A characterization and implementation of corank one map germs from $2$-space to $3$-space in the computer algebra system SINGULAR

The classification and the geometry of corank one map germs from $({\mathbb{C}}^2,0)\to ({\mathbb{C}}^3,0)$ have been studied by Mond ^[1,2]. In this paper we characterize the classification of map germs of corank at most $1$, in terms of certain invariants. Moreover, by using this characterization, we develop an algorithm to compute the type of map germs with out computing the normal form. Also, we give its implementation in the computer algebra system SINGULAR ^[15].