变形虫的不对称近似
Lopsided Approximation of Amoebas
摘要：
洛朗多项式的变形虫是对应的超曲面在坐标对数绝对值映射下的像。在这篇文章中，我们证明了一个理论上的阿米巴近似方法，由于Purbhoo可以有效地用于实践。要做到这一点，我们解决了Purbhoo的方法利用循环结式之间的关系的主要瓶颈。我们使用相同的方法，给出近似的对数原像的Laurent多项式的阿米巴使用半代数集。我们还提供了一个奇异/SAGE实现这些算法，这表明了显着的加速，当我们专门的循环结果计算使用，与通用的结果算法。
英文摘要：
The amoeba of a Laurent polynomial is the image of the corresponding hypersurface under the coordinatewise log absolute value map. In this article, we demonstrate that a theoretical amoeba approximation method due to Purbhoo can be used efficiently in practice. To do this, we resolve the main bottleneck in Purbhoo's method by exploiting relations between cyclic resultants. We use the same approach to give an approximation of the Log preimage of the amoeba of a Laurent polynomial using semi-algebraic sets. We also provide a SINGULAR/SAGE implementation of these algorithms, which shows a significant speedup when our specialized cyclic resultant computation is used, versus a general purpose resultant algorithm.
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