Integer relation algorithm

An integer relation between a set of real numbers x1, x2, ..., xn is a set of integers a1, a2, ..., an, not all 0, such that

a
          
            1
          
        
        
          x
          
            1
          
        
        +
        
          a
          
            2
          
        
        
          x
          
            2
          
        
        +
        ⋯
        +
        
          a
          
            n
          
        
        
          x
          
            n
          
        
        =
        0.
        
      
    
    {\displaystyle a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=0.\,}

An integer relation algorithm is an <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> for finding integer relations. Specifically, given a set of real numbers known to a given precision, an integer relation algorithm will either find an integer relation between them, or will determine that no integer relation exists with coefficients whose magnitudes are less than a certain <a href="/facts/Upper_bound/YJje9oC2">upper bound</a>.

Integer relation algorithm open-in-new

Integer relation algorithm