Derivation of specific conditions with Comprehensive Groebner Systems

Here we present an efficient calculation of comprehensive Gröbner systems to derive specific conditions for neural circuits as well as electric circuits. Comprehensive Gröbner systems (CGS) have been applied to problems with a small number of parameters such as the automatic geometric theorem proving and the inverse kinematics problem of a robot arm. In CGS, however, a larger number of parameters make its calculation less tractable. Therefore, we take ‘notequal’ conditions into account during CGS calculation, resulting in a reduced format of CGS of parametric systems even though many parameters exist. Using our implemented CGS, we derive specific conditions such as resonant conditions that play an important role in physical, mechanical, and biological phenomena. The obtained conditions lead to analysis of realistic neural circuits having many parameters, and provide us with a possibility of positive CGS.