用矩optimization计算实根
Computing real radicals by moment optimization
摘要：
我们提出了一个新的算法来计算一个理想的实根，更一般地说，根，这是基于凸矩优化。在求解矩最优化问题时，计算了在生成元上消失的截断正一般线性泛函。我们表明，对于一个足够大的程度的截断，零化子生成的真正的根。我们给出了一个有效的、一般的停止准则，它能检测出零化子上的素理想是实的，并计算出实根式为零化子上的实素理想的交集。该方法涉及几个成分，利用一般的正矩序列的属性。提出了一种计算截断正线性泛函零化子的分次基的新算法。我们提出了一个新的算法来检查一个代数簇的不可约分解是真实的，使用一个通用的真实投影减少到超曲面的情况。在那里，我们应用符号改变标准，有效地执行了一个确切的MOP。最后，我们说明我们的方法在一些例子。
英文摘要：
We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generic linear functional vanishing on the generators of is computed solving a Moment Optimization Problem (MOP). We show that, for a large enough degree of truncation, the annihilator of generates the real radical of. We give an effective, general stopping criterion on the degree to detect when the prime ideals lying over the annihilator are real and compute the real radical as the intersection of real prime ideals lying over. The method involves several ingredients, that exploit the properties of generic positive moment sequences. A new efficient algorithm is proposed to compute a graded basis of the annihilator of a truncated positive linear functional. We propose a new algorithm to check that an irreducible decomposition of an algebraic variety is real, using a generic real projection to reduce to the hypersurface case. There we apply the Sign Changing Criterion, effectively performed with an exact MOP. Finally we illustrate our approach in some examples.
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