P. Gianni

Publications43
h-index16
Citations1,880
Highly Influential Citations119
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Gröbner Bases and Primary Decomposition of Polynomial Ideals
TLDR
We present an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R. We show how basic ideal theoretic operations can be performed using Grobner bases and we exploit these constructions to inductively reduce the problem to zero dimensional ideals. Expand
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Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering
TLDR
We present an efficient algorithm for the transformation of a Grobner basis of a zero-dimensional ideal with respect to any given ordering into a GroBner basis withrespect to any other ordering. Expand
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  • 28
The singular value decomposition for polynomial systems
TLDR
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coecients are inexact or imperfectly known. Expand
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Properties of Gröbner bases under specializations
  • P. Gianni
  • Mathematics, Computer Science
  • EUROCAL
  • 2 June 1987
TLDR
We prove some properties of Grobner bases under specialization maps. Expand
  • 76
  • 8
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
TLDR
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 example) at least since the papers [2, 6, 9]. Expand
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  • 6
Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases
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GCD's and Factoring Multivariate Polynominals Using Gröbner Bases
TLDR
This paper shows how Grobner basis computations can be used to compute multivariate gcds, perform Hensel lifting, and reduce multivariate factorization to univariate. Expand
  • 14
  • 3
Decomposition of Algebras
TLDR
We solve this problem by reducing it to the problem of finding a decomposition of finite communtative Q-algebras as a direct product of local Q- algebnas over finite field. Expand
  • 23
  • 2
Integral closure of Noetherian rings
TLDR
We show that for the common case of affine domains, i.e. domains which are finitely generated over fields, we 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. Expand
  • 17
  • 2
Compensation of Laser Frequency Fluctuations and Phase Noise in 16-QAM Coherent Receivers
Frequency fluctuations caused by mechanical vibrations, power supply noise, and other mechanisms are detrimental to the phase estimator performance in high speed intradyne coherent optical receivers.… Expand
  • 9
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