We organise the constraints introduced in the previous section in the following four systems:
Plus
The first four systems have all the same structure, each one being a
linear homogeneous system subject to a quadratic
constraint, that is,
where 
is a vector composed by the the first three components of
x, and k is a real number.
The four systems above are solved in sequence, top to bottom. The
solution of each system is obtained by first computing (for example by
SVD factorisation [7]) a one-parameter
family of solutions to 
of the form 
, where 
is a nontrivial solution and
is an arbitrary real number, and then letting 
.