\begin{patch}{ugxMatrixOpsPagePatch1}
\begin{paste}{ugxMatrixOpsPageFull1}{ugxMatrixOpsPageEmpty1}
\pastebutton{ugxMatrixOpsPageFull1}{\hidepaste}
\tab{5}\spadcommand{m := matrix [[1,2],[3,4]]\bound{m }}
\indentrel{3}\begin{verbatim}
        Ú1  2¿
   (1)  ³    ³
        À3  4Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty1}
\begin{paste}{ugxMatrixOpsPageEmpty1}{ugxMatrixOpsPagePatch1}
\pastebutton{ugxMatrixOpsPageEmpty1}{\showpaste}
\tab{5}\spadcommand{m := matrix [[1,2],[3,4]]\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch2}
\begin{paste}{ugxMatrixOpsPageFull2}{ugxMatrixOpsPageEmpty2}
\pastebutton{ugxMatrixOpsPageFull2}{\hidepaste}
\tab{5}\spadcommand{4 * m * (-5)\free{m }}
\indentrel{3}\begin{verbatim}
        Ú- 20  - 40¿
   (2)  ³          ³
        À- 60  - 80Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty2}
\begin{paste}{ugxMatrixOpsPageEmpty2}{ugxMatrixOpsPagePatch2}
\pastebutton{ugxMatrixOpsPageEmpty2}{\showpaste}
\tab{5}\spadcommand{4 * m * (-5)\free{m }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch3}
\begin{paste}{ugxMatrixOpsPageFull3}{ugxMatrixOpsPageEmpty3}
\pastebutton{ugxMatrixOpsPageFull3}{\hidepaste}
\tab{5}\spadcommand{n := matrix([[1,0,-2],[-3,5,1]])\bound{n }}
\indentrel{3}\begin{verbatim}
        Ú 1   0  - 2¿
   (3)  ³           ³
        À- 3  5   1 Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty3}
\begin{paste}{ugxMatrixOpsPageEmpty3}{ugxMatrixOpsPagePatch3}
\pastebutton{ugxMatrixOpsPageEmpty3}{\showpaste}
\tab{5}\spadcommand{n := matrix([[1,0,-2],[-3,5,1]])\bound{n }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch4}
\begin{paste}{ugxMatrixOpsPageFull4}{ugxMatrixOpsPageEmpty4}
\pastebutton{ugxMatrixOpsPageFull4}{\hidepaste}
\tab{5}\spadcommand{m * n\free{m n }}
\indentrel{3}\begin{verbatim}
        Ú- 5  10   0 ¿
   (4)  ³            ³
        À- 9  20  - 2Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty4}
\begin{paste}{ugxMatrixOpsPageEmpty4}{ugxMatrixOpsPagePatch4}
\pastebutton{ugxMatrixOpsPageEmpty4}{\showpaste}
\tab{5}\spadcommand{m * n\free{m n }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch5}
\begin{paste}{ugxMatrixOpsPageFull5}{ugxMatrixOpsPageEmpty5}
\pastebutton{ugxMatrixOpsPageFull5}{\hidepaste}
\tab{5}\spadcommand{vec := column(n,3)\free{n }\bound{vec }}
\indentrel{3}\begin{verbatim}
   (5)  [- 2,1]
                                   Type: Vector Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty5}
\begin{paste}{ugxMatrixOpsPageEmpty5}{ugxMatrixOpsPagePatch5}
\pastebutton{ugxMatrixOpsPageEmpty5}{\showpaste}
\tab{5}\spadcommand{vec := column(n,3)\free{n }\bound{vec }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch6}
\begin{paste}{ugxMatrixOpsPageFull6}{ugxMatrixOpsPageEmpty6}
\pastebutton{ugxMatrixOpsPageFull6}{\hidepaste}
\tab{5}\spadcommand{vec * m\free{vec m }}
\indentrel{3}\begin{verbatim}
   (6)  [1,0]
                                   Type: Vector Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty6}
\begin{paste}{ugxMatrixOpsPageEmpty6}{ugxMatrixOpsPagePatch6}
\pastebutton{ugxMatrixOpsPageEmpty6}{\showpaste}
