diff options
author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/hyper/pages/INTHEORY.pht | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/hyper/pages/INTHEORY.pht')
-rw-r--r-- | src/hyper/pages/INTHEORY.pht | 348 |
1 files changed, 348 insertions, 0 deletions
diff --git a/src/hyper/pages/INTHEORY.pht b/src/hyper/pages/INTHEORY.pht new file mode 100644 index 00000000..7456ecbf --- /dev/null +++ b/src/hyper/pages/INTHEORY.pht @@ -0,0 +1,348 @@ +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch1} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull1}{IntegerNumberTheoryFunctionsXmpPageEmpty1} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{div144 := divisors(144)\bound{div144 }} +\indentrel{3}\begin{verbatim} + (1) [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty1} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty1}{IntegerNumberTheoryFunctionsXmpPagePatch1} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{div144 := divisors(144)\bound{div144 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch2} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull2}{IntegerNumberTheoryFunctionsXmpPageEmpty2} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{\#(div144)\free{div144 }} +\indentrel{3}\begin{verbatim} + (2) 15 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty2} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty2}{IntegerNumberTheoryFunctionsXmpPagePatch2} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{\#(div144)\free{div144 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch3} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull3}{IntegerNumberTheoryFunctionsXmpPageEmpty3} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{reduce(+,div144)\free{div144 }} +\indentrel{3}\begin{verbatim} + (3) 403 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty3} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty3}{IntegerNumberTheoryFunctionsXmpPagePatch3} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{reduce(+,div144)\free{div144 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch4} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull4}{IntegerNumberTheoryFunctionsXmpPageEmpty4} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{numberOfDivisors(144)} +\indentrel{3}\begin{verbatim} + (4) 15 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty4} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty4}{IntegerNumberTheoryFunctionsXmpPagePatch4} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{numberOfDivisors(144)} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch5} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull5}{IntegerNumberTheoryFunctionsXmpPageEmpty5} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{sumOfDivisors(144)} +\indentrel{3}\begin{verbatim} + (5) 403 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty5} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty5}{IntegerNumberTheoryFunctionsXmpPagePatch5} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{sumOfDivisors(144)} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch6} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull6}{IntegerNumberTheoryFunctionsXmpPageEmpty6} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty6} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty6}{IntegerNumberTheoryFunctionsXmpPagePatch6} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch7} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull7}{IntegerNumberTheoryFunctionsXmpPageEmpty7} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{f1(200)\free{f1 }} +\indentrel{3}\begin{verbatim} + (7) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty7} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty7}{IntegerNumberTheoryFunctionsXmpPagePatch7} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{f1(200)\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch8} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull8}{IntegerNumberTheoryFunctionsXmpPageEmpty8} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{f1(846)\free{f1 }} +\indentrel{3}\begin{verbatim} + (8) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty8} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty8}{IntegerNumberTheoryFunctionsXmpPagePatch8} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{f1(846)\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch9} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull9}{IntegerNumberTheoryFunctionsXmpPageEmpty9} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty9} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty9}{IntegerNumberTheoryFunctionsXmpPagePatch9} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch10} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull10}{IntegerNumberTheoryFunctionsXmpPageEmpty10} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{f2(200)\free{f2 }} +\indentrel{3}\begin{verbatim} + (10) 200 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty10} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty10}{IntegerNumberTheoryFunctionsXmpPagePatch10} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{f2(200)\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch11} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull11}{IntegerNumberTheoryFunctionsXmpPageEmpty11} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{f2(846)\free{f2 }} +\indentrel{3}\begin{verbatim} + (11) 846 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty11} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty11}{IntegerNumberTheoryFunctionsXmpPagePatch11} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{f2(846)\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch12} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull12}{IntegerNumberTheoryFunctionsXmpPageEmpty12} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{fibonacci(25)} +\indentrel{3}\begin{verbatim} + (12) 75025 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty12} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty12}{IntegerNumberTheoryFunctionsXmpPagePatch12} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{fibonacci(25)} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch13} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull13}{IntegerNumberTheoryFunctionsXmpPageEmpty13} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{[fibonacci(n) for n in 1..15]} +\indentrel{3}\begin{verbatim} + (13) [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty13} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty13}{IntegerNumberTheoryFunctionsXmpPagePatch13} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{[fibonacci(n) for n in 1..15]} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch14} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull14}{IntegerNumberTheoryFunctionsXmpPageEmpty14} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])\bound{fib }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty14} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty14}{IntegerNumberTheoryFunctionsXmpPagePatch14} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])\bound{fib }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch15} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull15}{IntegerNumberTheoryFunctionsXmpPageEmpty15} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{fib(25)\free{fib }} +\indentrel{3}\begin{verbatim} + (15) 75025 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty15} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty15}{IntegerNumberTheoryFunctionsXmpPagePatch15} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{fib(25)\free{fib }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch16} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull16}{IntegerNumberTheoryFunctionsXmpPageEmpty16} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{[fib(n) for n in 1..15]\free{fib }} +\indentrel{3}\begin{verbatim} + (16) [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty16} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty16}{IntegerNumberTheoryFunctionsXmpPagePatch16} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{[fib(n) for n in 1..15]\free{fib }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch17} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull17}{IntegerNumberTheoryFunctionsXmpPageEmpty17} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{legendre(3,5)} +\indentrel{3}\begin{verbatim} + (17) - 1 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty17} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty17}{IntegerNumberTheoryFunctionsXmpPagePatch17} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{legendre(3,5)} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch18} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull18}{IntegerNumberTheoryFunctionsXmpPageEmpty18} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{legendre(23,691)} +\indentrel{3}\begin{verbatim} + (18) - 1 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty18} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty18}{IntegerNumberTheoryFunctionsXmpPagePatch18} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{legendre(23,691)} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch19} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull19}{IntegerNumberTheoryFunctionsXmpPageEmpty19} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))\bound{h }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty19} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty19}{IntegerNumberTheoryFunctionsXmpPagePatch19} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch20} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull20}{IntegerNumberTheoryFunctionsXmpPageEmpty20} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{h(-163)\free{h }} +\indentrel{3}\begin{verbatim} + (20) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty20} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty20}{IntegerNumberTheoryFunctionsXmpPagePatch20} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{h(-163)\free{h }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch21} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull21}{IntegerNumberTheoryFunctionsXmpPageEmpty21} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{h(-499)\free{h }} +\indentrel{3}\begin{verbatim} + (21) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty21} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty21}{IntegerNumberTheoryFunctionsXmpPagePatch21} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{h(-499)\free{h }} +\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPagePatch22} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageFull22}{IntegerNumberTheoryFunctionsXmpPageEmpty22} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{h(-1832)\free{h }} +\indentrel{3}\begin{verbatim} + (22) 26 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntegerNumberTheoryFunctionsXmpPageEmpty22} +\begin{paste}{IntegerNumberTheoryFunctionsXmpPageEmpty22}{IntegerNumberTheoryFunctionsXmpPagePatch22} +\pastebutton{IntegerNumberTheoryFunctionsXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{h(-1832)\free{h }} +\end{paste}\end{patch} + |