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The local zero structure of a smooth map may qualitatively change, when themap is subjected to small perturbations. The changes may include births and/ordeaths of zeros. The qualitative properties are defined as the invariances ofan appropriate equivalence relation. The occurrence of a qualitative change inthe zero structures is called a bifurcation and the map is named a singularity.The local bifurcation analysis of singularities has been extensively studied insingularity theory and many powerful algebraic tools have been developed fortheir study. However, there does not exist any symbolic computer-library forthis purpose. We suitably generalize some powerful tools from algebraicgeometry for correct implementation of the results from singularity theory. Weprovide some required criteria along with rigorous proofs for efficient andcognitive computer-implementation. We have accordingly developed a Mapleend-user friendly library, named Singularity, for an efficient and completelocal bifurcation analysis of real zeros of scalar smooth maps. We have furtherwritten a comprehensive user-guide for Singularity. The main features ofSingularity are briefly illustrated along with a few examples.

Symbolic local bifurcation analysis of scalar smooth maps