Initial population.

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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input matrix.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
+ 
+-- A number of matrix computations over the integers and over the
+-- rationals using various algortihms and indexing schemes.
+ 
+-- Hilbert matrix
+ 
+mat : MATRIX FRAC INT := matrix [[1/(i + j) for i in 1..5] for j in 1..5]
+matinv := inverse mat
+mat * matinv
+ 
+-- same computation, different indexing
+ 
+mat1 : IMATRIX(FRAC INT,-3,47) := _
+   matrix [[1/(i + j) for i in 1..5] for j in 1..5]
+mat1inv := inverse mat1
+mat1 * mat1inv
+ 
+-- Vandermonde determinant
+ 
+mat2 : MATRIX INT := matrix [[j**i for i in 0..4] for j in 1..5]
+rowEchelon  mat2
+determinant mat2
+minordet    mat2
+ 
+-- same computation, different indexing
+ 
+mat3 : IMATRIX(INT,13,-7) := _
+   matrix [[j**i for i in 0..4] for j in 1..5]
+rowEchelon  mat3
+determinant mat3
+minordet    mat3
+ 
+-- same computation, work over the rationals
+ 
+mat4 : MATRIX FRAC INT := matrix [[j**i for i in 0..4] for j in 1..5]
+rowEchelon  mat4
+determinant mat4
+minordet    mat4
+ 
+-- same computation, different indexing
+ 
+mat5 : IMATRIX(FRAC INT,-113,37) := _
+   matrix [[j**i for i in 0..4] for j in 1..5]
+rowEchelon  mat5
+determinant mat5
+minordet    mat5
+ 
+mat6 : MATRIX INT := matrix [[1,2,3],[4,5,6],[7,8,9]]
+rowEchelon mat6
+rank       mat6
+nullity    mat6
+nullSpace  mat6
+ 
+mat7 : IMATRIX(FRAC INT,163,61657) := matrix [[1,2,3],[4,5,6],[7,8,9]]
+rowEchelon mat7
+rank       mat7
+nullity    mat7
+nullSpace  mat7
+ 
+mat8 : MATRIX INT := _
+ matrix [[1,-2,13,0,5,-47],[-4,15,0,16,-2,1],[-7,0,8,-11,9,0]]
+rowEchelon mat8
+rank       mat8
+nullity    mat8
+nullSpace  mat8
+ 
+mat9 : IMATRIX(FRAC INT,163,61657) := _
+ matrix [[1,-2,13,0,5,-47],[-4,15,0,16,-2,1],[-7,0,8,-11,9,0]]
+rowEchelon mat9
+rank       mat9
+nullity    mat9
+nullSpace  mat9
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}