In the lattice given by the basis B, the nearestp command returns a vector w that is near the vector alpha. The vector w will be a nearest vector to alpha in the lattice in the following sense:

There is a constant K depending only on n, the dimension of the lattice, such that for every other vector u in the lattice given by B,

The output of the nearestp command is of the form:

which is a list of integers such that

The command with(numtheory,nearestp) allows the use of the abbreviated form of this command.