The Differential Ideal [ P ] : M∞

Morrison, Sally

doi:10.1006/jsco.1999.0318

Cited by 22 publications

(15 citation statements)

References 5 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This practical way of defining the saturation of an ideal comes, to our knowledge, from Morrison (1999). When S is finite, we can match the usual definition by assigning s to the product of its elements.…”

Section: Ring Of Differential Polynomialsmentioning

confidence: 95%

Factorization-free Decomposition Algorithms in Differential Algebra

Hubert

2000

Journal of Symbolic Computation

106

103

View full text Add to dashboard Cite

show abstract

Section: Ring Of Differential Polynomialsmentioning

confidence: 95%

Factorization-free Decomposition Algorithms in Differential Algebra

Hubert

2000

Journal of Symbolic Computation

106

103

View full text Add to dashboard Cite

show abstract

“…The so-called Lazard Lemma [37,Proposition 3.4] implies the dimension claims; as a result, we can apply Proposition 3 to obtain the degree bound.…”

Section: The Homotopy Curve Zmentioning

confidence: 98%

Bit complexity for multi-homogeneous polynomial system solving—Application to polynomial minimization

Din

Schost

2018

Journal of Symbolic Computation

View full text Add to dashboard Cite

Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input system, under some genericity assumptions. The assumptions essentially imply that the Jacobian matrix of the system under study has maximal rank at the solution set and that this solution set is finite. The algorithm is probabilistic and a probability analysis is provided.Next, we apply these results to the problem of optimizing a linear map on the real trace of an algebraic set. Under some genericity assumptions, we provide bit complexity estimates for solving this polynomial minimization problem.

show abstract

“…During the Special Year in Differential Algebra and Algebraic Geometry organized in 1995 at the City College of New York by Prof. Hoobler and Sit, a weakness in the proof was pointed out 2 : there was a claim which was true but not proved. Morrison [1995] proved then a generalized version of the lemma which is presented in [Morrison, 1999]. Another proof was written later by Schicho and Li [1995].…”

Section: Lazard's Lemmamentioning

confidence: 99%

Computing representations for radicals of finitely generated differential ideals

Boulier

Lazard

Ollivier

et al. 2009

AAECC

135

View full text Add to dashboard Cite

International audienceThis paper deals with systems of polynomial di erential equations, ordinary or with partial derivatives. The embedding theory is the di erential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld-Gröbner, which computes a representation for the radical p of the diff erential ideal generated by any such sys- tem . The computed representation constitutes a normal simpli er for the equivalence relation modulo p (it permits to test embership in p). It permits also to compute Taylor expansions of solutions of . The algorithm is implemented within a package in MAPLE

show abstract

The Differential Ideal [ P ] : M∞

Cited by 22 publications

References 5 publications

Factorization-free Decomposition Algorithms in Differential Algebra

Factorization-free Decomposition Algorithms in Differential Algebra

Bit complexity for multi-homogeneous polynomial system solving—Application to polynomial minimization

Computing representations for radicals of finitely generated differential ideals

Contact Info

Product

Resources

About