\tab{5}\spadcommand{vec * m\free{vec m }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch7}
\begin{paste}{ugxMatrixOpsPageFull7}{ugxMatrixOpsPageEmpty7}
\pastebutton{ugxMatrixOpsPageFull7}{\hidepaste}
\tab{5}\spadcommand{m * vec\free{vec m }}
\indentrel{3}\begin{verbatim}
   (7)  [0,- 2]
                                   Type: Vector Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty7}
\begin{paste}{ugxMatrixOpsPageEmpty7}{ugxMatrixOpsPagePatch7}
\pastebutton{ugxMatrixOpsPageEmpty7}{\showpaste}
\tab{5}\spadcommand{m * vec\free{vec m }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch8}
\begin{paste}{ugxMatrixOpsPageFull8}{ugxMatrixOpsPageEmpty8}
\pastebutton{ugxMatrixOpsPageFull8}{\hidepaste}
\tab{5}\spadcommand{hilb := matrix([[1/(i + j) for i in 1..3] for j in 1..3])\bound{hilb }}
\indentrel{3}\begin{verbatim}
        Ú1  1  1¿
        ³Ä  Ä  ij
        ³2  3  4³
        ³       ³
        ³1  1  1³
   (8)  ³Ä  Ä  ij
        ³3  4  5³
        ³       ³
        ³1  1  1³
        ³Ä  Ä  ij
        À4  5  6Ù
                          Type: Matrix Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty8}
\begin{paste}{ugxMatrixOpsPageEmpty8}{ugxMatrixOpsPagePatch8}
\pastebutton{ugxMatrixOpsPageEmpty8}{\showpaste}
\tab{5}\spadcommand{hilb := matrix([[1/(i + j) for i in 1..3] for j in 1..3])\bound{hilb }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch9}
\begin{paste}{ugxMatrixOpsPageFull9}{ugxMatrixOpsPageEmpty9}
\pastebutton{ugxMatrixOpsPageFull9}{\hidepaste}
\tab{5}\spadcommand{inverse(hilb)\free{hilb }}
\indentrel{3}\begin{verbatim}
        Ú 72    - 240   180 ¿
        ³                   ³
   (9)  ³- 240   900   - 720³
        ³                   ³
        À 180   - 720   600 Ù
               Type: Union(Matrix Fraction Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty9}
\begin{paste}{ugxMatrixOpsPageEmpty9}{ugxMatrixOpsPagePatch9}
\pastebutton{ugxMatrixOpsPageEmpty9}{\showpaste}
\tab{5}\spadcommand{inverse(hilb)\free{hilb }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch10}
\begin{paste}{ugxMatrixOpsPageFull10}{ugxMatrixOpsPageEmpty10}
\pastebutton{ugxMatrixOpsPageFull10}{\hidepaste}
\tab{5}\spadcommand{mm := matrix([[1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16]])\bound{mm }}
\indentrel{3}\begin{verbatim}
         Ú1   2   3   4 ¿
         ³              ³
         ³5   6   7   8 ³
   (10)  ³              ³
         ³9   10  11  12³
         ³              ³
         À13  14  15  16Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty10}
\begin{paste}{ugxMatrixOpsPageEmpty10}{ugxMatrixOpsPagePatch10}
\pastebutton{ugxMatrixOpsPageEmpty10}{\showpaste}
\tab{5}\spadcommand{mm := matrix([[1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16]])\bound{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch11}
\begin{paste}{ugxMatrixOpsPageFull11}{ugxMatrixOpsPageEmpty11}
\pastebutton{ugxMatrixOpsPageFull11}{\hidepaste}
\tab{5}\spadcommand{inverse(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
   (11)  "failed"
                              Type: Union("failed",...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty11}
\begin{paste}{ugxMatrixOpsPageEmpty11}{ugxMatrixOpsPagePatch11}
