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\begin{patch}{IntegerLinearDependenceXmpPagePatch1}
\begin{paste}{IntegerLinearDependenceXmpPageFull1}{IntegerLinearDependenceXmpPageEmpty1}
\pastebutton{IntegerLinearDependenceXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{M := SQMATRIX(2,INT)\bound{M }}
\indentrel{3}\begin{verbatim}
(1) SquareMatrix(2,Integer)
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty1}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty1}{IntegerLinearDependenceXmpPagePatch1}
\pastebutton{IntegerLinearDependenceXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{M := SQMATRIX(2,INT)\bound{M }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch2}
\begin{paste}{IntegerLinearDependenceXmpPageFull2}{IntegerLinearDependenceXmpPageEmpty2}
\pastebutton{IntegerLinearDependenceXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{m1: M := squareMatrix matrix [[1, 2], [0, -1]]\free{M }\bound{m1 }}
\indentrel{3}\begin{verbatim}
�1 2 �
(2) � �
�0 - 1�
Type: SquareMatrix(2,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty2}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty2}{IntegerLinearDependenceXmpPagePatch2}
\pastebutton{IntegerLinearDependenceXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{m1: M := squareMatrix matrix [[1, 2], [0, -1]]\free{M }\bound{m1 }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch3}
\begin{paste}{IntegerLinearDependenceXmpPageFull3}{IntegerLinearDependenceXmpPageEmpty3}
\pastebutton{IntegerLinearDependenceXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{m2: M := squareMatrix matrix [[2, 3], [1, -2]]\free{M }\bound{m2 }}
\indentrel{3}\begin{verbatim}
�2 3 �
(3) � �
�1 - 2�
Type: SquareMatrix(2,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty3}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty3}{IntegerLinearDependenceXmpPagePatch3}
\pastebutton{IntegerLinearDependenceXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{m2: M := squareMatrix matrix [[2, 3], [1, -2]]\free{M }\bound{m2 }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch4}
\begin{paste}{IntegerLinearDependenceXmpPageFull4}{IntegerLinearDependenceXmpPageEmpty4}
\pastebutton{IntegerLinearDependenceXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{m3: M := squareMatrix matrix [[3, 4], [2, -3]]\free{M }\bound{m3 }}
\indentrel{3}\begin{verbatim}
�3 4 �
(4) � �
�2 - 3�
Type: SquareMatrix(2,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty4}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty4}{IntegerLinearDependenceXmpPagePatch4}
\pastebutton{IntegerLinearDependenceXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{m3: M := squareMatrix matrix [[3, 4], [2, -3]]\free{M }\bound{m3 }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch5}
\begin{paste}{IntegerLinearDependenceXmpPageFull5}{IntegerLinearDependenceXmpPageEmpty5}
\pastebutton{IntegerLinearDependenceXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{linearlyDependentOverZ? vector [m1, m2, m3]\free{m1 m2 m3 }}
\indentrel{3}\begin{verbatim}
(5) true
Type: Boolean
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty5}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty5}{IntegerLinearDependenceXmpPagePatch5}
\pastebutton{IntegerLinearDependenceXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{linearlyDependentOverZ? vector [m1, m2, m3]\free{m1 m2 m3 }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch6}
\begin{paste}{IntegerLinearDependenceXmpPageFull6}{IntegerLinearDependenceXmpPageEmpty6}
\pastebutton{IntegerLinearDependenceXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{c := linearDependenceOverZ vector [m1, m2, m3]\free{m1 m2 m3 }\bound{c }}
\indentrel{3}\begin{verbatim}
(6) [1,- 2,1]
Type: Union(Vector Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty6}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty6}{IntegerLinearDependenceXmpPagePatch6}
\pastebutton{IntegerLinearDependenceXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{c := linearDependenceOverZ vector [m1, m2, m3]\free{m1 m2 m3 }\bound{c }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch7}
\begin{paste}{IntegerLinearDependenceXmpPageFull7}{IntegerLinearDependenceXmpPageEmpty7}
\pastebutton{IntegerLinearDependenceXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{c.1 * m1 + c.2 * m2 + c.3 * m3\free{c m1 m2 m3 }}
\indentrel{3}\begin{verbatim}
�0 0�
(7) � �
�0 0�
Type: SquareMatrix(2,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty7}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty7}{IntegerLinearDependenceXmpPagePatch7}
\pastebutton{IntegerLinearDependenceXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{c.1 * m1 + c.2 * m2 + c.3 * m3\free{c m1 m2 m3 }}
\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPagePatch8}
\begin{paste}{IntegerLinearDependenceXmpPageFull8}{IntegerLinearDependenceXmpPageEmpty8}
\pastebutton{IntegerLinearDependenceXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{solveLinearlyOverQ(vector [m1, m3], m2)\free{m1 m2 m3 }}
\indentrel{3}\begin{verbatim}
1 1
(8) [�,�]
2 2
Type: Union(Vector Fraction Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{IntegerLinearDependenceXmpPageEmpty8}
\begin{paste}{IntegerLinearDependenceXmpPageEmpty8}{IntegerLinearDependenceXmpPagePatch8}
\pastebutton{IntegerLinearDependenceXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{solveLinearlyOverQ(vector [m1, m3], m2)\free{m1 m2 m3 }}
\end{paste}\end{patch}
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