\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: Type
\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)  [particular = [-, -], basis = []]
                       2  2
Type: Record(particular: Union(Vector(Fraction(Integer)),"failed"),basis: List(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}

