Symbolic Integration in Weierstrass-like Extensions
🤖 AI Summary
This study addresses the problem of symbolic integration in differential fields containing the Weierstrass ℘-function. Focusing on Weierstrass-like extensions defined by first-order nonlinear differential equations, the authors generalize the classical theory of special polynomials to construct an integration reduction framework and develop corresponding algorithms for symbolic integration. The main contributions include the derivation of new explicit formulas for integrals of powers of the ℘-function and the validation of the proposed algorithm’s effectiveness and applicability within such extensions. This work provides novel theoretical tools and computational methods for symbolic integration in nonlinear differential-algebraic systems involving elliptic functions.
Application Category
📝 Abstract
This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass $\wp$ function, which are defined by a first-order nonlinear differential equation. We extend the classical notion of special polynomials to elements of Weierstrass-like extensions and present algorithms for reduction in such extensions. As an application of these results, we derive some new formulae for integrals of powers of $\wp$.
Problem
Research questions and friction points this paper is trying to address.
symbolic integration
Weierstrass function
differential fields
nonlinear differential equation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Weierstrass-like extensions
symbolic integration
differential fields
special polynomials
elliptic functions
🔎 Similar Papers
No similar papers found.
