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NumberTheory

  

NearestLatticePoint

  

solution to the nearby lattice point problem

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

NearestLatticePoint(B, v)

Parameters

B

-

list of lists or Matrix of real numbers; must be square

v

-

list or Vector of real numbers; the number of elements must equal the number of rows of B

Description

• 

The NearestLatticePoint function returns a w such that there exists a constant C that depends only on the dimension of the lattice with basis B such that for every point u in the lattice with basis B we have

wvCuv

• 

If B is a list of lists, then each inner list is interpreted as a basis vector.

• 

If B is a Matrix, then each row is interpreted as a basis vector.

Examples

withNumberTheory:

B213,0,0,ⅇ2,1,0,0,Pi100,1:

v7.01,8.01,gamma:

NearestLatticePointB,v

−36,7,0

(1)

BMatrix127230625746351104,1,0,9032571691,0,0,7265292251119526656,4772995,1:

vVector71.01,18.01,Pi4:

NearestLatticePointB,v

2,107,97

(2)

Compatibility

• 

The NumberTheory[NearestLatticePoint] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

NumberTheory

NumberTheory:-HomogeneousDiophantine

NumberTheory:-InhomogeneousDiophantine