Douglas Leonard

Areas of Interest

Desingularization of function fields, integral closures of rings and ideals, AG codes. algebraic combinatorics

Downloads as of December 26, 2019

• A LaTex version of my desingularization of function fields paper, ArXiv 2019
• Beta version of the FunctionFieldDesingularization Package for Macaulay2
• A LaTex version of my extension paper, ArXiv 2019
• Beta version of the Macaulay2 code for extension of a multi-homogeneous variety by parts
• A tutorial on AG code construction from a Grobner basis perspective, Linz, 2006
• A tutorial on AG code decoding from a Grobner basis perspective, Linz, 2006
• A weighted module view of integral closures of affine domains of type I, Advances in Mathematics of Communication, Feb. 2009, 1-11.
• Addendum to a weighted module view of integral closures of affine domains of type I.
• MAGMA implementation of the q-th power algorithm
• MACAULAY2 implementation of the qth power algorithm, as of January 25,2013
• Paper justifying lifting results of the qth-power algorithm from Z_q to Q
• example of the q-th power algorithm with two free variables and a larger than expected module generating set
• example of the q-th power algorithm with one free variable with minimization
• further generic example of the q-th power algorithm in one free variable with minimization
• example of the q-th power algorithm (simple second tower example)
• Using Groebner bases to investigate flag algebras and association scheme fusion , Linz, 2006
• PDF of overview of the following examples from my point of view of the state of various integral closure implementations.
• PDF of why weights matter from my point of view of the state of various integral closure implementations.
• LaTeX of Hermitian example from my point of view of the state of various integral closure implementations.
• PDF of Hermitian example from my point of view of the state of various integral closure implementations.
• LaTeX of Singular 3.7.3 example from my point of view of the state of various integral closure implementations.
• PDF of Singular 3.7.3 example from my point of view of the state of various integral closure implementations.
• LaTeX of a generic curve example from my point of view of the state of various integral closure implementations.
• PDF of a generic example from my point of view of the state of various integral closure implementations.
• LaTeX of an example for reconstructing rational coefficients from my point of view of the state of various integral closure implementations.
• PDF of an example for reconstructing rational coefficients from my point of view of the state of various integral closure implementations.
• LaTeX of modular curve example in Normalisation documentation from my point of view of the state of various integral closure implementations.
• PDF of modular curve example in Normalisation documentation from my point of view of the state of various integral closure implementations.
• LaTeX of sixth example from my point of view of the state of various integral closure implementations.
• PDF of sixth example from my point of view of the state of various integral closure implementations.
• LaTeX of my 2009 AMC paper example from my point of view of the state of various integral closure implementations.
• PDF of my 2009 AMC paper example from my point of view of the state of various integral closure implementations.
• LaTeX of example 3.67 from Vasconcelas from my point of view of the state of various integral closure implementations.
• PDF of example 3.67 from Vasconcelas from my point of view of the state of various integral closure implementations.
• LaTeX of ninth example from my point of view of the state of various integral closure implementations. A reducible example
• PDF of ninth example from my point of view of the state of various integral closure implementations. A reducible example
• LaTeX of two non-integral examples with units from my point of view of the state of various integral closure implementations.
• PDF of two non-integral examples with units from my point of view of the state of various integral closure implementations.
• PDF of example 2.3 from Singh and Swanson's 2009 paper from my point of view of the state of various integral closure implementations.
• LaTeX of simple examples of integral closures of ideals using local monomial orderings.
• PDF of simple examples of integral closures of ideals using local monomial orderings.
• LaTeX of an example of integral closures of ideals wherein it is not obvious from a global ordering how many levels of the Rees algebra are important.
• PDF of an example of integral closures of ideals wherein it is not obvious from a global ordering how many levels of the Rees algebra are important.

Selected publications

• Orthogonal polynomials, duality and association schemes, SIAM Journal on Mathematical Analysis, 13(4) (1982), 656--663.
• Error-locator ideals for algebraic-geometric codes, IEEE Trans. Inform. Theory, 41(3) (1995), 819--824.
• Finding the missing functions for one-point AG codes, IEEE Trans. Inform. Theory 47(6) (2001) 2566--2573.
• Integral closures and weight functions over finite fields (with R. Pellikaan), Finite fields and their applications, 9(4) (2003), 479--504.
• A weighted module view of integral closures of affine domains of type I, Advances in Mathematics of Communication, 3(1) (2009), 1-11.

(334) 844-3643

leonada@auburn.edu