6 papers
A decision method for the integrability of differential-algebraic Pfaffian systems
Lisi D'Alfonso, Gabriela Jeronimo, Pablo Solernó
We prove an effective integrability criterion for differential-algebraic Pfaffian systems leading to a decision method of consistency with a triple exponential complexity bound. As…
Effective Differential Nullstellensatz for Ordinary DAE Systems with Constant Coefficients
Lisi D'Alfonso, Gabriela Jeronimo, Pablo Solernó
We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants of characteristic .…
Effective Differential Lüroth's Theorem
Lisi D'Alfonso, Gabriela Jeronimo, Pablo Solernó
This paper focuses on effectivity aspects of the Lüroth's theorem in differential fields. Let be an ordinary differential field of characteristic 0 and $\mathcal{F}<u…
A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations
Lisi D'Alfonso, Gabriella Jeronimo, François Ollivier +2
This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent f…
On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations
Lisi D'Alfonso, Gabriela Jeronimo, Gustavo Massaccesi +1
This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an a…
A linear algebra approach to the differentiation index of generic DAE systems
Lisi D'Alfonso, Gabriela Jeronimo, Pablo Solerno
The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobi…