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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}
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