\pastebutton{ugxMatrixOpsPageEmpty11}{\showpaste}
\tab{5}\spadcommand{inverse(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch12}
\begin{paste}{ugxMatrixOpsPageFull12}{ugxMatrixOpsPageEmpty12}
\pastebutton{ugxMatrixOpsPageFull12}{\hidepaste}
\tab{5}\spadcommand{determinant(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
   (12)  0
                               Type: NonNegativeInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty12}
\begin{paste}{ugxMatrixOpsPageEmpty12}{ugxMatrixOpsPagePatch12}
\pastebutton{ugxMatrixOpsPageEmpty12}{\showpaste}
\tab{5}\spadcommand{determinant(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch13}
\begin{paste}{ugxMatrixOpsPageFull13}{ugxMatrixOpsPageEmpty13}
\pastebutton{ugxMatrixOpsPageFull13}{\hidepaste}
\tab{5}\spadcommand{trace(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
   (13)  34
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty13}
\begin{paste}{ugxMatrixOpsPageEmpty13}{ugxMatrixOpsPagePatch13}
\pastebutton{ugxMatrixOpsPageEmpty13}{\showpaste}
\tab{5}\spadcommand{trace(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch14}
\begin{paste}{ugxMatrixOpsPageFull14}{ugxMatrixOpsPageEmpty14}
\pastebutton{ugxMatrixOpsPageFull14}{\hidepaste}
\tab{5}\spadcommand{rank(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
   (14)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty14}
\begin{paste}{ugxMatrixOpsPageEmpty14}{ugxMatrixOpsPagePatch14}
\pastebutton{ugxMatrixOpsPageEmpty14}{\showpaste}
\tab{5}\spadcommand{rank(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch15}
\begin{paste}{ugxMatrixOpsPageFull15}{ugxMatrixOpsPageEmpty15}
\pastebutton{ugxMatrixOpsPageFull15}{\hidepaste}
\tab{5}\spadcommand{nullity(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
   (15)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty15}
\begin{paste}{ugxMatrixOpsPageEmpty15}{ugxMatrixOpsPagePatch15}
\pastebutton{ugxMatrixOpsPageEmpty15}{\showpaste}
\tab{5}\spadcommand{nullity(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch16}
\begin{paste}{ugxMatrixOpsPageFull16}{ugxMatrixOpsPageEmpty16}
\pastebutton{ugxMatrixOpsPageFull16}{\hidepaste}
\tab{5}\spadcommand{nullSpace(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
   (16)  [[1,- 2,1,0],[2,- 3,0,1]]
                              Type: List Vector Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty16}
\begin{paste}{ugxMatrixOpsPageEmpty16}{ugxMatrixOpsPagePatch16}
\pastebutton{ugxMatrixOpsPageEmpty16}{\showpaste}
\tab{5}\spadcommand{nullSpace(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPagePatch17}
\begin{paste}{ugxMatrixOpsPageFull17}{ugxMatrixOpsPageEmpty17}
\pastebutton{ugxMatrixOpsPageFull17}{\hidepaste}
\tab{5}\spadcommand{rowEchelon(mm)\free{mm }}
\indentrel{3}\begin{verbatim}
         Ú1  2  3  4 ¿
         ³           ³
         ³0  4  8  12³
   (17)  ³           ³
         ³0  0  0  0 ³
         ³           ³
         À0  0  0  0 Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixOpsPageEmpty17}
\begin{paste}{ugxMatrixOpsPageEmpty17}{ugxMatrixOpsPagePatch17}
\pastebutton{ugxMatrixOpsPageEmpty17}{\showpaste}
