diff options
author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
---|---|---|
committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/input/divisor.input.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/input/divisor.input.pamphlet')
-rw-r--r-- | src/input/divisor.input.pamphlet | 49 |
1 files changed, 49 insertions, 0 deletions
diff --git a/src/input/divisor.input.pamphlet b/src/input/divisor.input.pamphlet new file mode 100644 index 00000000..fee4e32c --- /dev/null +++ b/src/input/divisor.input.pamphlet @@ -0,0 +1,49 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input divisor.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1991. +@ +<<*>>= +<<license>> + +)cl all +P0 := UP(x, FRAC INT) +P1 := UP(y, FRAC P0) +-- curve given by y^2 = x^8 + 1 (genus = 3) +R := RADFF(FRAC INT, P0, P1, 1 + x**8, 2) +genus()$R +fd := FDIV(FRAC INT, P0, P1, R) +-- let P be the place (x = 0, y = 1), +-- Q be the place (x = 0, y = -1), +-- and d be the divisor P - Q +d1 := divisor(0, 1)$fd +d2 := divisor(0, -1)$fd +d := d1 - d2 +d := reduce d +-- it turns out that d has order 4: +generator d +generator reduce(2 * d) +generator reduce(3 * d) +generator reduce(4 * d) +-- let's verify the RiemannRoch theorem: +lSpaceBasis d1 +lSpaceBasis(2 * d1) +lSpaceBasis(3 * d1) +lSpaceBasis(4 * d1) +lSpaceBasis(5 * d1) +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |