Computational aspects of reduction strategies to construct resolutions of monomial ideals
Proceedings of the 2nd international conference, AAECC-2 on Applied algebra, algorithmics and error-correcting codes
Resolutions via homological perturbation
Journal of Symbolic Computation
Concrete Math
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
The computation of the Hilbert function
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
A Reduction Strategy for the Taylor Resolution
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Applicable Algebra in Engineering, Communication and Computing
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
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Taylor presented an explicit resolution for arbitrary monomial ideals. Later, Lyubeznik found that a subcomplex already defines a resolution. We show that the Taylor resolution may be obtained by repeated application of the Schreyer Theorem from the theory of Gröbner bases, whereas the Lyubeznik resolution is a consequence of Buchberger's chain criterion. Finally, we relate Fröberg's contracting homotopy for the Taylor complex to normal forms with respect to our Gröbner bases and use it to derive a splitting homotopy that leads to the Lyubeznik complex.