@inproceedings{10.1145/3326229.3326279,
    Abstract = {Given a zero-dimensional ideal I in a polynomial ring, many algorithms start by finding univariate polynomials in\textasciitilde I, or by computing a lex-Groebner basis of\textasciitilde I. These are related to considering the minimal polynomial of an element in P/I, which may be computed using Linear Algebra from a Groebner Basis (for any term-ordering). In this tutorial we'll see algorithms for computing minimal polynomials, applications of modular methods, and then some applications, namely algorithms for computing radicals and primary decompositions of zero-dimensional ideals, and also for testing radicality and maximality. We'll also address a kind of opposite problem: given a "geometrical description'', such as a finite set of points, find the ideal of polynomials which vanish at it. We start from the original Buchberger-Moeller algorithm, and we show some developments. All this will be done with a special eye on the practical implementations, and with demostrations in CoCoA.},
    Address = {New York, NY, USA},
    Author = {Bigatti, Anna Maria},
    BookTitle = {Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation},
    File = {Linear Algebra for Zero-Dimensional Ideals - Bigatti.pdf},
    ISBN = {9781450360845},
    Keywords = {solving polynomial systems, zero-dimensional ideals, border bases, minimal and characteristic polynomial, ideals of points, cocoalib, primary decomposition, cocoa, radical ideals},
    Location = {Beijing, China},
    Pages = {21--25},
    Publisher = {Association for Computing Machinery},
    Series = {ISSAC '19},
    Title = {Linear Algebra for Zero-Dimensional Ideals},
    URL = {https://doi.org/10.1145/3326229.3326279},
    Year = {2019},
    bdsk-url-1 = {https://doi.org/10.1145/3326229.3326279},
    date-added = {2022-03-12 15:31:40 +0100},
    date-modified = {2022-03-12 15:31:40 +0100},
    numpages = {5},
    doi = {10.1145/3326229.3326279}
}

@inproceedings{10.1145/3326229.3326279, Abstract = {Given a zero-dimensional ideal I in a polynomial ring, many algorithms start by finding univariate polynomials in\textasciitilde I, or by computing a lex-Groebner basis of\textasciitilde I. These are related to considering the minimal polynomial of an element in P/I, which may be computed using Linear Algebra from a Groebner Basis (for any term-ordering). In this tutorial we'll see algorithms for computing minimal polynomials, applications of modular methods, and then some applications, namely algorithms for computing radicals and primary decompositions of zero-dimensional ideals, and also for testing radicality and maximality. We'll also address a kind of opposite problem: given a "geometrical description'', such as a finite set of points, find the ideal of polynomials which vanish at it. We start from the original Buchberger-Moeller algorithm, and we show some developments. All this will be done with a special eye on the practical implementations, and with demostrations in CoCoA.}, Address = {New York, NY, USA}, Author = {Bigatti, Anna Maria}, BookTitle = {Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation}, File = {Linear Algebra for Zero-Dimensional Ideals - Bigatti.pdf}, ISBN = {9781450360845}, Keywords = {solving polynomial systems, zero-dimensional ideals, border bases, minimal and characteristic polynomial, ideals of points, cocoalib, primary decomposition, cocoa, radical ideals}, Location = {Beijing, China}, Pages = {21--25}, Publisher = {Association for Computing Machinery}, Series = {ISSAC '19}, Title = {Linear Algebra for Zero-Dimensional Ideals}, URL = {https://doi.org/10.1145/3326229.3326279}, Year = {2019}, bdsk-url-1 = {https://doi.org/10.1145/3326229.3326279}, date-added = {2022-03-12 15:31:40 +0100}, date-modified = {2022-03-12 15:31:40 +0100}, numpages = {5}, doi = {10.1145/3326229.3326279} }