diff options
Diffstat (limited to 'src/hyper/pages/OP.pht')
| -rw-r--r-- | src/hyper/pages/OP.pht | 373 |
1 files changed, 373 insertions, 0 deletions
diff --git a/src/hyper/pages/OP.pht b/src/hyper/pages/OP.pht new file mode 100644 index 00000000..4b553864 --- /dev/null +++ b/src/hyper/pages/OP.pht @@ -0,0 +1,373 @@ +\begin{patch}{OperatorXmpPagePatch1} +\begin{paste}{OperatorXmpPageFull1}{OperatorXmpPageEmpty1} +\pastebutton{OperatorXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{R := SQMATRIX(2, INT)\bound{r }} +\indentrel{3}\begin{verbatim} + (1) SquareMatrix(2,Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty1} +\begin{paste}{OperatorXmpPageEmpty1}{OperatorXmpPagePatch1} +\pastebutton{OperatorXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{R := SQMATRIX(2, INT)\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch2} +\begin{paste}{OperatorXmpPageFull2}{OperatorXmpPageEmpty2} +\pastebutton{OperatorXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{t := operator("tilde") :: OP(R)\free{r }\bound{t }} +\indentrel{3}\begin{verbatim} + (2) tilde + Type: Operator SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty2} +\begin{paste}{OperatorXmpPageEmpty2}{OperatorXmpPagePatch2} +\pastebutton{OperatorXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{t := operator("tilde") :: OP(R)\free{r }\bound{t }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch3} +\begin{paste}{OperatorXmpPageFull3}{OperatorXmpPageEmpty3} +\pastebutton{OperatorXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{)set expose add constructor Operator\free{t }\bound{expose }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty3} +\begin{paste}{OperatorXmpPageEmpty3}{OperatorXmpPagePatch3} +\pastebutton{OperatorXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{)set expose add constructor Operator\free{t }\bound{expose }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch4} +\begin{paste}{OperatorXmpPageFull4}{OperatorXmpPageEmpty4} +\pastebutton{OperatorXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{evaluate(t, m +-> transpose m)\free{expose }\free{t }\bound{evt }} +\indentrel{3}\begin{verbatim} + (3) tilde + Type: Operator SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty4} +\begin{paste}{OperatorXmpPageEmpty4}{OperatorXmpPagePatch4} +\pastebutton{OperatorXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{evaluate(t, m +-> transpose m)\free{expose }\free{t }\bound{evt }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch5} +\begin{paste}{OperatorXmpPageFull5}{OperatorXmpPageEmpty5} +\pastebutton{OperatorXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{s : R := matrix [[0, 1], [1, 0]]\bound{s }} +\indentrel{3}\begin{verbatim} + Ú0 1¿ + (4) ³ ³ + À1 0Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty5} +\begin{paste}{OperatorXmpPageEmpty5}{OperatorXmpPagePatch5} +\pastebutton{OperatorXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{s : R := matrix [[0, 1], [1, 0]]\bound{s }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch6} +\begin{paste}{OperatorXmpPageFull6}{OperatorXmpPageEmpty6} +\pastebutton{OperatorXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{rho := t * s\free{evt s }\bound{rho }} +\indentrel{3}\begin{verbatim} + Ú0 1¿ + (5) tilde³ ³ + À1 0Ù + Type: Operator SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty6} +\begin{paste}{OperatorXmpPageEmpty6}{OperatorXmpPagePatch6} +\pastebutton{OperatorXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{rho := t * s\free{evt s }\bound{rho }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch7} +\begin{paste}{OperatorXmpPageFull7}{OperatorXmpPageEmpty7} +\pastebutton{OperatorXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{z := rho**4 - 1\free{rho }\bound{z }} +\indentrel{3}\begin{verbatim} + (6) + Ú0 1¿ Ú0 1¿ Ú0 1¿ Ú0 1¿ + - 1 + tilde³ ³tilde³ ³tilde³ ³tilde³ ³ + À1 0Ù À1 0Ù À1 0Ù À1 0Ù + Type: Operator SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty7} +\begin{paste}{OperatorXmpPageEmpty7}{OperatorXmpPagePatch7} +\pastebutton{OperatorXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{z := rho**4 - 1\free{rho }\bound{z }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch8} +\begin{paste}{OperatorXmpPageFull8}{OperatorXmpPageEmpty8} +\pastebutton{OperatorXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{m:R := matrix [[1, 2], [3, 4]]\bound{m }} +\indentrel{3}\begin{verbatim} + Ú1 2¿ + (7) ³ ³ + À3 4Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty8} +\begin{paste}{OperatorXmpPageEmpty8}{OperatorXmpPagePatch8} +\pastebutton{OperatorXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{m:R := matrix [[1, 2], [3, 4]]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch9} +\begin{paste}{OperatorXmpPageFull9}{OperatorXmpPageEmpty9} +\pastebutton{OperatorXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{z m\free{z m }} +\indentrel{3}\begin{verbatim} + Ú0 0¿ + (8) ³ ³ + À0 0Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty9} +\begin{paste}{OperatorXmpPageEmpty9}{OperatorXmpPagePatch9} +\pastebutton{OperatorXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{z m\free{z m }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch10} +\begin{paste}{OperatorXmpPageFull10}{OperatorXmpPageEmpty10} +\pastebutton{OperatorXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{rho m\free{rho m }} +\indentrel{3}\begin{verbatim} + Ú3 1¿ + (9) ³ ³ + À4 2Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty10} +\begin{paste}{OperatorXmpPageEmpty10}{OperatorXmpPagePatch10} +\pastebutton{OperatorXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{rho m\free{rho m }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch11} +\begin{paste}{OperatorXmpPageFull11}{OperatorXmpPageEmpty11} +\pastebutton{OperatorXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{rho