We prove that a general homogeneous polynomial can be reconstructed up to a multiplicative constant factor from its partial derivatives, extending the property about determination of homogeneous polynomials by Jacobian ideals.

中文翻译：

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关于由偏导数确定的齐次多项式

我们证明了一般齐次多项式可以从其偏导数重构为乘法常数因子，扩展了关于由雅可比理想确定齐次多项式的性质。