On Monomial Reduction and Polynomial Expressions with Respect to Binomial Ideals

REFERENCES

• Adams , W. W. , Loustanau , P. ( 1996 ). An Introduction to Gröbner Bases . Graduate Studies in Mathematics, American Mathematical Society .
   Google Scholar
• Adrovic , D. ( 2012 ). Solving Polynomial Systems With Tropical Methods. Ph.D. thesis, University of Illinois at Chicago, Chicago .
   Google Scholar
• Adrovic , D. , Verschelde , J. ( 2012 ). Computing Puiseux series for algebraic surfaces. In: The Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC 2012). Grenoble, France. July 22–25, 2012. van der Hoeven, J., van Hoeij, M. (eds.) ACM, pp. 20–27 .
   Google Scholar
• Adrovic , D. , Verschelde , J. (2013). Polyhedral methods for space curves exploiting symmetry applied to the cyclic n-roots problem. Computer Algebra in Scientic Computing, 15th International Workshop, CASC 2013, Berlin, Germany, edited by Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, and Evgenii V. Vorozhtsov. Lecture Notes in Computer Science. 8136:10–29.
   Google Scholar
• Backelin , J. , Fröberg , R. ( 1991 ). How to prove that there are 924 cyclic-7 roots? Proc. ISSAC’91 . Watt , S. M. (ed.) ACM , pp. 103 – 111 .
   Google Scholar
• Bini , D. , Morrain , B. Polynomial test suit. Available at http://www-sop.inria.fr/saga/POL/BASE/2.multipol/cyclic.hml. Accessed April 3, 2015 .
   Google Scholar
• Björck , G. , Fröberg , R. ( 1991 ). A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots . J. Symbolic Comput. 12 : 329 – 336 .
   Web of Science ®Google Scholar
• Björck , G. , Fröberg , R. ( 1992 ). Methods to “divide out” certain solutions from systems of algebraic equations, applied to find all cyclic-8 roots . Analysis, Algebra, and Computers in Mathematical Research . Lecture Notes in Pure and Appl. Math., 156 . New York : Dekker , pp. 57 – 70 .
   Google Scholar
• Eisenbud , D. ( 2004 ). Commutative Algebra with a View toward Algebraic Geometry . New York : Springer-Verlag .
   Google Scholar
• Eisenbud , D. , Sturmfels , B. ( 1996 ). Binomial ideals . Duke Math. J. 84 ( 1 ): 1 – 45 .
   Web of Science ®Google Scholar
• Faugère , J. C. ( 2001 ). Finding all the solutions of Cyclic-9 using Gröbner basis techniques . Computer mathematics (Matsuyama), Lecture Notes Ser. Comput . 9 . River Edge , N.J. : World Sci. Publ , pp. 1 – 12 .
   Google Scholar
• Herzog , J. , Hibi , T. ( 2011 ). Monomial Ideals . Graduate Texts in Mathematics 260 . London-Dordrecht-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Merris , R. ( 2003 ). Combinatorics. , 2 ed edition . Hoboken , New Jersey : Wiley Interscience .
   Google Scholar
• Sabeti , R. ( 2011 ). Numerical-symbolic exact irreducible decomposition of cyclic-12 . LMS Journal of Computation and Mathematics 14 : 155 – 172 .
   Web of Science ®Google Scholar
• Verschelde , J. ( 2009 ). Polyhedral methods in numerical algebraic geometry . In: Interactions of Classical and Numerical Algebraic Geometry . Bates , D. , Besana , G.M. , Di Rocco , S. , Wampler , C. (eds.) Contemporary Mathematics 496 , AMS , pp. 243 – 263 .
   Google Scholar
• Communicated by S. Bazzoni.
   Google Scholar
• Dedicated to Professor Siavash M. Shahshahani.
   Google Scholar