Here we present an efficient calculation of  comprehensive Groebner system to derive specific conditions  for neural circuits as well as electric circuits. Comprehensive Groebner system (CGS) has 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 `not-equal' and `positive' conditions into account during CGS calculation, resulting in a reduced format of CGS of parametric systems even if many parameters exist. Using our algorithm for computing CGS, we derive specific conditions such as resonant conditions that play an important role in physical,  medical, and biological phenomena. The obtained conditions lead to analysis of more realistic neural circuits having many parameters, and  provide us with possibility of positive CGS.