gram(b) = bs=matrix(matsize(b)[1],matsize(b)[2],x,y,0);mu=matrix(matsize(b)[1],matsize(b)[2],x,y,0);bs[1,]=b[1,];for(i=2,matsize(b)[1],for(j=1,i-1,mu[i,j]=(b[i,]*bs[j,]~)/(bs[j,]*bs[j,]~));bs[i,]=b[i,]-sum(j=1,i-1,mu[i,j]*bs[j,]));bs

nor(v)=v*v~

testlll(b) = gram(b);flag=1;for(k=2,matsize(b)[1],print(nor(bs[k,])-(3/4-mu[k,k-1]^2)*nor(bs[k-1,])));for(i=1,matsize(b)[1],for(j=1,matsize(b)[2],flag=flag*abs(mu[i,j]<=1/2)));flag

testconj(v) = B=floor(abs(v^(-1)));C=B*B~;sum(i=1,matsize(v)[1],C[i,i]^2)!=0

A=[1,1,1,1,0,0;0,0,-2,0,1,1;-1,1,-1,1,0,0;1,1,1,-1,0,0;1,0,-1,1,0,0;0,1,0,0,0,-1]

testlll(A)

testconj(A)



an(n)=matrix(n,n,k,l,if(k<7,if(l<7,A[k,l],0),k==l))