This is a note on the classical Waring's problem for algebraic forms.Fix integers $(n,d,r,s)$, and let $Lambda$ be a general $r$-dimensionalsubspace of degree $d$ homogeneous polynomials in $n+1$ variables. Let$mathcal{A}$ denote the variety of $s$-sided polar polyhedra of $Lambda$.We carry out a case-by-case study of the structure of $mathcal{A}$ for severalspecific values of $(n,d,r,s)$. In the first batch of examples, $mathcal{A}$ isshown to be a rational variety. In the second batch, $mathcal{A}$ is afinite set of which we calculate the cardinality.}
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机译：这是关于经典Waring问题的代数形式的注记。固定整数$（n，d，r，s）$，并使$ Lambda $是$ n中度为$ d $齐次多项式的一般$ r $维子空间+ 1 $个变量。设$ mathcal {A} $表示$ Lambda $的$ s $边的极性多面体的多样性。我们对$ {n}的几个特定值，对$ mathcal {A} $的结构进行了个案研究。 ，d，r，s）$。在第一批示例中，$ mathcal {A} $被证明是一个有理数。在第二批中，$ mathcal {A} $是我们计算基数的有限集合。}
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