\tab{5}\spadcommand{rowEchelon(mm)\free{mm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch1}
\begin{paste}{ugxMatrixCreatePageFull1}{ugxMatrixCreatePageEmpty1}
\pastebutton{ugxMatrixCreatePageFull1}{\hidepaste}
\tab{5}\spadcommand{m : Matrix(Integer) := new(3,3,0)\bound{m }}
\indentrel{3}\begin{verbatim}
        Ú0  0  0¿
        ³       ³
   (1)  ³0  0  0³
        ³       ³
        À0  0  0Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty1}
\begin{paste}{ugxMatrixCreatePageEmpty1}{ugxMatrixCreatePagePatch1}
\pastebutton{ugxMatrixCreatePageEmpty1}{\showpaste}
\tab{5}\spadcommand{m : Matrix(Integer) := new(3,3,0)\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch2}
\begin{paste}{ugxMatrixCreatePageFull2}{ugxMatrixCreatePageEmpty2}
\pastebutton{ugxMatrixCreatePageFull2}{\hidepaste}
\tab{5}\spadcommand{setelt(m,2,3,5)\free{m }\bound{m1 }}
\indentrel{3}\begin{verbatim}
   (2)  5
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty2}
\begin{paste}{ugxMatrixCreatePageEmpty2}{ugxMatrixCreatePagePatch2}
\pastebutton{ugxMatrixCreatePageEmpty2}{\showpaste}
\tab{5}\spadcommand{setelt(m,2,3,5)\free{m }\bound{m1 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch3}
\begin{paste}{ugxMatrixCreatePageFull3}{ugxMatrixCreatePageEmpty3}
\pastebutton{ugxMatrixCreatePageFull3}{\hidepaste}
\tab{5}\spadcommand{m(1,2) := 10\free{m1 }\bound{m2 }}
\indentrel{3}\begin{verbatim}
   (3)  10
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty3}
\begin{paste}{ugxMatrixCreatePageEmpty3}{ugxMatrixCreatePagePatch3}
\pastebutton{ugxMatrixCreatePageEmpty3}{\showpaste}
\tab{5}\spadcommand{m(1,2) := 10\free{m1 }\bound{m2 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch4}
\begin{paste}{ugxMatrixCreatePageFull4}{ugxMatrixCreatePageEmpty4}
\pastebutton{ugxMatrixCreatePageFull4}{\hidepaste}
\tab{5}\spadcommand{m\free{m2 }}
\indentrel{3}\begin{verbatim}
        Ú0  10  0¿
        ³        ³
   (4)  ³0  0   5³
        ³        ³
        À0  0   0Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty4}
\begin{paste}{ugxMatrixCreatePageEmpty4}{ugxMatrixCreatePagePatch4}
\pastebutton{ugxMatrixCreatePageEmpty4}{\showpaste}
\tab{5}\spadcommand{m\free{m2 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch5}
\begin{paste}{ugxMatrixCreatePageFull5}{ugxMatrixCreatePageEmpty5}
\pastebutton{ugxMatrixCreatePageFull5}{\hidepaste}
\tab{5}\spadcommand{matrix [[1,2,3,4],[0,9,8,7]]}
\indentrel{3}\begin{verbatim}
        Ú1  2  3  4¿
   (5)  ³          ³
        À0  9  8  7Ù
                                   Type: Matrix Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty5}
\begin{paste}{ugxMatrixCreatePageEmpty5}{ugxMatrixCreatePagePatch5}
\pastebutton{ugxMatrixCreatePageEmpty5}{\showpaste}
\tab{5}\spadcommand{matrix [[1,2,3,4],[0,9,8,7]]}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch6}
\begin{paste}{ugxMatrixCreatePageFull6}{ugxMatrixCreatePageEmpty6}
\pastebutton{ugxMatrixCreatePageFull6}{\hidepaste}
\tab{5}\spadcommand{dm := diagonalMatrix [1,x**2,x**3,x**4,x**5]\bound{dm }}
\indentrel{3}\begin{verbatim}
        Ú1  0   0   0   0 ¿
        ³                 ³
