# FindIntegerNullVector

FindIntegerNullVector[{x1,x2,,xn}]

finds a list of integers such that .

FindIntegerNullVector[{x1,x2,,xn},d]

finds a list of integers with such that .

# Details and Options • Not all ai are zero. The numbers xi can be real or complex. For complex numbers xi the numbers ai are Gaussian integers.
• In FindIntegerNullVector[{x1,x2,},d] no integer null vector may exist with the given norm bound. The input is then returned unevaluated.
• The following options can be given:
•  WorkingPrecision Automatic precision to use in internal computation ZeroTest Automatic method to test whether a number is zero
• The setting automatically determines the method to test the integer relation .
• For inexact numbers xi, the relation found holds up to the precision of the input. For exact numbers xi, the relation found is validated using PossibleZeroQ.
• For inexact numbers xi and the precision is taken to be the precision of the input.
• For exact numbers xi and the precision is taken to start with MachinePrecision and use up to \$MaxExtraPrecision extra precision when searching for an integer null vector when no norm bound d is specified. In the case of a norm bound d, enough precision is used to either find a null vector or prove that none exist.

# Examples

open all close all

## Basic Examples(3)

Exact input:

 In:= Out= In:= Out= Inexact input:

 In:= Out= Exact input with norm bound:

 In:= Out= There is no null vector with norm less than or equal to 2:

 In:=  Out= ## Possible Issues(2)

Introduced in 2010
(8.0)