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/SET.pht | 326 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 326 insertions(+) create mode 100644 src/hyper/pages/SET.pht (limited to 'src/hyper/pages/SET.pht') diff --git a/src/hyper/pages/SET.pht b/src/hyper/pages/SET.pht new file mode 100644 index 00000000..aef8d01e --- /dev/null +++ b/src/hyper/pages/SET.pht @@ -0,0 +1,326 @@ +\begin{patch}{SetXmpPagePatch1} +\begin{paste}{SetXmpPageFull1}{SetXmpPageEmpty1} +\pastebutton{SetXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{s := set [x**2-1, y**2-1, z**2-1]\bound{s }} +\indentrel{3}\begin{verbatim} + 2 2 2 + (1) {x - 1,y - 1,z - 1} + Type: Set Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty1} +\begin{paste}{SetXmpPageEmpty1}{SetXmpPagePatch1} +\pastebutton{SetXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{s := set [x**2-1, y**2-1, z**2-1]\bound{s }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch2} +\begin{paste}{SetXmpPageFull2}{SetXmpPageEmpty2} +\pastebutton{SetXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{t := set [x**i - i+1 for i in 2..10 | prime? i]\bound{t }} +\indentrel{3}\begin{verbatim} + 2 3 5 7 + (2) {x - 1,x - 2,x - 4,x - 6} + Type: Set Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty2} +\begin{paste}{SetXmpPageEmpty2}{SetXmpPagePatch2} +\pastebutton{SetXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{t := set [x**i - i+1 for i in 2..10 | prime? i]\bound{t }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch3} +\begin{paste}{SetXmpPageFull3}{SetXmpPageEmpty3} +\pastebutton{SetXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{i := intersect(s,t)\free{s t }\bound{i }} +\indentrel{3}\begin{verbatim} + 2 + (3) {x - 1} + Type: Set Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty3} +\begin{paste}{SetXmpPageEmpty3}{SetXmpPagePatch3} +\pastebutton{SetXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{i := intersect(s,t)\free{s t }\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch4} +\begin{paste}{SetXmpPageFull4}{SetXmpPageEmpty4} +\pastebutton{SetXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{u := union(s,t)\free{s t }\bound{u }} +\indentrel{3}\begin{verbatim} + 2 3 5 7 2 2 + (4) {x - 1,x - 2,x - 4,x - 6,y - 1,z - 1} + Type: Set Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty4} +\begin{paste}{SetXmpPageEmpty4}{SetXmpPagePatch4} +\pastebutton{SetXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{u := union(s,t)\free{s t }\bound{u }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch5} +\begin{paste}{SetXmpPageFull5}{SetXmpPageEmpty5} +\pastebutton{SetXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{difference(s,t)\free{s t }} +\indentrel{3}\begin{verbatim} + 2 2 + (5) {y - 1,z - 1} + Type: Set Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty5} +\begin{paste}{SetXmpPageEmpty5}{SetXmpPagePatch5} +\pastebutton{SetXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{difference(s,t)\free{s t }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch6} +\begin{paste}{SetXmpPageFull6}{SetXmpPageEmpty6} +\pastebutton{SetXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{symmetricDifference(s,t)\free{s t }} +\indentrel{3}\begin{verbatim} + 3 5 7 2 2 + (6) {x - 2,x - 4,x - 6,y - 1,z - 1} + Type: Set Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty6} +\begin{paste}{SetXmpPageEmpty6}{SetXmpPagePatch6} +\pastebutton{SetXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{symmetricDifference(s,t)\free{s t }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch7} +\begin{paste}{SetXmpPageFull7}{SetXmpPageEmpty7} +\pastebutton{SetXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{member?(y, s)\free{s }} +\indentrel{3}\begin{verbatim} + (7) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty7} +\begin{paste}{SetXmpPageEmpty7}{SetXmpPagePatch7} +\pastebutton{SetXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{member?(y, s)\free{s }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch8} +\begin{paste}{SetXmpPageFull8}{SetXmpPageEmpty8} +\pastebutton{SetXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{member?((y+1)*(y-1), s)\free{s }} +\indentrel{3}\begin{verbatim} + (8) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty8} +\begin{paste}{SetXmpPageEmpty8}{SetXmpPagePatch8} +\pastebutton{SetXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{member?((y+1)*(y-1), s)\free{s }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch9} +\begin{paste}{SetXmpPageFull9}{SetXmpPageEmpty9} +\pastebutton{SetXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{subset?(i, s)\free{i s }} +\indentrel{3}\begin{verbatim} + (9) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty9} +\begin{paste}{SetXmpPageEmpty9}{SetXmpPagePatch9} +\pastebutton{SetXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{subset?(i, s)\free{i s }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch10} +\begin{paste}{SetXmpPageFull10}{SetXmpPageEmpty10} +\pastebutton{SetXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{subset?(u, s)\free{u s }} +\indentrel{3}\begin{verbatim} + (10) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty10} +\begin{paste}{SetXmpPageEmpty10}{SetXmpPagePatch10} +\pastebutton{SetXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{subset?