\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: Domain
\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: Domain
\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)  Ä D  + D + Ä
        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)  4x  + Ä
              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)  4x  + 8x + Ä
                   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)  2x  + 12x + ÄÄ= 2x  + 12x + ÄÄ
                     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
   ÄÄ D  + ÄÄ D  + ÄÄ D  + ÄÄ D  + ÄÄ D  + ÄÄ D + Ä
   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)  3x  + ÄÄ x + ÄÄÄ
                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: Domain
\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: Domain
\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: Domain
\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: Domain
\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}
        Ú 2         ¿
        ³x   1    0 ³
        ³           ³
   (6)  ³     4     ³
        ³1   x    0 ³
        ³           ³
        ³          2³
        À0   0   4x Ù
  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)  [3x  + 1,2x,7x  + 2x]
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)  [3x  + x  + 2x,2x  + 3x  + 1,28x  + 8x ]
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}
             Ú 2         ¿
             ³x   1    0 ³
             ³           ³
   (10)  D + ³     4     ³
             ³1   x    0 ³
             ³           ³
             ³          2³
             À0   0   4x Ù
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}
         Ú 2         ¿
         ³x   1    0 ³    Ú1  0  0¿
         ³           ³    ³       ³
   (11)  ³     4     ³D + ³0  1  0³
         ³1   x    0 ³    ³       ³
         ³           ³    À0  0  1Ù
         ³          2³
         À0   0   4x Ù
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)
     Ú 2         ¿
     ³x   1    0 ³
     ³           ³ 2
     ³     4     ³D
     ³1   x    0 ³
     ³           ³
     ³          2³
     À0   0   4x Ù
   + 
     Ú 4              4    2                  ¿
     ³x  + 2x + 2    x  + x            0      ³
     ³                                        ³
     ³   4    2     8     3                   ³D
     ³  x  + x     x  + 4x  + 2        0      ³
     ³                                        ³
     ³                              4         ³
     À     0            0        16x  + 8x + 1Ù
   + 
     Ú 2         ¿
     ³x   1    0 ³
     ³           ³
     ³     4     ³
     ³1   x    0 ³
     ³           ³
     ³          2³
     À0   0   4x Ù
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        5     3      2
   [3x  + x  + 8x,2x  + 3x  + 3,28x  + 8x  + 21x  + 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}
            3     2       4         4     3     2
   (14)  [6x  + 3x  + 3,2x  + 8x,84x  + 7x  + 8x  + 2x]
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      2
       10x  + 12x  + 16x  + 30x  + 85x  + 94x  + 40x
     + 
       40x + 17
     ,

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

            8       7        6        5       4       3
       2240x  + 224x  + 1280x  + 3508x  + 492x  + 751x
     + 
          2
       98x  + 18x + 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}

