congratulations, you have implmented the Zariski tangent space using nilpotent matrices. welcome to the beautiful theory of algebraic geometry and schemes. ht

congratulations, you have implmented the Zariski tangent space using nilpotent matrices. welcome to the beautiful theory of algebraic geometry and schemes. http://math.stanford.edu/~vakil/0708-216/216class21.pdf http://math.stanford.edu/~vakil/0708-216/216class21.pdf This really does fall in the ream of algebraic geometry since this method only works for rational functions - as he implemented it. To numerically compute sin(x + ε) you need the Taylor series.