//---------------------------------------------------------------------------
// Miranda Moore
// COS488/MAT474
// Problem Set 10, Q3
//---------------------------------------------------------------------------
// The command "java Bitstring1"
// plots the OGF for the set of bitstrings not containing the pattern
// 0000000001.
//
// Dependencies: Complex.java, ComplexFunction.java, Plot2Dez.java
//---------------------------------------------------------------------------

public class Bitstring1 implements ComplexFunction
{
    // The OGF for bitstrings not containing 0000000001
    public Complex eval(Complex z)
    {   // {1 \over z^10-2z+1}
        Complex one = new Complex(1, 0);
        Complex two = new Complex(2, 0);
        Complex fifth = z.times(z).times(z).times(z).times(z);
        Complex tenth = fifth.times(fifth);
        Complex denom = tenth.minus(two.times(z)).plus(one);
        return denom.reciprocal();
    }
    
   public static void main(String[] args)
   {
       Plot2Dez.show(new Bitstring1(), 512);
   }
}