        ³    2            ³
        ³0  x   0   0   0 ³
        ³                 ³
        ³        3        ³
   (6)  ³0  0   x   0   0 ³
        ³                 ³
        ³            4    ³
        ³0  0   0   x   0 ³
        ³                 ³
        ³                5³
        À0  0   0   0   x Ù
                        Type: Matrix Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty6}
\begin{paste}{ugxMatrixCreatePageEmpty6}{ugxMatrixCreatePagePatch6}
\pastebutton{ugxMatrixCreatePageEmpty6}{\showpaste}
\tab{5}\spadcommand{dm := diagonalMatrix [1,x**2,x**3,x**4,x**5]\bound{dm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch7}
\begin{paste}{ugxMatrixCreatePageFull7}{ugxMatrixCreatePageEmpty7}
\pastebutton{ugxMatrixCreatePageFull7}{\hidepaste}
\tab{5}\spadcommand{setRow!(dm,5,vector [1,1,1,1,1])\free{dm }\bound{dm1 }}
\indentrel{3}\begin{verbatim}
        Ú1  0   0   0   0¿
        ³                ³
        ³    2           ³
        ³0  x   0   0   0³
        ³                ³
   (7)  ³        3       ³
        ³0  0   x   0   0³
        ³                ³
        ³            4   ³
        ³0  0   0   x   0³
        ³                ³
        À1  1   1   1   1Ù
                        Type: Matrix Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty7}
\begin{paste}{ugxMatrixCreatePageEmpty7}{ugxMatrixCreatePagePatch7}
\pastebutton{ugxMatrixCreatePageEmpty7}{\showpaste}
\tab{5}\spadcommand{setRow!(dm,5,vector [1,1,1,1,1])\free{dm }\bound{dm1 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch8}
\begin{paste}{ugxMatrixCreatePageFull8}{ugxMatrixCreatePageEmpty8}
\pastebutton{ugxMatrixCreatePageFull8}{\hidepaste}
\tab{5}\spadcommand{setColumn!(dm,2,vector [y,y,y,y,y])\free{dm1 }\bound{dm2 }}
\indentrel{3}\begin{verbatim}
        Ú1  y  0   0   0¿
        ³               ³
        ³0  y  0   0   0³
        ³               ³
        ³       3       ³
   (8)  ³0  y  x   0   0³
        ³               ³
        ³           4   ³
        ³0  y  0   x   0³
        ³               ³
        À1  y  1   1   1Ù
                        Type: Matrix Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty8}
\begin{paste}{ugxMatrixCreatePageEmpty8}{ugxMatrixCreatePagePatch8}
\pastebutton{ugxMatrixCreatePageEmpty8}{\showpaste}
\tab{5}\spadcommand{setColumn!(dm,2,vector [y,y,y,y,y])\free{dm1 }\bound{dm2 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch9}
\begin{paste}{ugxMatrixCreatePageFull9}{ugxMatrixCreatePageEmpty9}
\pastebutton{ugxMatrixCreatePageFull9}{\hidepaste}
\tab{5}\spadcommand{cdm := copy(dm)\free{dm2 }\bound{cdm }}
\indentrel{3}\begin{verbatim}
        Ú1  y  0   0   0¿
        ³               ³
        ³0  y  0   0   0³
        ³               ³
        ³       3       ³
   (9)  ³0  y  x   0   0³
        ³               ³
        ³           4   ³
        ³0  y  0   x   0³
        ³               ³
        À1  y  1   1   1Ù
                        Type: Matrix Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty9}
\begin{paste}{ugxMatrixCreatePageEmpty9}{ugxMatrixCreatePagePatch9}
\pastebutton{ugxMatrixCreatePageEmpty9}{\showpaste}
