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+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\SquareMatrixXmpTitle}{SquareMatrix}
+\newcommand{\SquareMatrixXmpNumber}{9.74}
+%
+% =====================================================================
+\begin{page}{SquareMatrixXmpPage}{9.74 SquareMatrix}
+% =====================================================================
+\beginscroll
+ 
+The top level matrix type in \Language{} is \spadtype{Matrix}
+(see \downlink{`Matrix'}{MatrixXmpPage}\ignore{Matrix}), which
+provides basic arithmetic and linear algebra functions.
+However, since the matrices can be of any size it is not true that any pair
+can be added or multiplied.
+Thus \spadtype{Matrix} has little algebraic structure.
+ 
+Sometimes you want to use matrices as coefficients for polynomials
+or in other algebraic contexts.  In this case, \spadtype{SquareMatrix}
+%-% \HDindex{matrix!square}{SquareMatrixXmpPage}{9.74}{SquareMatrix}
+should be used.  The domain \spadtype{SquareMatrix(n,R)} gives the ring of
+\spad{n} by \spad{n} square matrices over \spad{R}.
+ 
+\xtc{
+Since \spadtype{SquareMatrix} is not normally exposed at the top level,
+you must expose it before it can be used.
+}{
+\spadpaste{)set expose add constructor SquareMatrix \bound{SQ}}
+}
+\xtc{
+Once \spad{SQMATRIX} has been exposed,
+values can be created using the \spadfunFrom{squareMatrix}{SquareMatrix}
+function.
+}{
+\spadpaste{m := squareMatrix [[1,-\%i],[\%i,4]] \bound{m}\free{SQ}}
+}
+\xtc{
+The usual arithmetic operations are available.
+}{
+\spadpaste{m*m - m \free{m}}
+}
+\xtc{
+Square matrices can be used where ring elements are required.
+For example, here is a matrix with matrix entries.
+}{
+\spadpaste{mm := squareMatrix [[m, 1], [1-m, m**2]] \free{m}\bound{mm}}
+}
+\xtc{
+Or you can construct a polynomial with  square matrix coefficients.
+}{
+\spadpaste{p := (x + m)**2 \free{m}\bound{p}}
+}
+\xtc{
+This value can be converted to a square matrix with polynomial coefficients.
+}{
+\spadpaste{p::SquareMatrix(2, ?) \free{p}}
+}
+ 
+For more information on related topics, see
+\downlink{``\ugTypesWritingModesTitle''}{ugTypesWritingModesPage} in Section \ugTypesWritingModesNumber\ignore{ugTypesWritingModes},
+\downlink{``\ugTypesExposeTitle''}{ugTypesExposePage} in Section \ugTypesExposeNumber\ignore{ugTypesExpose}, and
+\downlink{`Matrix'}{MatrixXmpPage}\ignore{Matrix}.
+\showBlurb{SquareMatrix}
+\endscroll
+\autobuttons
+\end{page}
+%