The transcendental Risch differential equation

✍ Scribed by Manuel Bronstein

• Book ID: 104344953
• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 506 KB
• Volume: 9
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1016/s0747-7171(08)80006-5

✦ Synopsis

We present a new rational algorithm for solving Risch differential equations in towers of transcendental elementary extensions. In contrast to a recent algorithm of Davenport we do not require a progressive reduction of the denominators involved, but use weak normality to obtain a formula for the denominator of a possible solution. Implementation timings show this approach to be faster than a Hermite-like reduction.