1<TeXmacs|1.99.2>
2
3<style|<tuple|generic|french|maxima>>
4
5<\body>
6  <\session|maxima|default>
7    <\output>
8      \;
9
10      Maxima 5.34.1 http://maxima.sourceforge.net
11
12      using Lisp GNU Common Lisp (GCL) GCL 2.6.12 (a.k.a. GCL)
13
14      Distributed under the GNU Public License. See the file COPYING.
15
16      Dedicated to the memory of William Schelter.
17
18      The function bug_report() provides bug reporting information.
19    </output>
20
21    <\unfolded-io>
22      <with|color|red|(<with|math-font-family|rm|%i>13) >
23    <|unfolded-io>
24      U:matrix([U0,U3/sqrt(2),U4/sqrt(2)],[U3/sqrt(2),U1,U5/sqrt(2)],[U4/sqrt(2),U5/sqrt(2),U2])
25    <|unfolded-io>
26      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o13>)
27      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|U0>>|<cell|<frac|<with|math-font-family|rm|U3>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|U4>|<sqrt|2>>>>|<row|<cell|<frac|<with|math-font-family|rm|U3>|<sqrt|2>>>|<cell|<with|math-font-family|rm|U1>>|<cell|<frac|<with|math-font-family|rm|U5>|<sqrt|2>>>>|<row|<cell|<frac|<with|math-font-family|rm|U4>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|U5>|<sqrt|2>>>|<cell|<with|math-font-family|rm|U2>>>>>>>>
28    </unfolded-io>
29
30    <\unfolded-io>
31      <with|color|red|(<with|math-font-family|rm|%i>14) >
32    <|unfolded-io>
33      S:matrix([S0,S3/sqrt(2),S4/sqrt(2)],[S3/sqrt(2),S1,S5/sqrt(2)],[S4/sqrt(2),S5/sqrt(2),S2])
34    <|unfolded-io>
35      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o14>)
36      >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|S0>>|<cell|<frac|<with|math-font-family|rm|S3>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|S4>|<sqrt|2>>>>|<row|<cell|<frac|<with|math-font-family|rm|S3>|<sqrt|2>>>|<cell|<with|math-font-family|rm|S1>>|<cell|<frac|<with|math-font-family|rm|S5>|<sqrt|2>>>>|<row|<cell|<frac|<with|math-font-family|rm|S4>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|S5>|<sqrt|2>>>|<cell|<with|math-font-family|rm|S2>>>>>>>>
37    </unfolded-io>
38
39    <\unfolded-io>
40      <with|color|red|(<with|math-font-family|rm|%i>15) >
41    <|unfolded-io>
42      s:U.S.U
43    <|unfolded-io>
44      <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o15>)
45      >><matrix|<tformat|<table|<row|<cell|<frac|<with|math-font-family|rm|U3>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U3>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U0>|<sqrt|2>>|)>|<sqrt|2>>+<with|math-font-family|rm|U0>*<around*|(|<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>|2>+<with|math-font-family|rm|S0>*<with|math-font-family|rm|U0>|)>+<frac|<with|math-font-family|rm|U4>*<around*|(|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U4>|<sqrt|2>>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U3>|2>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U0>|<sqrt|2>>|)>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|U3>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>|2>+<with|math-font-family|rm|S1>*<with|math-font-family|rm|U1>|)>|<sqrt|2>>+<with|math-font-family|rm|U0>*<around*|(|<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S0>*<with|math-font-family|rm|U3>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U1>|<sqrt|2>>|)>+<frac|<with|math-font-family|rm|U4>*<around*|(|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U3>|2>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U1>|<sqrt|2>>|)>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|U4>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>|2>+<with|math-font-family|rm|S2>*<with|math-font-family|rm|U2>|)>|<sqrt|2>>+<with|math-font-family|rm|U0>*<around*|(|<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S0>*<with|math-font-family|rm|U4>|<sqrt|2>>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U2>|<sqrt|2>>|)>+<frac|<with|math-font-family|rm|U3>*<around*|(|<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U2>|<sqrt|2>>|)>|<sqrt|2>>>>|<row|<cell|<frac|<around*|(|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U4>|<sqrt|2>>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U3>|2>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U0>|<sqrt|2>>|)>*<with|math-font-family|rm|U5>|<sqrt|2>>+<with|math-font-family|rm|U1>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U3>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U0>|<sqrt|2>>|)>+<frac|<with|math-font-family|rm|U3>*<around*|(|<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>|2>+<with|math-font-family|rm|S0>*<with|math-font-family|rm|U0>|)>|<sqrt|2>>>|<cell|<with|math-font-family|rm|U1>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>|2>+<with|math-font-family|rm|S1>*<with|math-font-family|rm|U1>|)>+<frac|<with|math-font-family|rm|U3>*<around*|(|<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S0>*<with|math-font-family|rm|U3>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U1>|<sqrt|2>>|)>|<sqrt|2>>+<frac|<with|math-font-family|rm|U5>*<around*|(|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