P. Gianni

Publications42
h-index16
Citations1,973
Highly Influential Citations115
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Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering
TLDR
The lexicographical GroBner basis can be obtained by applying this algorithm after a total degree Grobner basis computation: it is usually much faster to compute the basis this way than with a direct application of Buchberger's algorithm.
Gröbner Bases and Primary Decomposition of Polynomial Ideals
TLDR
This work presents an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R and shows how the reduction process can be applied to computing radicals and testing ideals for primality.
The singular value decomposition for polynomial systems
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coecients are inexact or imperfectly known. We first give an…
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
The technique of solving systems of multivariate polynomial equations via rigenproblems has become a topic of active research (with applications in computer-aided design and {untrul theory, for…
Properties of Gröbner bases under specializations
  • P. Gianni
  • Mathematics, Computer Science
    EUROCAL
  • 2 June 1987
TLDR
It is shown that, if the system has a finite number of solutions, the problem is totally reduced to a single Grobner basis computation (w.r.t. purely lexicographical ordering).
Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases
Decomposition of Algebras
TLDR
It is shown that it is possible to define a lifting process that allows to reconstruct the answer over the rational numbers and this lifting appears to be very efficient since it is a quadratic lifting that doesn't require stepwise inversions.
Integral closure of Noetherian rings
TLDR
It is shown that for the common case of affine domains, i.e. domains which are finitely generated over fields, of characteristic zero, the authors can use an effective localization in order to perform most of the computation in one dimensional rings where it can be done with linear algebra.
The singular value decomposition for approximate polynomial systems
Shape determination for real curves and surfaces
RiassuntoSi descrivono algoritmi per determinare la forma di una curva algebrica reale piana, e la topologia di una superficie reale inP3.La forma di una curvaC si ottiene proiettandoC suP1, ed…
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