Weil differentials

This thesis focuses upon how to calculate local components of Weil differentials of an elliptic function field. Because Weil differentials constitute a one-dimension vector space then one Weil differential is fixed. An algorithm calculating a local component is developed for the fixed one. The first algorithm computes local components of places of degree one. It is based upon elementary properties of local components. The definition of the Weil differential does not say enough about why it is defined in this way and about why it is useful. Thus there is the relationship between the Weil differential and some objects from complex analysis like the Laurent series and the residue. It provides a better understanding of properties of the Weil differential. The result of this thesis are other two algorithms calculating local components of Weil differentials. The algorithms employ the residue.