Computing Chow Forms and Some Applications

We prove the existence of an algorithm that, from a finite set of polynomials defining an algebraic projective variety, computes the Chow form of its equidimensional component of the greatest dimension. Applying this algorithm, a finite set of polynomials defining the equidimensional component of th...

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Bibliographic Details
Published in:Journal of algorithms 2001-10, Vol.41 (1), p.52-68
Main Authors: Jeronimo, Gabriela, Puddu, Susana, Sabia, Juan
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
algorithmic algebraic geometry
Algorithmics. Computability. Computer arithmetics
Applied sciences
Chow form
complexity theory
Computer science
control theory
systems
Data processing. List processing. Character string processing
equidimensional decomposition
Exact sciences and technology
Mathematics
Memory organisation. Data processing
polynomial equations
Sciences and techniques of general use
Software
Theoretical computing
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Summary:We prove the existence of an algorithm that, from a finite set of polynomials defining an algebraic projective variety, computes the Chow form of its equidimensional component of the greatest dimension. Applying this algorithm, a finite set of polynomials defining the equidimensional component of the greatest dimension of an algebraic (projective or affine) variety can be computed. The complexities of the algorithms involved are lower than the complexities of the known algorithms solving the same tasks. This is due to a special way of coding output polynomials, called straight-line programs.
ISSN:0196-6774
1090-2678
DOI:10.1006/jagm.2001.1177