1 citations · 3 across the 14 of their papers we have counts for
17 papers
Parallel Integration over Simple Radical Extensions III: Antiderivatives in Terms of Special Functions
Sam Blake
We extend the parallel integration method for mixed towers of Part~II from elementary antiderivatives to antiderivatives in special functions. The class covered is the incomplete g…
Parallel Integration over Simple Radical Extensions in Mixed Towers: Charlwood's Integrals
Sam Blake
We evaluate a SymPy implementation of the parallel Risch-Norman method using Charlwood's 2008 suite of 50 challenging indefinite integrals. The system automatically builds integran…
Parallel Integration over Simple Radical Extensions II: Mixed Towers
Sam Blake
In Part I we extended the structure theorems underlying the Risch--Norman (parallel Risch) method to a simple radical extension , , of a differential field $K=F(t_1,…
Parallel Integration over Simple Radical Extensions
Sam Blake
The parallel Risch (Risch--Norman) method is a fast heuristic for computing elementary integrals over towers of transcendental extensions. Its justification rests on two structural…
Rational Base Descent: A Deterministic Algorithm for Factoring Structured Semiprimes
Sam Blake
We present a special-purpose algorithm for factoring semiprimes in which one prime factor satisfies for positive integers with …
A Generalisation of Goursat's Algorithm for Integration in Finite Terms
Sam Blake
We give a self-contained, modern exposition of Édouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with a c…