Symbolic Integration in Weierstrass-like Extensions

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 $\wp$.

💡 Research Summary

This paper investigates symbolic integration in differential fields that contain functions defined by first‑order nonlinear differential equations, with the Weierstrass ℘‑function as the prototypical example. The authors introduce the notion of a “Weierstrass‑like extension” K = k(t, t′) of a base differential field (k, ′), where t is transcendental over k, its derivative t′ lies in k