\tab{5}\spadcommand{cdm := copy(dm)\free{dm2 }\bound{cdm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch10}
\begin{paste}{ugxMatrixCreatePageFull10}{ugxMatrixCreatePageEmpty10}
\pastebutton{ugxMatrixCreatePageFull10}{\hidepaste}
\tab{5}\spadcommand{setelt(dm,4,1,1-x**7)\free{dm2 }\bound{setdm }}
\indentrel{3}\begin{verbatim}
            7
   (10)  - x  + 1
                               Type: Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty10}
\begin{paste}{ugxMatrixCreatePageEmpty10}{ugxMatrixCreatePagePatch10}
\pastebutton{ugxMatrixCreatePageEmpty10}{\showpaste}
\tab{5}\spadcommand{setelt(dm,4,1,1-x**7)\free{dm2 }\bound{setdm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch11}
\begin{paste}{ugxMatrixCreatePageFull11}{ugxMatrixCreatePageEmpty11}
\pastebutton{ugxMatrixCreatePageFull11}{\hidepaste}
\tab{5}\spadcommand{[dm,cdm]\free{setdm cdm }}
\indentrel{3}\begin{verbatim}
          Ú   1      y  0   0   0¿ Ú1  y  0   0   0¿
          ³                      ³ ³               ³
          ³   0      y  0   0   0³ ³0  y  0   0   0³
          ³                      ³ ³               ³
          ³              3       ³ ³       3       ³
   (11)  [³   0      y  x   0   0³,³0  y  x   0   0³]
          ³                      ³ ³               ³
          ³   7              4   ³ ³           4   ³
          ³- x  + 1  y  0   x   0³ ³0  y  0   x   0³
          ³                      ³ ³               ³
          À   1      y  1   1   1Ù À1  y  1   1   1Ù
                   Type: List Matrix Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty11}
\begin{paste}{ugxMatrixCreatePageEmpty11}{ugxMatrixCreatePagePatch11}
\pastebutton{ugxMatrixCreatePageEmpty11}{\showpaste}
\tab{5}\spadcommand{[dm,cdm]\free{setdm cdm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch12}
\begin{paste}{ugxMatrixCreatePageFull12}{ugxMatrixCreatePageEmpty12}
\pastebutton{ugxMatrixCreatePageFull12}{\hidepaste}
\tab{5}\spadcommand{subMatrix(dm,2,3,2,4)\free{setdm }}
\indentrel{3}\begin{verbatim}
         Úy  0   0¿
   (12)  ³        ³
         ³    3   ³
         Ày  x   0Ù
                        Type: Matrix Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty12}
\begin{paste}{ugxMatrixCreatePageEmpty12}{ugxMatrixCreatePagePatch12}
\pastebutton{ugxMatrixCreatePageEmpty12}{\showpaste}
\tab{5}\spadcommand{subMatrix(dm,2,3,2,4)\free{setdm }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch13}
\begin{paste}{ugxMatrixCreatePageFull13}{ugxMatrixCreatePageEmpty13}
\pastebutton{ugxMatrixCreatePageFull13}{\hidepaste}
\tab{5}\spadcommand{d := diagonalMatrix [1.2,-1.3,1.4,-1.5]\bound{d }}
\indentrel{3}\begin{verbatim}
         Ú1.2   0.0   0.0   0.0 ¿
         ³                      ³
         ³0.0  - 1.3  0.0   0.0 ³
   (13)  ³                      ³
         ³0.0   0.0   1.4   0.0 ³
         ³                      ³
         À0.0   0.0   0.0  - 1.5Ù
                                     Type: Matrix Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty13}
\begin{paste}{ugxMatrixCreatePageEmpty13}{ugxMatrixCreatePagePatch13}
\pastebutton{ugxMatrixCreatePageEmpty13}{\showpaste}
