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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/lindep.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input lindep.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
+v(i:INT):DIRPROD(5, FRAC INT) ==
+ directProduct vector [i / (i + j) for j in 0..4]
+-- Create several elements of Q^5
+V := vector [v i for i in 1..6]
+-- Are they linearly dependent over Z?
+linearlyDependentOverZ? V
+-- Get the linear dependence relation over Z explicitly
+linearDependenceOverZ V
+-- the Vi's are linearly dependent, express V.2 in terms of the others
+solveLinearlyOverQ(delete(V, 2), V.2)
+w(i:INT):SQMATRIX(2, INT) ==
+ squareMatrix matrix [[i, i + 1], [i - 1, -i]]
+-- Create several elements of Z(2)
+W := vector [w i for i in 1..3]
+-- Are they linearly dependent over Z?
+linearlyDependentOverZ? W
+-- Get the linear dependence relation over Z explicitly
+linearDependenceOverZ W
+-- the Wi's are linearly dependent, express W.2 in terms of the others
+solveLinearlyOverQ(delete(W, 2), W.2)
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}