\\ 9542 Perfect Napias lattices (dimension 8) 
\\ The file is a concatenation of 9 files containing each 1000 matrices 
\\ and one containing 542 matrices 
\\ np puts in PARI-GP format the matrix NAPIASk (0 <= k <= 9) 
\\============================================================

read("NAPIAS0");print("N");
read("NAPIAS1");print("NA");
read("NAPIAS2");print("NAP");
read("NAPIAS3");print("NAPI");
read("NAPIAS4");print("NAPIA");
read("NAPIAS5");print("NAPIAS");
read("NAPIAS6");print("NAPIAS : ");
read("NAPIAS7");print("NAPIAS : P");
read("NAPIAS8");print("NAPIAS : P8");
read("NAPIAS9");print("NAPIAS : P8 :");

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

NAP=vector(10,k,0);
NAP[1]=Nap0;
NAP[2]=Nap1;
NAP[3]=Nap2;
NAP[4]=Nap3;
NAP[5]=Nap4;
NAP[6]=Nap5;
NAP[7]=Nap6;
NAP[8]=Nap7;
NAP[9]=Nap8;
NAP[10]=Nap9;

\\ v2m transforms a n(n+1)/2 vector into a symmetric n X n matrix 
{v2m(v,n,a,k,l)=
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}

{np(k,k0,k1)=
if(k>9542,print(" There are only 9542 Napias lattices"),
k0=(k-1)%1000;k1=(k-1)\1000;v2m(NAP[k1+1][k0+1,]))}