\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch1}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull1}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty1}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull1}{\hidepaste}
\tab{5}\spadcommand{Q := Fraction Integer\bound{Q }}
\indentrel{3}\begin{verbatim}
   (1)  Fraction(Integer)
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty1}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty1}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch1}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty1}{\showpaste}
\tab{5}\spadcommand{Q := Fraction Integer\bound{Q }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch2}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull2}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty2}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull2}{\hidepaste}
\tab{5}\spadcommand{PQ := UnivariatePolynomial('x, Q)\free{Q }\bound{PQ0 }}
\indentrel{3}\begin{verbatim}
   (2)  UnivariatePolynomial(x,Fraction(Integer))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty2}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty2}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch2}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty2}{\showpaste}
\tab{5}\spadcommand{PQ := UnivariatePolynomial('x, Q)\free{Q }\bound{PQ0 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch3}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull3}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty3}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull3}{\hidepaste}
\tab{5}\spadcommand{x: PQ := 'x\free{PQ0 }\bound{x }}
\indentrel{3}\begin{verbatim}
   (3)  x
        Type: UnivariatePolynomial(x,Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty3}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty3}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch3}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty3}{\showpaste}
\tab{5}\spadcommand{x: PQ := 'x\free{PQ0 }\bound{x }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch4}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull4}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty4}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull4}{\hidepaste}
\tab{5}\spadcommand{Dx: LODO2(Q, PQ) := D()\free{Q PQ0 }\bound{Dx }}
\indentrel{3}\begin{verbatim}
   (4)  D
Type: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty4}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty4}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch4}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty4}{\showpaste}
\tab{5}\spadcommand{Dx: LODO2(Q, PQ) := D()\free{Q PQ0 }\bound{Dx }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch5}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull5}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty5}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull5}{\hidepaste}
\tab{5}\spadcommand{a := Dx + 1\bound{a }\free{Dx }}
\indentrel{3}\begin{verbatim}
   (5)  D + 1
Type: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty5}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty5}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch5}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty5}{\showpaste}
\tab{5}\spadcommand{a := Dx + 1\bound{a }\free{Dx }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch6}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull6}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty6}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull6}{\hidepaste}
\tab{5}\spadcommand{b := a + 1/2*Dx^2 - 1/2\bound{b }\free{Dx }}
\indentrel{3}\begin{verbatim}
        1  2       1
   (6)  - D  + D + -
        2          2
Type: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty6}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty6}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch6}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty6}{\showpaste}
\tab{5}\spadcommand{b := a + 1/2*Dx^2 - 1/2\bound{b }\free{Dx }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch7}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull7}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty7}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull7}{\hidepaste}
\tab{5}\spadcommand{p := 4*x^2 + 2/3\free{x }\bound{p }}
\indentrel{3}\begin{verbatim}
           2   2
   (7)  4 x  + -
               3
        Type: UnivariatePolynomial(x,Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty7}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty7}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch7}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty7}{\showpaste}
\tab{5}\spadcommand{p := 4*x^2 + 2/3\free{x }\bound{p }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch8}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull8}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty8}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull8}{\hidepaste}
\tab{5}\spadcommand{a p\free{a p }}
\indentrel{3}\begin{verbatim}
           2         2
   (8)  4 x  + 8 x + -
                     3
        Type: UnivariatePolynomial(x,Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty8}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty8}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch8}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty8}{\showpaste}
\tab{5}\spadcommand{a p\free{a p }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch9}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull9}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty9}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull9}{\hidepaste}
\tab{5}\spadcommand{(a * b) p = a b p\free{a b p }}
\indentrel{3}\begin{verbatim}
           2          37      2          37
   (9)  2 x  + 12 x + -- = 2 x  + 12 x + --
                       3                  3
Type: Equation(UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty9}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty9}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch9}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty9}{\showpaste}
\tab{5}\spadcommand{(a * b) p = a b p\free{a b p }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch10}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull10}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty10}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull10}{\hidepaste}
\tab{5}\spadcommand{c := (1/9)*b*(a + b)^2\free{a b }\bound{c }}
\indentrel{3}\begin{verbatim}
   (10)
    1  6    5  5   13  4   19  3   79  2    7     1
   -- D  + -- D  + -- D  + -- D  + -- D  + -- D + -
   72      36      24      18      72      12     8
