The range of a trigonometric polynomial with complex coefficients can be interpreted as the image of the unit circle under a Laurent polynomial. We show that this range is contained in a real algebraic subset of the complex plane. Although the containment may be proper, the difference between the two sets is finite, except for polynomials with a certain symmetry.

中文翻译：

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三角多项式的范围的代数结构

具有复系数的三角多项式的范围可以解释为洛朗多项式下的单位圆的图像。我们证明了这个范围包含在复平面的实数代数子集中。尽管包含可能是适当的，但两组之间的差异是有限的，除了具有一定对称性的多项式。