dc.contributor.author Canny, John en_US dc.contributor.author Pedersen, Paul en_US dc.date.accessioned 2007-04-23T16:33:17Z dc.date.available 2007-04-23T16:33:17Z dc.date.issued 1993-10 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1394 en_US dc.identifier.uri https://hdl.handle.net/1813/6172 dc.description.abstract Given a system of $n+1$ generic Laurent polynomials, for $i \,=\, 1, \ldots, n+1$, $$\eqlabel(\InputSystem) f_i(\x) \quad = \quad \sum_{q\in \A_i} c_{iq} \,x^q; \qquad q \,=\, (q_1,\ldots,q_n); \qquad \x^q \,=\, x_1^{q_1}x_2^{q_2}\cdots x_n^{q_n}; \eqno(\InputSystem)$$ with (finite) support sets $\A_i \subset L$, where $L$ is some affine lattice isomorphic to $\Z^n$; we consider algorithms for the {\it Newton resultant} $R(f_1,f_2, \ldots, f_{n+1})$. This is the unique (up to sign) irreducible polynomial with coefficients in $\Z$ and monomials in the $c_{iq}$ which determines whether or not system~(\InputSystem) has common roots in the {\it algebraic torus} $(\C-\{0\})^n$. The resultant depends only on the {\it Newton polytopes} $N_i \,:=\, conv(\A_i) \subset \R^n$ of the sets $\A_i$. Our terminology emphasizes the dependence on the combinatorics of the Newton polytopes. The algebraic torus is the natural setting for us because we are interested in the properties of systems of polynomials which are invariant under symmetries of the affine lattice $L$, and translation by $q\in L$ corresponds to multiplication by $x^q$ at the level of polynomials. Since $x^q$ may have negative exponents, we restrict to points none of whose coordinates are zero. en_US dc.format.extent 1069711 bytes dc.format.extent 308538 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject computer science en_US dc.subject technical report en_US dc.title An Algorithm for the Newton Resultant en_US dc.type technical report en_US
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