Computer algebra and a generalized mth root ecological FINSLER metric

Finsler geometry involves the study of the lengths of paths in space. A Finsler metric which has biological applications is the mth root ecological metric. Due to the complexity of the calculations involved, an investigation of an expanded version of this metric has not been done. The FINSLER package written on Maple, however, provides an effective means to obtain new results. The first section of this thesis introduces some of the necessary geometrical background. The second discusses mth root metrics. The third contains a description of the FINSLER program, and a new theorem about the Douglas tensor for the generalized metric.