Quantifier elimination is the removal of all quantifiers (the universal quantifier and existential
quantifier )
from a quantified system. A first-order theory
allows quantifier elimination if, for each quantified formula, there exists an equivalent
quantifier-free formula. Examples of such theories include the real numbers with
,
,
,
and ,
and the theory of complex numbers with , , and . Quantifier elimination is implemented in as Resolve[expr].
Unfortunately, the worst-case time-complexity for real quantifier elimination is doubly exponential in the number of quantifier blocks
(Weispfenning 1988, Davenport and Heintz 1988, Heintz et al. 1989, Caviness
and Johnson 1998).
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