Type: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty10}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty10}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch10}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty10}{\showpaste}
\tab{5}\spadcommand{c := (1/9)*b*(a + b)^2\free{a b }\bound{c }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch11}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull11}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty11}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageFull11}{\hidepaste}
\tab{5}\spadcommand{(a^2 - 3/4*b + c) (p + 1)\free{a b c p }}
\indentrel{3}\begin{verbatim}
            2   44     541
   (11)  3 x  + -- x + ---
                 3      36
        Type: UnivariatePolynomial(x,Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty11}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty11}{ugxLinearOrdinaryDifferentialOperatorTwoConstPagePatch11}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoConstPageEmpty11}{\showpaste}
\tab{5}\spadcommand{(a^2 - 3/4*b + c) (p + 1)\free{a b c p }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch1}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull1}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty1}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull1}{\hidepaste}
\tab{5}\spadcommand{PZ := UnivariatePolynomial(x,Integer)\bound{PZ0 }}
\indentrel{3}\begin{verbatim}
   (1)  UnivariatePolynomial(x,Integer)
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty1}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty1}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch1}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty1}{\showpaste}
\tab{5}\spadcommand{PZ := UnivariatePolynomial(x,Integer)\bound{PZ0 }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch2}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull2}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty2}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull2}{\hidepaste}
\tab{5}\spadcommand{x:PZ := 'x\free{PZ0 }\bound{PZ }}
\indentrel{3}\begin{verbatim}
   (2)  x
                  Type: UnivariatePolynomial(x,Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty2}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty2}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch2}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty2}{\showpaste}
\tab{5}\spadcommand{x:PZ := 'x\free{PZ0 }\bound{PZ }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch3}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull3}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty3}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull3}{\hidepaste}
\tab{5}\spadcommand{Mat := SquareMatrix(3,PZ)\free{PZ }\bound{Mat }}
\indentrel{3}\begin{verbatim}
   (3)  SquareMatrix(3,UnivariatePolynomial(x,Integer))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty3}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty3}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch3}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty3}{\showpaste}
\tab{5}\spadcommand{Mat := SquareMatrix(3,PZ)\free{PZ }\bound{Mat }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch4}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull4}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty4}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull4}{\hidepaste}
\tab{5}\spadcommand{Vect := DPMM(3, PZ, Mat, PZ);\free{PZ Mat }\bound{Vect }}
\indentrel{3}\begin{verbatim}
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty4}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty4}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch4}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty4}{\showpaste}
\tab{5}\spadcommand{Vect := DPMM(3, PZ, Mat, PZ);\free{PZ Mat }\bound{Vect }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch5}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull5}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty5}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull5}{\hidepaste}
\tab{5}\spadcommand{Modo := LODO2(Mat, Vect);\free{Mat Vect }\bound{Modo }}
\indentrel{3}\begin{verbatim}
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty5}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty5}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch5}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty5}{\showpaste}
\tab{5}\spadcommand{Modo := LODO2(Mat, Vect);\free{Mat Vect }\bound{Modo }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch6}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull6}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty6}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull6}{\hidepaste}
\tab{5}\spadcommand{m:Mat := matrix [[x^2,1,0],[1,x^4,0],[0,0,4*x^2]]\free{Mat }\bound{m }}
\indentrel{3}\begin{verbatim}
        + 2          +
        |x   1    0  |
        |            |
   (6)  |     4      |
        |1   x    0  |
        |            |
        |           2|
        +0   0   4 x +
  Type: SquareMatrix(3,UnivariatePolynomial(x,Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty6}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty6}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch6}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty6}{\showpaste}
\tab{5}\spadcommand{m:Mat := matrix [[x^2,1,0],[1,x^4,0],[0,0,4*x^2]]\free{Mat }\bound{m }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch7}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull7}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty7}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull7}{\hidepaste}
\tab{5}\spadcommand{p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x]\free{Vect }\bound{p }}
\indentrel{3}\begin{verbatim}
            2              3
   (7)  [3 x  + 1, 2 x, 7 x  + 2 x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty7}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty7}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch7}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty7}{\showpaste}
\tab{5}\spadcommand{p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x]\free{Vect }\bound{p }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch8}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull8}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty8}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull8}{\hidepaste}
\tab{5}\spadcommand{q: Vect := m * p\free{m p Vect }\bound{q }}
\indentrel{3}\begin{verbatim}
            4    2           5      2          5      3
