  The local zero structure of a smooth map may qualitatively change, when the
map is subjected to small perturbations. The changes may include births and/or
deaths of zeros. The qualitative properties are defined as the invariances of
an appropriate equivalence relation. The occurrence of a qualitative change in
the zero structures is called a bifurcation and the map is named a singularity.
The local bifurcation analysis of singularities has been extensively studied in
singularity theory and many powerful algebraic tools have been developed for
their study. However, there does not exist any symbolic computer-library for
this purpose. We suitably generalize some powerful tools from algebraic
geometry for correct implementation of the results from singularity theory. We
provide some required criteria along with rigorous proofs for efficient and
cognitive computer-implementation. We have accordingly developed a Maple
end-user friendly library, named Singularity, for an efficient and complete
local bifurcation analysis of real zeros of scalar smooth maps. We have further
written a comprehensive user-guide for Singularity. The main features of
Singularity are briefly illustrated along with a few examples.
