1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
|
\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input realclos.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
)clear all
-- computing without a table manipulation when creating objects
Ran := RECLOS(FRAC INT)
-- Some simple signs for square roots, these correspond to an extension
-- of degree 16 of the rational numbers.
fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran ==
sqrt(a)+sqrt(b) - sqrt(c)-sqrt(d)
squareDiff := fourSquares(73,548,60,586)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(165,778,86,990)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(217,708,226,692)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(155,836,162,820)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(591,772,552,818)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(434,1053,412,1088)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(514,1049,446,1152)
recip(squareDiff)
sign(squareDiff)
squareDiff := fourSquares(190,1751,208,1698)
recip(squareDiff)
sign(squareDiff)
)cl prop s2 s5 s10 l
-- a more complicated test that involve an extension of degree 256
(s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran);
sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10)
%::Boolean
-- the sum of these 4 numbers is 0
l := allRootsOf((x^2-2)^2-2)$Ran
l.1+l.2+l.3+l.4
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