   (8)  [3 x  + x  + 2 x, 2 x  + 3 x  + 1, 28 x  + 8 x ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty8}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty8}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch8}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty8}{\showpaste}
\tab{5}\spadcommand{q: Vect := m * p\free{m p Vect }\bound{q }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch9}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull9}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty9}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull9}{\hidepaste}
\tab{5}\spadcommand{Dx : Modo := D()\bound{Dx }\free{Modo }}
\indentrel{3}\begin{verbatim}
   (9)  D
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty9}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty9}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch9}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty9}{\showpaste}
\tab{5}\spadcommand{Dx : Modo := D()\bound{Dx }\free{Modo }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch10}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull10}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty10}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull10}{\hidepaste}
\tab{5}\spadcommand{a : Modo := Dx + m\bound{a }\free{m Dx }}
\indentrel{3}\begin{verbatim}
             + 2          +
             |x   1    0  |
             |            |
   (10)  D + |     4      |
             |1   x    0  |
             |            |
             |           2|
             +0   0   4 x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty10}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty10}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch10}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty10}{\showpaste}
\tab{5}\spadcommand{a : Modo := Dx + m\bound{a }\free{m Dx }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch11}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull11}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty11}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull11}{\hidepaste}
\tab{5}\spadcommand{b : Modo := m*Dx + 1\bound{b }\free{m Dx }}
\indentrel{3}\begin{verbatim}
         + 2          +
         |x   1    0  |    +1  0  0+
         |            |    |       |
   (11)  |     4      |D + |0  1  0|
         |1   x    0  |    |       |
         |            |    +0  0  1+
         |           2|
         +0   0   4 x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty11}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty11}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch11}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty11}{\showpaste}
\tab{5}\spadcommand{b : Modo := m*Dx + 1\bound{b }\free{m Dx }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch12}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull12}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty12}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull12}{\hidepaste}
\tab{5}\spadcommand{c := a*b\bound{c }\free{a b }}
\indentrel{3}\begin{verbatim}
   (12)
     + 2          +
     |x   1    0  |
     |            | 2
     |     4      |D
     |1   x    0  |
     |            |
     |           2|
     +0   0   4 x +
   + 
     + 4                4    2                    +
     |x  + 2 x + 2     x  + x             0       |
     |                                            |
     |   4    2      8      3                     |D
     |  x  + x      x  + 4 x  + 2         0       |
     |                                            |
     |                                 4          |
     +     0              0        16 x  + 8 x + 1+
   + 
     + 2          +
     |x   1    0  |
     |            |
     |     4      |
     |1   x    0  |
     |            |
     |           2|
     +0   0   4 x +
Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty12}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty12}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch12}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty12}{\showpaste}
\tab{5}\spadcommand{c := a*b\bound{c }\free{a b }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch13}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull13}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty13}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull13}{\hidepaste}
\tab{5}\spadcommand{a p\free{p a }}
\indentrel{3}\begin{verbatim}
   (13)
       4    2           5      2
   [3 x  + x  + 8 x, 2 x  + 3 x  + 3,
        5      3       2
    28 x  + 8 x  + 21 x  + 2]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty13}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty13}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch13}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty13}{\showpaste}
\tab{5}\spadcommand{a p\free{p a }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch14}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull14}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty14}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull14}{\hidepaste}
\tab{5}\spadcommand{b p\free{p b }}
\indentrel{3}\begin{verbatim}
   (14)
       3      2         4
   [6 x  + 3 x  + 3, 2 x  + 8 x,
        4      3      2
    84 x  + 7 x  + 8 x  + 2 x]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty14}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty14}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch14}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty14}{\showpaste}
\tab{5}\spadcommand{b p\free{p b }}
\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch15}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull15}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty15}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageFull15}{\hidepaste}
\tab{5}\spadcommand{(a + b + c) (p + q)\free{a b c p q }}
\indentrel{3}\begin{verbatim}
   (15)
   [
           8       7       6       5       4       3
       10 x  + 12 x  + 16 x  + 30 x  + 85 x  + 94 x
     + 
           2
       40 x  + 40 x + 17
     ,

           12       9       8       7      6       5
       10 x   + 10 x  + 12 x  + 92 x  + 6 x  + 32 x
     + 
           4       3       2
       72 x  + 28 x  + 49 x  + 32 x + 19
     ,

             8        7         6         5        4
       2240 x  + 224 x  + 1280 x  + 3508 x  + 492 x
     + 
            3       2
       751 x  + 98 x  + 18 x + 4
     ]
Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty15}
\begin{paste}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty15}{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPagePatch15}
\pastebutton{ugxLinearOrdinaryDifferentialOperatorTwoMatrixPageEmpty15}{\showpaste}
\tab{5}\spadcommand{(a + b + c) (p + q)\free{a b c p q }}
\end{paste}\end{patch}

