAIHEM1175");

\\ lh puts in PARI-GP format the matrix LAIHEM1175[k] (1 <= k <= 1175) 
{lh(n,v,r7,k,b,m)=
if(n>1175,print(" There are only 1175 Laihem lattices!"),
v=LAIHEM1175[n];b=v[9];m=v[10];
r7=p7lh[m,];if(b>1,r7=b*r7,);r7=v2m(r7);
m=matrix(8,8,k,l,0);
for(k=1,7,for(l=1,7,m[k,l]=r7[k,l]));
for(k=1,8,m[k,8]=v[k];m[8,k]=v[k]));
m}

print(" To get a Gram matrix for an index j, use the command lh(j)"); 

\\============================================================

\\v=vector(300,k,m2v(lh(k)));    LH1=matrix(300,36,k,l,v[k][l]);
\\v=vector(300,k,m2v(lh(k+300)));LH2=matrix(300,36,k,l,v[k][l]);
\\v=vector(300,k,m2v(lh(k+600)));LH3=matrix(300,36,k,l,v[k][l]);
\\v=vector(271,k,m2v(lh(k+900)));LH4=matrix(271,36,k,l,v[k][l]);

\\ b = 1 except 
\\ b = 2 for k in {7,49,116,150,154,177,181,254,259,374,379,694} and 
\\ b = 3 for k = 25.