\tab{5}\spadcommand{d := diagonalMatrix [1.2,-1.3,1.4,-1.5]\bound{d }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch14}
\begin{paste}{ugxMatrixCreatePageFull14}{ugxMatrixCreatePageEmpty14}
\pastebutton{ugxMatrixCreatePageFull14}{\hidepaste}
\tab{5}\spadcommand{e := matrix [[6.7,9.11],[-31.33,67.19]]\bound{e }}
\indentrel{3}\begin{verbatim}
         Ú  6.7    9.11 ¿
   (14)  ³              ³
         À- 31.33  67.19Ù
                                     Type: Matrix Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty14}
\begin{paste}{ugxMatrixCreatePageEmpty14}{ugxMatrixCreatePagePatch14}
\pastebutton{ugxMatrixCreatePageEmpty14}{\showpaste}
\tab{5}\spadcommand{e := matrix [[6.7,9.11],[-31.33,67.19]]\bound{e }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch15}
\begin{paste}{ugxMatrixCreatePageFull15}{ugxMatrixCreatePageEmpty15}
\pastebutton{ugxMatrixCreatePageFull15}{\hidepaste}
\tab{5}\spadcommand{setsubMatrix!(d,1,2,e)\free{d e }\bound{d1 }}
\indentrel{3}\begin{verbatim}
         Ú1.2    6.7    9.11    0.0 ¿
         ³                          ³
         ³0.0  - 31.33  67.19   0.0 ³
   (15)  ³                          ³
         ³0.0    0.0     1.4    0.0 ³
         ³                          ³
         À0.0    0.0     0.0   - 1.5Ù
                                     Type: Matrix Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty15}
\begin{paste}{ugxMatrixCreatePageEmpty15}{ugxMatrixCreatePagePatch15}
\pastebutton{ugxMatrixCreatePageEmpty15}{\showpaste}
\tab{5}\spadcommand{setsubMatrix!(d,1,2,e)\free{d e }\bound{d1 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch16}
\begin{paste}{ugxMatrixCreatePageFull16}{ugxMatrixCreatePageEmpty16}
\pastebutton{ugxMatrixCreatePageFull16}{\hidepaste}
\tab{5}\spadcommand{d\free{d1 }}
\indentrel{3}\begin{verbatim}
         Ú1.2    6.7    9.11    0.0 ¿
         ³                          ³
         ³0.0  - 31.33  67.19   0.0 ³
   (16)  ³                          ³
         ³0.0    0.0     1.4    0.0 ³
         ³                          ³
         À0.0    0.0     0.0   - 1.5Ù
                                     Type: Matrix Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty16}
\begin{paste}{ugxMatrixCreatePageEmpty16}{ugxMatrixCreatePagePatch16}
\pastebutton{ugxMatrixCreatePageEmpty16}{\showpaste}
\tab{5}\spadcommand{d\free{d1 }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch17}
\begin{paste}{ugxMatrixCreatePageFull17}{ugxMatrixCreatePageEmpty17}
\pastebutton{ugxMatrixCreatePageFull17}{\hidepaste}
\tab{5}\spadcommand{a := matrix [[1/2,1/3,1/4],[1/5,1/6,1/7]]\bound{a }}
\indentrel{3}\begin{verbatim}
         Ú1  1  1¿
         ³Ä  Ä  ij
         ³2  3  4³
   (17)  ³       ³
         ³1  1  1³
         ³Ä  Ä  ij
         À5  6  7Ù
                          Type: Matrix Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty17}
\begin{paste}{ugxMatrixCreatePageEmpty17}{ugxMatrixCreatePagePatch17}
\pastebutton{ugxMatrixCreatePageEmpty17}{\showpaste}
\tab{5}\spadcommand{a := matrix [[1/2,1/3,1/4],[1/5,1/6,1/7]]\bound{a }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch18}
