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TR07-095 | 13th July 2007
Vikraman Arvind, Partha Mukhopadhyay

#### The Ideal Membership Problem and Polynomial Identity Testing

Revisions: 2

\begin{abstract}
Given a monomial ideal $I=\angle{m_1,m_2,\cdots,m_k}$ where $m_i$
are monomials and a polynomial $f$ as an arithmetic circuit the
\emph{Ideal Membership Problem } is to test if $f\in I$. We study
this problem and show the following results.
\begin{itemize}
\item[(a)] If the ideal $I=\angle{m_1,m_2,\cdots,m_k}$ for a
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