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Diffstat (limited to 'src/input/kovacic.input.pamphlet')
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diff --git a/src/input/kovacic.input.pamphlet b/src/input/kovacic.input.pamphlet new file mode 100644 index 00000000..7ddd2eba --- /dev/null +++ b/src/input/kovacic.input.pamphlet @@ -0,0 +1,53 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kovacic.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1994. +@ +<<*>>= +<<license>> +y := operator y + +--I've added case 2 of Kovacic's algorithm for version 1.5 +--(version 1.0 had case 1 only, version 2.0 will have case 3). +--For order 2 equations, we can now find those solutions whose +--logarithmic derivative is an algebraic function of degree 2 +--(version 1.0 found the solutions whose logarithmic derivatives +--were rational functions). +--Here is an example of an equation that we can solve in 1.5 and not in 1.0: + +eq := 2*x**3 * differentiate(y x,x,2) + 3*x**2 * differentiate(y x,x) - 2 * y x + + +solve(eq,y,x).basis + +--(should be:) +-- +-- 2 +-- - ---- +-- +-+ +-- \|x 1 +-- (3) [%e ,--------] +-- 2 +-- - ---- +-- +-+ +-- \|x +-- %e +-- Type: List Expression Integer + + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |