\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}