真值表不变的正则链柱形代数分解
Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
摘要：
基于最近的两个进展，提出了一种计算柱形代数分解的新算法。首先，输出是真值表不变的（TTICAD），这意味着给定的公式在分解的每个单元上具有恒定的真值。其次，计算使用规则链理论，首先建立一个圆柱形分解的复杂空间（CCD）递增多项式。对规则链技术进行了重大修改，以实现更复杂的不变性准则。在RegularChains Library for Maple中实现的实验结果验证了将这些进步相结合可以提供优于其各个组件的算法，并与最先进的算法竞争。
英文摘要：
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art.
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