2 citations · 8 across the 5 of their papers we have counts for
6 papers
Real Liouvillian Extensions of Partial Differential Fields
Teresa Crespo, Zbigniew Hajto, Rouzbeh Mohseni
In this paper, we establish Galois theory for partial differential systems defined over formally real differential fields with a real closed field of constants and over formally $p…
Jacobian Conjecture via Differential Galois Theory
Elzbieta Adamus, Teresa Crespo, Zbigniew Hajto
We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking t…
An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
Elzbieta Adamus, Pawel Bogdan, Zbigniew Hajto
In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem completes the earlier work of T.…
An inversion algorithm for polynomial maps
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polyn…
The unicity of real Picard-Vessiot fields
Teresa Crespo, Zbigniew Hajto, Marius van der Put
The unicity of real Picard-Vessiot fields for differential modules over a real differential field is proved.
Real Picard-Vessiot theory
Teresa Crespo, Zbigniew Hajto, Elzbieta Sowa
The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has a…