A short proof for the parameter continuation theorem

被引：0
作者：
Borovik, Viktoriia [1 ]
Breiding, Paul [1 ]
机构：
[1] Univ Osnabruck, Fachbereich Math Informat, Albrechtstr 28a, D-49076 Osnabruck, Germany
来源：
JOURNAL OF SYMBOLIC COMPUTATION | 2025年 / 127卷
关键词：
Gr & ouml; bner bases; Polynomial homotopy continuation; Discriminants;
D O I：
10.1016/j.jsc.2024.102373
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a short proof using Gr & ouml;bner bases. Our approach gives a method for computing discriminants. (c) 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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相关论文
共 19 条
  • [1] Bates DJ, 2024, Arxiv, DOI arXiv:2302.08585
  • [2] Complexity and real computation: A manifesto
    Blum, L
    Cucker, F
    Shub, M
    Smale, S
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1996, 6 (01): : 3 - 26
  • [3] Cox D.A., 2015, Undergraduate Texts in Mathematics
  • [4] Davidenko D.F., 1953, Ukrain. Mat. Zurnal, V5, P196
  • [5] Davidenko D. F., 1953, Dokl. Akad. Nauk SSSR, V88, P601
  • [6] Dogan M.L., 2024, ACM Commun. Comput. Algebra, V57, P167
  • [7] Grayson D., 2020, Macaulay2, a software system for research in algebraic geometry
  • [8] Kapranov MM, 1994, DISCRIMINANTS RESULT
  • [9] An efficient method for computing comprehensive Grobner bases
    Kapur, Deepak
    Sun, Yao
    Wang, Dingkang
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2013, 52 : 124 - 142
  • [10] A new algorithm for discussing Grobner bases with parameters
    Montes, A
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2002, 33 (02) : 183 - 208
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