Complex quantifier elimination in HOL

Building on a simple construction of the complex numbers and a proof of the Fundamental Theorem of Algebra, we implement, as a HOL derived inference rule, a decision method for the first order algebraic theory of C based on quantifier elimination. Although capable of solving some mildly interesting problems, we also implement a more efficient semidecision procedure for the universal fragment based on Gr öbner bases. This is applied to examples including the automatic proof of some simple geometry theorems. The general and universal procedures present an interesting contrast in that the latter can exploit the finding-checking separation to achieve greater efficiency, though this feature is only partly exploited in the present implementation.