(u, s)\free{u s }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch11} +\begin{paste}{SetXmpPageFull11}{SetXmpPageEmpty11} +\pastebutton{SetXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{gs := set [g for i in 1..11 | primitive?(g := i::PF 11)]\bound{gs }} +\indentrel{3}\begin{verbatim} + (11) {2,6,7,8} + Type: Set PrimeField 11 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty11} +\begin{paste}{SetXmpPageEmpty11}{SetXmpPagePatch11} +\pastebutton{SetXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{gs := set [g for i in 1..11 | primitive?(g := i::PF 11)]\bound{gs }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch12} +\begin{paste}{SetXmpPageFull12}{SetXmpPageEmpty12} +\pastebutton{SetXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{complement gs\free{gs }} +\indentrel{3}\begin{verbatim} + (12) {1,3,4,5,9,10,0} + Type: Set PrimeField 11 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty12} +\begin{paste}{SetXmpPageEmpty12}{SetXmpPagePatch12} +\pastebutton{SetXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{complement gs\free{gs }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch13} +\begin{paste}{SetXmpPageFull13}{SetXmpPageEmpty13} +\pastebutton{SetXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{a := set [i**2 for i in 1..5]\bound{a }} +\indentrel{3}\begin{verbatim} + (13) {1,4,9,16,25} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty13} +\begin{paste}{SetXmpPageEmpty13}{SetXmpPagePatch13} +\pastebutton{SetXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{a := set [i**2 for i in 1..5]\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch14} +\begin{paste}{SetXmpPageFull14}{SetXmpPageEmpty14} +\pastebutton{SetXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{insert!(32, a)\free{a }\bound{ainsert }} +\indentrel{3}\begin{verbatim} + (14) {1,4,9,16,25,32} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty14} +\begin{paste}{SetXmpPageEmpty14}{SetXmpPagePatch14} +\pastebutton{SetXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{insert!(32, a)\free{a }\bound{ainsert }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch15} +\begin{paste}{SetXmpPageFull15}{SetXmpPageEmpty15} +\pastebutton{SetXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{remove!(25, a)\free{a }\bound{aremove }} +\indentrel{3}\begin{verbatim} + (15) {1,4,9,16,32} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty15} +\begin{paste}{SetXmpPageEmpty15}{SetXmpPagePatch15} +\pastebutton{SetXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{remove!(25, a)\free{a }\bound{aremove }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch16} +\begin{paste}{SetXmpPageFull16}{SetXmpPageEmpty16} +\pastebutton{SetXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{a\free{aremove ainsert }} +\indentrel{3}\begin{verbatim} + (16) {1,4,9,16,32} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty16} +\begin{paste}{SetXmpPageEmpty16}{SetXmpPagePatch16} +\pastebutton{SetXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{a\free{aremove ainsert }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch17} +\begin{paste}{SetXmpPageFull17}{SetXmpPageEmpty17} +\pastebutton{SetXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{b := b0 := set [i**2 for i in 1..5]\bound{b }} +\indentrel{3}\begin{verbatim} + (17) {1,4,9,16,25} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty17} +\begin{paste}{SetXmpPageEmpty17}{SetXmpPagePatch17} +\pastebutton{SetXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{b := b0 := set [i**2 for i in 1..5]\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch18} +\begin{paste}{SetXmpPageFull18}{SetXmpPageEmpty18} +\pastebutton{SetXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{b := union(b,32)\free{b }\bound{binsert }} +\indentrel{3}\begin{verbatim} + (18) {1,4,9,16,25,32} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty18} +\begin{paste}{SetXmpPageEmpty18}{SetXmpPagePatch18} +\pastebutton{SetXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{b := union(b,32)\free{b }\bound{binsert }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch19} +\begin{paste}{SetXmpPageFull19}{SetXmpPageEmpty19} +\pastebutton{SetXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{b := difference(b,25)\free{binsert }\bound{bremove }} +\indentrel{3}\begin{verbatim} + (19) {1,4,9,16,32} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty19} +\begin{paste}{SetXmpPageEmpty19}{SetXmpPagePatch19} +\pastebutton{SetXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{b := difference(b,25)\free{binsert }\bound{bremove }} +\end{paste}\end{patch} + +\begin{patch}{SetXmpPagePatch20} +\begin{paste}{SetXmpPageFull20}{SetXmpPageEmpty20} +\pastebutton{SetXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{b0\free{bremove }} +\indentrel{3}\begin{verbatim} + (20) {1,4,9,16,25} + Type: Set PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SetXmpPageEmpty20} +\begin{paste}{SetXmpPageEmpty20}{SetXmpPagePatch20} +\pastebutton{SetXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{b0\free{bremove }} +\end{paste}\end{patch} + -- cgit v1.2.3