This Mathematica notebook accompanies the paper "Local, algebraic simplifications of Gaussian random fields" by Theodor Bjorkmo and M. C. David Marsh. It can be used to 1) generate Gaussian random fields (with a square exponential covariance function) through a local Taylor expansion; 2) constrain the hyperparameters of the covariance function given training data in the form of such Taylor coefficients. The script is commented throughout.