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|
\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) � 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) 4x + �
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 + �
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 + ��= 2x + 12x + ��
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) 3x + �� 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: 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}
� 2 �
�x 1 0 �
� �
(6) � 4 �
�1 x 0 �
� �
� 2�
�0 0 4x �
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}
� 2 �
�x 1 0 �
� �
(10) D + � 4 �
�1 x 0 �
� �
� 2�
�0 0 4x �
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 4x �
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 4x �
+
� 4 4 2 �
�x + 2x + 2 x + x 0 �
� �
� 4 2 8 3 �D
� x + x x + 4x + 2 0 �
� �
� 4 �
� 0 0 16x + 8x + 1�
+
� 2 �
�x 1 0 �
� �
� 4 �
�1 x 0 �
� �
� 2�
�0 0 4x �
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}
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