Quantifier elimination over the reals is a central problem in computational real algebraic geometry, polynomial system solving and symbolic computation. Given a semi-algebraic formula (whose atoms are polynomial constraints) with quantifiers on some variables, it consists in computing a logically equivalent formula involving only unquantified variables. When there is no alternation of quantifiers, one has a one block quantifier elimination problem. This paper studies a variant of the one block quantifier elimination in which we compute an almost equivalent formula of the input. We design a new probabilistic efficient algorithm for solving this variant when the input is a system of polynomial equations satisfying some regularity assumptions. When the input is generic, involves $s$ polynomials of degree bounded by $D$ with $n$ quantified variables and $t$ unquantified ones, we prove that this algorithm outputs semi-algebraic formulas of degree bounded by $\mathcal{D}$ using $O\ {\widetilde{~}}\left ((n-s+1)\ 8^{t}\ \mathcal{D}^{3t+2} \binom{t+\mathcal{D}}{t} \right )$ arithmetic operations in the ground field where $\mathcal{D} = 2(n+s)\ D^s(D-1)^{n-s+1}\ \binom{n}{s}$. In practice, it allows us to solve quantifier elimination problems which are out of reach of the state-of-the-art (up to $8$ variables).

翻译：真实值的量化除去是计算真实值{ 数值几何、 多元系统解析和符号计算中的一个中心问题。 半数值公式( 原子是多数值限制) 在某些变量上带有量化假设的半数值公式( 其原子是多数值限制 ), 它包括计算一个逻辑等值公式, 仅涉及未量化变量。 当量化变量没有交替时, 就会有一个区块量化除去问题。 本文研究一个区块量化除去变量的变种, 其中我们计算输入的公式几乎等同。 当输入是满足某些常规假设的多数值方程式系统时, 我们设计了一个新的概率有效算法来解决这个变量。 当输入为通用时, 涉及以美元和美元量化变量和未量化的美元捆绑在一起的 。 我们证明这一算法输出由 $\ madcal{ d_ bal_ dal_ lix_\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\