//---------------------------------------------------------------------------
// Miranda Moore
// COS488/MAT474
// Problem Set 10, Q3
//---------------------------------------------------------------------------
// The command "java Bitstring2"
// plots the OGF for the set of bitstrings not containing the pattern
// 0101010101.
//
// Dependencies: Complex.java, ComplexFunction.java, Plot2Dez.java
//---------------------------------------------------------------------------

public class Bitstring2 implements ComplexFunction
{
    // The OGF for bitstrings not containing 0101010101
    public Complex eval(Complex z)
    {   // {c(z) \over z^10+(1-2z)c(z)},  where c(z)=1+z^2+z^4+z^6+z^8
        Complex one = new Complex(1, 0);
        Complex two = new Complex(2, 0);
        Complex squared = z.times(z);
        Complex fourth = squared.times(squared);
        Complex sixth = fourth.times(squared);
        Complex eighth = sixth.times(squared);
        Complex tenth = eighth.times(squared);
        Complex c = one.plus(squared).plus(fourth).plus(sixth).plus(eighth);
        return c.divides((one.minus(two.times(z))).times(c).plus(tenth));
    }
    
   public static void main(String[] args)
   {
       Plot2Dez.show(new Bitstring2(), 512);
   }
}