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We study the ideal membership problem for the univariate ideals and show the following results.\n  \\item Let $f(X)\\in\\mathbb{F}[\\ell_1, \\ldots, \\ell_r]$ be a (low rank) polynomial given by an arithmetic circuit where $\\ell_i : 1\\leq i\\leq r$ are linear forms, and $I=\\langle p_1(x_1), \\ldots, p_n(x_n)\\rangle$ be a univariate ideal. 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Arvind","submitted_at":"2018-08-31T14:38:53Z","abstract_excerpt":"Let $\\mathbb{F}[X]$ be the polynomial ring over the variables $X=\\{x_1,x_2, \\ldots, x_n\\}$. An ideal $I=\\langle p_1(x_1), \\ldots, p_n(x_n)\\rangle$ generated by univariate polynomials $\\{p_i(x_i)\\}_{i=1}^n$ is a \\emph{univariate ideal}. We study the ideal membership problem for the univariate ideals and show the following results.\n  \\item Let $f(X)\\in\\mathbb{F}[\\ell_1, \\ldots, \\ell_r]$ be a (low rank) polynomial given by an arithmetic circuit where $\\ell_i : 1\\leq i\\leq r$ are linear forms, and $I=\\langle p_1(x_1), \\ldots, p_n(x_n)\\rangle$ be a univariate ideal. 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