function [xList,errorList] = Bisection(f, lowerValue, upperValue, allowError)
%
%Bisection(f, lowerValue, upperValue, allowError)
%Uses the bisection method to find the possible answers to the root of the function f
%

	%Check that the number of input variables is correct
	if(nargin ~= 4)
		error('That is not the correct number of arguments')
	end
	%A few necesary things before we begin
	pkg load symbolic;
	warning('off','OctSymPy:sym:rationalapprox');
	%Constant Variables
	maxItterations = 50;
	%Variables
	cnt = 1;
	errorValue = 1;
	currentValue = 0.0;


	%If the lower and upper bounds are mixed up swap them
	if(double(subs(f,lowerValue)) > 0)
		[lowerValue,upperValue] = swap(lowerValue, upperValue);
	end

	%Loop until the error is within bounds or the Maximum number of iterations is reached
	while((abs(errorValue) > allowError) && (cnt < maxItterations))
		currentValue = (lowerValue + upperValue)/ 2;
		errorValue = double(subs(f,currentValue));
		%Replace the correct value with the new value
		%if error == 0 then the value has been found
		if(errorValue < 0)
			lowerValue = currentValue;
		else
			upperValue = currentValue;
		end
		xList(cnt) = currentValue;
		errorList(cnt) = errorValue;
		++cnt;
	end
end