\begin{paste}{ugxMatrixCreatePageFull18}{ugxMatrixCreatePageEmpty18}
\pastebutton{ugxMatrixCreatePageFull18}{\hidepaste}
\tab{5}\spadcommand{b := matrix [[3/5,3/7,3/11],[3/13,3/17,3/19]]\bound{b }}
\indentrel{3}\begin{verbatim}
         Ú3   3    3¿
         ³Ä   Ä   Äij
         ³5   7   11³
   (18)  ³          ³
         ³ 3   3   3³
         ³ÄÄ  ÄÄ  Äij
         À13  17  19Ù
                          Type: Matrix Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty18}
\begin{paste}{ugxMatrixCreatePageEmpty18}{ugxMatrixCreatePagePatch18}
\pastebutton{ugxMatrixCreatePageEmpty18}{\showpaste}
\tab{5}\spadcommand{b := matrix [[3/5,3/7,3/11],[3/13,3/17,3/19]]\bound{b }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch19}
\begin{paste}{ugxMatrixCreatePageFull19}{ugxMatrixCreatePageEmpty19}
\pastebutton{ugxMatrixCreatePageFull19}{\hidepaste}
\tab{5}\spadcommand{horizConcat(a,b)\free{a b }}
\indentrel{3}\begin{verbatim}
         Ú1  1  1  3   3    3¿
         ³Ä  Ä  Ä  Ä   Ä   Äij
         ³2  3  4  5   7   11³
   (19)  ³                   ³
         ³1  1  1   3   3   3³
         ³Ä  Ä  Ä  ÄÄ  ÄÄ  Äij
         À5  6  7  13  17  19Ù
                          Type: Matrix Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty19}
\begin{paste}{ugxMatrixCreatePageEmpty19}{ugxMatrixCreatePagePatch19}
\pastebutton{ugxMatrixCreatePageEmpty19}{\showpaste}
\tab{5}\spadcommand{horizConcat(a,b)\free{a b }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch20}
\begin{paste}{ugxMatrixCreatePageFull20}{ugxMatrixCreatePageEmpty20}
\pastebutton{ugxMatrixCreatePageFull20}{\hidepaste}
\tab{5}\spadcommand{vab := vertConcat(a,b)\free{a b }\bound{vab }}
\indentrel{3}\begin{verbatim}
         Ú1   1   1 ¿
         ³Ä   Ä   Ä ³
         ³2   3   4 ³
         ³          ³
         ³1   1   1 ³
         ³Ä   Ä   Ä ³
         ³5   6   7 ³
   (20)  ³          ³
         ³3   3    3³
         ³Ä   Ä   Äij
         ³5   7   11³
         ³          ³
         ³ 3   3   3³
         ³ÄÄ  ÄÄ  Äij
         À13  17  19Ù
                          Type: Matrix Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty20}
\begin{paste}{ugxMatrixCreatePageEmpty20}{ugxMatrixCreatePagePatch20}
\pastebutton{ugxMatrixCreatePageEmpty20}{\showpaste}
\tab{5}\spadcommand{vab := vertConcat(a,b)\free{a b }\bound{vab }}
\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePagePatch21}
\begin{paste}{ugxMatrixCreatePageFull21}{ugxMatrixCreatePageEmpty21}
\pastebutton{ugxMatrixCreatePageFull21}{\hidepaste}
\tab{5}\spadcommand{transpose vab\free{vab }}
\indentrel{3}\begin{verbatim}
         Ú1  1  3    3¿
         ³Ä  Ä  Ä   Äij
         ³2  5  5   13³
         ³            ³
         ³1  1  3    3³
   (21)  ³Ä  Ä  Ä   Äij
         ³3  6  7   17³
         ³            ³
         ³1  1   3   3³
         ³Ä  Ä  ÄÄ  Äij
         À4  7  11  19Ù
                          Type: Matrix Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxMatrixCreatePageEmpty21}
\begin{paste}{ugxMatrixCreatePageEmpty21}{ugxMatrixCreatePagePatch21}
\pastebutton{ugxMatrixCreatePageEmpty21}{\showpaste}
\tab{5}\spadcommand{transpose vab\free{vab }}
\end{paste}\end{patch}