# Edge Ideals Using Macaulay2

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## Abstract

Computer algebra systems, like *Macaulay 2* [80], Singular [47], and CoCoA [39], have become essential tools for many mathematicians in commutative algebra and algebraic geometry. These systems provide a “laboratory” in which we can experiment and play with new ideas. From these experiments, a researcher can formulate new conjectures, and hopefully, new theorems. Computer algebra systems are especially good at dealing with monomial ideals. As a consequence, the study of edge and cover ideals is well suited to experiments using computer algebra systems.

## Keywords

Ideal Edge Cover Ideals Identical Monomers Computer Algebra System EdgeIdeals
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

- 39.CoCoATeam, CoCoA: A system for doing Computations in Commutative Algebra (2011). Available at http://cocoa.dima.unige.it
- 42.D.W. Cook II, Simplicial decomposability. J. Softw. Algebra Geom.
**2**, 20–23 (2010)Google Scholar - 47.W. Decker, G.-M. Greuel, G. Pfister, H. Schönemann, Singular 3-1-3 — A computer algebra system for polynomial computations (2011). http://www.singular.uni-kl.de
- 54.D. Eisenbud, M. Green, K. Hulek, S. Popescu, Restricting linear syzygies: Algebra and geometry. Compos. Math.
**141**, 1460–1478 (2005)MathSciNetzbMATHCrossRefGoogle Scholar - 69.C.A. Francisco, A. Hoefel, A. Van Tuyl, EdgeIdeals: A package for (hyper)graphs. J. Softw. Algebra Geom.
**1**, 1–4 (2009)MathSciNetGoogle Scholar - 80.D. Grayson, M. Stillman, Macaulay2, A software system for research in algebraic geometry (2011). Available at: http://www.math.uiuc.edu/Macaulay2
- 83.H.T. Hà, A. Van Tuyl, Splittable ideals and the resolution of monomial ideals. J. Algebra
**309**, 405–425 (2007)MathSciNetzbMATHCrossRefGoogle Scholar - 108.S. Ho sten, G.G. Smith, Monomial ideals, in
*Computations in Algebraic Geometry with Macaulay 2*. Algorithms and Computations in Mathematics, vol. 8 (Springer, New York, 2001), pp. 73–100Google Scholar - 114.S. Jacques, Betti Numbers of Graph Ideals. Ph.D. Thesis, University of Sheffield, 2004 [arXiv:math/0410107v1]Google Scholar
- 151.E. Nevo, I. Peeva, Linear resolutions of powers of edge ideals (2010). PreprintGoogle Scholar

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