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Birational properties of the gap subresultant varieties

M'hammed El Kahoui
2005 Journal of symbolic computation  
In this paper we address the problem of understanding the gaps that may occur in the subresultant sequence of two polynomials.  ...  We define the gap subresultant varieties and prove that they are rational and have the expected dimension. We also give explicitly their corresponding prime ideals.  ...  Acknowledgments I would like to thank the anonymous referees for their very constructive comments and their great help in improving the results and the quality of this paper.  ... 
doi:10.1016/j.jsc.2004.09.005 fatcat:xjfrrxeifjerdksumtnpn22a6e

Macaulay style formulas for toric residues

Carlos D'Andrea, Amit Khetan
2005 Compositio Mathematica  
We also give an irreducible representation of toric residues by extending the theory of subresultants to monomials of critical degree in the homogeneous coordinate ring of the corresponding toric variety  ...  We present an explicit formula for computing toric residues of ample divisors as a quotient of two determinants,à la Macaulay, where the numerator is a minor of the denominator.  ...  We thank Eduardo Cattani and Alicia Dickenstein for pointing out that the original proof of Theorem 2.1 was incomplete and providing a suggestion on how to fill the gap.  ... 
doi:10.1112/s0010437x05001326 fatcat:pa5w62akgngytpsvwird7nbgom

Macaulay Style Formulas for the Toric Residue [article]

Carlos D'Andrea, Amit Khetan
2003 arXiv   pre-print
We also give an irreducible representation of toric residues by extending the theory of subresultants to monomials of critical degree in the homogeneous coordinate ring of the corresponding toric variety  ...  We present an explicit formula for computing toric residues as a quotient of two determinants, a la Macaulay, where the numerator is a minor of the denominator.  ...  Hence, ω(h) may be regarded as the numerator of the residue of h. Several properties of this morphism are studied in [J2, J3] .  ... 
arXiv:math/0307154v1 fatcat:3v6vw25w5vbfnb5j3nt2f2ol2e

On reliable visualization algorithms for real algebraic curves and surfaces [article]

Christian Stussak, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Schenzel, Peter, Dr., Chalmoviansky, Pavel, Dr.
2018
Certain embeddings of blowups of the plane are visualized using real time ray casting of their implicit form.  ...  The efficiency of the new method, which combines symbolic and certified numerical methods, is illustrated by means of complexity analysis and practical experiments.  ...  The structure that arises in the sequence of signed subresultants is often called the gap structure due to the gaps that occur in defective sequences.  ... 
doi:10.25673/993 fatcat:fdo77mocw5fi5em7x34inqr7lq

Algebraic-geometric codes and their decoding algorithm [article]

BZ Ba-Zhong Shen, JH Van Lint, GBM Gerard Van Der Geer, GR Ruud Pellikaan
1992
Jack H. van Lint, who gave me a great opportunity to carry out my doctorate research in the group of Discrete Mathernaties at the Eindhoven University of Technology.  ...  It is his guidance and encouragement that led to the completion of this thesis.  ...  The moduli variety M 0 , parametrizing all isomorphism classes of curves of genus g, has dirneusion 3g-3, if g > 1.  ... 
doi:10.6100/ir381307 fatcat:3sis2br5nzeljolxkqiotwnylm