From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

---
 src/input/divisor.input.pamphlet | 49 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 src/input/divisor.input.pamphlet

(limited to 'src/input/divisor.input.pamphlet')

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}
-- 
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