rho m\free{rho m }} +\indentrel{3}\begin{verbatim} + Ú4 3¿ + (10) ³ ³ + À2 1Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty11} +\begin{paste}{OperatorXmpPageEmpty11}{OperatorXmpPagePatch11} +\pastebutton{OperatorXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{rho rho m\free{rho m }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch12} +\begin{paste}{OperatorXmpPageFull12}{OperatorXmpPageEmpty12} +\pastebutton{OperatorXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{(rho**3) m\free{rho m }} +\indentrel{3}\begin{verbatim} + Ú2 4¿ + (11) ³ ³ + À1 3Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty12} +\begin{paste}{OperatorXmpPageEmpty12}{OperatorXmpPagePatch12} +\pastebutton{OperatorXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{(rho**3) m\free{rho m }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch13} +\begin{paste}{OperatorXmpPageFull13}{OperatorXmpPageEmpty13} +\pastebutton{OperatorXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{b := t * s - s * t\free{s evt }\bound{b }} +\indentrel{3}\begin{verbatim} + Ú0 1¿ Ú0 1¿ + (12) - ³ ³tilde + tilde³ ³ + À1 0Ù À1 0Ù + Type: Operator SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty13} +\begin{paste}{OperatorXmpPageEmpty13}{OperatorXmpPagePatch13} +\pastebutton{OperatorXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{b := t * s - s * t\free{s evt }\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch14} +\begin{paste}{OperatorXmpPageFull14}{OperatorXmpPageEmpty14} +\pastebutton{OperatorXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{b m\free{b m }} +\indentrel{3}\begin{verbatim} + Ú1 - 3¿ + (13) ³ ³ + À3 - 1Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty14} +\begin{paste}{OperatorXmpPageEmpty14}{OperatorXmpPagePatch14} +\pastebutton{OperatorXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{b m\free{b m }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch15} +\begin{paste}{OperatorXmpPageFull15}{OperatorXmpPageEmpty15} +\pastebutton{OperatorXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{L n == + n = 0 => 1 + n = 1 => x + (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2) +\bound{l }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty15} +\begin{paste}{OperatorXmpPageEmpty15}{OperatorXmpPagePatch15} +\pastebutton{OperatorXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{L n == + n = 0 => 1 + n = 1 => x + (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2) +\bound{l }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch16} +\begin{paste}{OperatorXmpPageFull16}{OperatorXmpPageEmpty16} +\pastebutton{OperatorXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{dx := operator("D") :: OP(POLY FRAC INT)\bound{dx }} +\indentrel{3}\begin{verbatim} + (15) D + Type: Operator Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty16} +\begin{paste}{OperatorXmpPageEmpty16}{OperatorXmpPagePatch16} +\pastebutton{OperatorXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{dx := operator("D") :: OP(POLY FRAC INT)\bound{dx }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch17} +\begin{paste}{OperatorXmpPageFull17}{OperatorXmpPageEmpty17} +\pastebutton{OperatorXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{evaluate(dx, p +-> D(p, 'x))\free{dx }\bound{edx }} +\indentrel{3}\begin{verbatim} + (16) D + Type: Operator Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty17} +\begin{paste}{OperatorXmpPageEmpty17}{OperatorXmpPagePatch17} +\pastebutton{OperatorXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{evaluate(dx, p +-> D(p, 'x))\free{dx }\bound{edx }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch18} +\begin{paste}{OperatorXmpPageFull18}{OperatorXmpPageEmpty18} +\pastebutton{OperatorXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)\free{edx }\bound{E }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty18} +\begin{paste}{OperatorXmpPageEmpty18}{OperatorXmpPagePatch18} +\pastebutton{OperatorXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1)\free{edx }\bound{E }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch19} +\begin{paste}{OperatorXmpPageFull19}{OperatorXmpPageEmpty19} +\pastebutton{OperatorXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{L 15\free{L }} +\indentrel{3}\begin{verbatim} + (18) + 9694845 15 35102025 13 50702925 11 + ÄÄÄÄÄÄÄ x - ÄÄÄÄÄÄÄÄ x + ÄÄÄÄÄÄÄÄ x + 2048 2048 2048 + + + 37182145 9 14549535 7 2909907 5 255255 3 + - ÄÄÄÄÄÄÄÄ x + ÄÄÄÄÄÄÄÄ x - ÄÄÄÄÄÄÄ x + ÄÄÄÄÄÄ x + 2048 2048 2048 2048 + + + 6435 + - ÄÄÄÄ x + 2048 + Type: Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty19} +\begin{paste}{OperatorXmpPageEmpty19}{OperatorXmpPagePatch19} +\pastebutton{OperatorXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{L 15\free{L }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch20} +\begin{paste}{OperatorXmpPageFull20}{OperatorXmpPageEmpty20} +\pastebutton{OperatorXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{E 15\free{E }} +\indentrel{3}\begin{verbatim} + 2 2 + (19) 240 - 2x D - (x - 1)D + Type: Operator Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty20} +\begin{paste}{OperatorXmpPageEmpty20}{OperatorXmpPagePatch20} +\pastebutton{OperatorXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{E 15\free{E }} +\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPagePatch21} +\begin{paste}{OperatorXmpPageFull21}{OperatorXmpPageEmpty21} +\pastebutton{OperatorXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{(E 15)(L 15)\free{L E }} +\indentrel{3}\begin{verbatim} + (20) 0 + Type: Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OperatorXmpPageEmpty21} +\begin{paste}{OperatorXmpPageEmpty21}{OperatorXmpPagePatch21} +\pastebutton{OperatorXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{(E 15)(L 15)\free{L E }} +\end{paste}\end{patch} + |