FindIntegerNullVector

FindIntegerNullVector[{x1, x2, ..., xn}]
finds a list of integers such that .

FindIntegerNullVector[{x1, x2, ..., xn}, d]
finds a list of integers with TemplateBox[{{{, {{a, _, 1}, ,, ..., ,, {a, _, n}}, }}}, Norm]<=d such that .

Details and OptionsDetails and Options

  • Not all are zero. The numbers can be real or complex. For complex numbers the numbers 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:
  • WorkingPrecisionAutomaticprecision to use in internal computation
    ZeroTestAutomaticmethod to test whether a number is zero
  • The setting ZeroTest->Automatic automatically determines the method to test the integer relation .
  • For inexact numbers , the relation found holds up to the precision of the input. For exact numbers , the relation found is validated using PossibleZeroQ.
  • For inexact numbers and WorkingPrecision->Automatic the precision is taken to be the precision of the input.
  • For exact numbers and WorkingPrecision->Automatic 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.
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