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3 results for “Liouvillian”

Minimality of the

\mathcal D

-groupoid of symmetries of a projective structuremath.AG

The $\mathcal D$ -groupoid of symmetries is minimal under specific conditions.

problem Conditions for the minimality of the

\mathcal D

-groupoid of symmetries of a projective structure.

method Analyzing the

\mathcal D

-groupoid and its sub-groupoids, and relating it to the non-integrability of certain equations.

result The minimality of the

\mathcal D

-groupoid is equivalent to the non-integrability of specific equations.

$\mathcal D$-groupoid projective structure minimality Kummer Schwarzian equation

2023-09-14abs ↗pdf ↗

Symbolic integration on planar differential foliationsmath.DG

Algorithm finds Liouvillian solutions for planar rational vector fields.

problem Finding Liouvillian solutions for planar rational vector fields.

method Algorithm to compute telescoper for specific foliations and rational vector fields.

result Algorithm finds Liouvillian solutions for planar rational vector fields, given a large enough complexity bound.

Liouvillian solutions planar rational vector fields telescoper symbolic integration differential foliations

2023-06-21abs ↗pdf ↗

Symbolic integration of hyperexponential 1-formsmath.DG

Algorithm constructs integrals of hyperexponential 1-forms.

problem Computing integrals of hyperexponential 1-forms.

method Using Schanuel's conjecture, decomposes

Hω

into

f(F(x)) + H(x)R(x)

result Algorithm constructs a basis of cohomology of differential 1-forms.

hyperexponential 1-forms Schanuel's conjecture cohomology Liouvillian

2019-01-25abs ↗pdf ↗