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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/input/divisor.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\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}