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BUILT-IN MATHEMATICA SYMBOL
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](Files/FindIntegerNullVector.en/4.png "TemplateBox[{{{, {{a, _, 1}, ,, ..., ,, {a, _, n}}, }}}, Norm]<=d"){kind=small}
such that 
.
Details 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:
-
WorkingPrecision Automatic precision to use in internal computation ZeroTest Automatic method 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.
New in 8
