From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001 From: dos-reis Date: Tue, 14 Aug 2007 05:14:52 +0000 Subject: Initial population. --- src/hyper/pages/LODO2.pht | 499 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 499 insertions(+) create mode 100644 src/hyper/pages/LODO2.pht (limited to 'src/hyper/pages/LODO2.pht') diff --git a/src/hyper/pages/LODO2.pht b/src/hyper/pages/LODO2.pht new file mode 100644 index 00000000..9c267563 --- /dev/null +++ b/src/hyper/pages/LODO2.pht @@ -0,0 +1,499 @@ +\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} + -- cgit v1.2.3