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numtheory(deprecated)

  

nearestp

  

the nearby lattice point problem

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

nearestp(B, alpha)

Parameters

B

-

list of lists of real numbers (the basis of the lattice)

alpha

-

list of real numbers (a given point)

Description

• 

Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[NearestLatticePoint] instead.

• 

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,

|w - alpha| <= C_n |u - alpha|.

• 

The output of the nearestp command is of the form:

C=&lsqb;c1,...,cn&rsqb;&period;

  

which is a list of integers such that

w=c1b1+...+cnbn&period;

• 

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

Examples

Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[NearestLatticePoint] instead.

withnumtheory&colon;

B213&comma;0&comma;0&comma;exp2&comma;1&comma;0&comma;0&comma;π100&comma;1

B213&comma;0&comma;0&comma;&ExponentialE;2&comma;1&comma;0&comma;0&comma;100π&comma;1

(1)

alp7.01&comma;8.01&comma;γ

alp7.01&comma;8.01&comma;γ

(2)

nearestpB&comma;alp

−36&comma;7&comma;0

(3)

b127230625746351104&comma;1&comma;0&comma;9032571691&comma;0&comma;0&comma;7265292251119526656&comma;4772995&comma;1

b127230625746351104&comma;1&comma;0&comma;9032571691&comma;0&comma;0&comma;7265292251119526656&comma;4772995&comma;1

(4)

blp71.01&comma;18.01&comma;π4

blp71.01&comma;18.01&comma;π4

(5)

nearestpb&comma;blp

2&comma;107&comma;97

(6)

See Also

NumberTheory[NearestLatticePoint]

numtheory(deprecated)[kronecker]

numtheory(deprecated)[minkowski]