real procedure SYMDET (A,i,j,n); value n; integer i,j,n; real A;
	begin	integer k; real d,r; array v[1:n];
		d:= 1;
		for k:= 1 step 1 until n do
		begin	j:= k; for i:= 1 step 1 until k do v[i]:= A;
			r:= v[k] - SUM (i,1,k-1,v[i] ** 2);
			d:= r * d; i:= k; A:= r:= 1 / sqrt (r);
			for j:= k+1 step 1 until n do
			begin	i:= k; A:= (A - SUM (i,1,k-1,A * v[i])) * r end
		end	LU;
		SYMDET:= d
	end	SYMDET;
	procedure SYMSOL (A,i,j,n,b); value n; integer i,j,n; real A; array b;
	begin	for j:= 1 step 1 until n do b[j]:= (b[j] - SUM (i,1,j-1,A * b[i])) * A;
		for i:= n step -1 until 1 do
		begin	j:= i; b[i]:= A * (b[i] - SUM (j,i+1,n,A * b[j])) end
	end	SYMSOL;
	procedure SYMINV (A,i,j,n); value n; integer i,j,n; real A;
	begin	integer k; array v[1:n];
		for k:= 1 step 1 until n do
		begin	i:= j:= k; v[k]:= A;
			for j:= k+1 step 1 until n do
			begin	i:= k; A:= v[j]:= - SUM (i,k,j-1,A * v[i]) * A end;
			for i:= 1 step 1 until k do
			begin	j:= k; A:= SUM (j,k,n,A * v[j]) end
		end
	end	SYMINV;
	procedure syminv (A,i,j,n); value n; integer i,j,n; real A;
	begin	integer k; array v[1:n];
		for k:= 1 step 1 until n do
		begin	i:= j:= k; v[k]:= A;
			for j:= k+1 step 1 until n do v[j]:= - SUM (i,k,j-1,A * v[i]) * A;
			i:= j:= k; A:= SUM (j,k,n,v[j] ** 2)
		end
	end	syminv;