  We present algorithms and their implementation to compute limit cycles and
their isochrons for state-dependent delay equations (SDDE's) which are
perturbed from a planar differential equation with a limit cycle.
  Note that the space of solutions of an SDDE is infinite dimensional. We
compute a two parameter family of solutions of the SDDE which converge to the
solutions of the ODE as the perturbation goes to zero in a neighborhood of the
limit cycle.
  The method we use formulates functional equations among periodic functions
(or functions converging exponentially to periodic). The functional equations
express that the functions solve the SDDE. Therefore, rather than evolving
initial data and finding solutions of a certain shape, we consider spaces of
functions with the desired shape and require that they are solutions.
  The mathematical theory of these invariance equations is developed in a
companion paper, which develops "a posteriori" theorems. They show that, if
there is a sufficiently approximate solution (with respect to some explicit
condition numbers), then there is a true solution close to the approximate one.
Since the numerical methods produce an approximate solution, and provide
estimates of the condition numbers, we can make sure that the numerical
solutions we consider approximate true solutions.
  In this paper, we choose a systematic way to approximate functions by a
finite set of numbers (Taylor-Fourier series) and develop a toolkit of
algorithms that implement the operators -- notably composition -- that enter
into the theory. We also present several implementation results and present the
results of running the algorithms and their implementation in some
representative cases.