U3>|2>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U1>|<sqrt|2>>|)>|<sqrt|2>>>|<cell|<frac|<with|math-font-family|rm|U5>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>|2>+<with|math-font-family|rm|S2>*<with|math-font-family|rm|U2>|)>|<sqrt|2>>+<frac|<with|math-font-family|rm|U3>*<around*|(|<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S0>*<with|math-font-family|rm|U4>|<sqrt|2>>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U2>|<sqrt|2>>|)>|<sqrt|2>>+<with|math-font-family|rm|U1>*<around*|(|<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U2>|<sqrt|2>>|)>>>|<row|<cell|<frac|<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U3>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U0>|<sqrt|2>>|)>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|U4>*<around*|(|<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>|2>+<with|math-font-family|rm|S0>*<with|math-font-family|rm|U0>|)>|<sqrt|2>>+<with|math-font-family|rm|U2>*<around*|(|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U4>|<sqrt|2>>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U3>|2>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U0>|<sqrt|2>>|)>>|<cell|<frac|<with|math-font-family|rm|U5>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>|2>+<with|math-font-family|rm|S1>*<with|math-font-family|rm|U1>|)>|<sqrt|2>>+<frac|<with|math-font-family|rm|U4>*<around*|(|<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S0>*<with|math-font-family|rm|U3>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U1>|<sqrt|2>>|)>|<sqrt|2>>+<with|math-font-family|rm|U2>*<around*|(|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U3>|2>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U1>|<sqrt|2>>|)>>|<cell|<with|math-font-family|rm|U2>*<around*|(|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>|2>+<with|math-font-family|rm|S2>*<with|math-font-family|rm|U2>|)>+<frac|<with|math-font-family|rm|U4>*<around*|(|<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U5>|2>+<frac|<with|math-font-family|rm|S0>*<with|math-font-family|rm|U4>|<sqrt|2>>+<frac|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U2>|<sqrt|2>>|)>|<sqrt|2>>+<frac|<with|math-font-family|rm|U5>*<around*|(|<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U5>|<sqrt|2>>+<frac|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U4>|2>+<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U2>|<sqrt|2>>|)>|<sqrt|2>>>>>>>>>
46    </unfolded-io>
47
48    <\unfolded-io>
49      <with|color|red|(<with|math-font-family|rm|%i>18) >
50    <|unfolded-io>
51      fullratsimp(transpose(matrix([s[1,1],s[2,2],s[3,3],sqrt(2)*s[1,2],sqrt(2)*s[1,3],sqrt(2)*s[2,3]])))
52    <|unfolded-io>
53      \;
54
55      \ <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o18>)
56      >><matrix|<tformat|<table|<row|<cell|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U4><rsup|2>+<around*|(|<sqrt|2>*<with|math-font-family|rm|S5>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S4>*<with|math-font-family|rm|U0>|)>*<with|math-font-family|rm|U4>+<with|math-font-family|rm|S1>*<with|math-font-family|rm|U3><rsup|2>+2*<with|math-font-family|rm|S3>*<with|math-font-family|rm|U0>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S0>*<with|math-font-family|rm|U0><rsup|2>|2>>>|<row|<cell|<frac|<with|math-font-family|rm|S2>*<with|math-font-family|rm|U5><rsup|2>+<around*|(|<sqrt|2>*<with|math-font-family|rm|S4>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S5>*<with|math-font-family|rm|U1>|)>*<with|math-font-family|rm|U5>+<with|math-font-family|rm|S0>*<with|math-font-family|rm|U3><rsup|2>+2*<with|math-font-family|rm|S3>*<with|math-font-family|rm|U1>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S1>*<with|math-font-family|rm|U1><rsup|2>|2>>>|<row|<cell|<frac|<with|math-font-family|rm|S1>*<with|math-font-family|rm|U5><rsup|2>+<around*|(|<sqrt|2>*<with|math-font-family|rm|S3>*<with|math-font-family|rm|U4>+2*<with|math-font-family|rm|S5>*<with|math-font-family|rm|U2>|)>*<with|math-font-family|rm|U5>+<with|math-font-family|rm|S0>*<with|math-font-family|rm|U4><rsup|2>+2*<with|math-font-family|rm|S4>*<with|math-font-family|rm|U2>*<with|math-font-family|rm|U4>+2*<with|math-font-family|rm|S2>*<with|math-font-family|rm|U2><rsup|2>|2>>>|<row|<cell|<frac|<around*|(|<sqrt|2>*<with|math-font-family|rm|S2>*<with|math-font-family|rm|U4>+<with|math-font-family|rm|S5>*<with|math-font-family|rm|U3>+<sqrt|2>*<with|math-font-family|rm|S4>*<with|math-font-family|rm|U0>|)>*<with|math-font-family|rm|U5>+<around*|(|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U3>+<sqrt|2>*<with|math-font-family|rm|S5>*<with|math-font-family|rm|U1>|)>*<with|math-font-family|rm|U4>+<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3><rsup|2>+<around*|(|2*<with|math-font-family|rm|S1>*<with|math-font-family|rm|U1>+2*<with|math-font-family|rm|S0>*<with|math-font-family|rm|U0>|)>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S3>*<with|math-font-family|rm|U0>*<with|math-font-family|rm|U1>|2>>>|<row|<cell|<frac|<around*|(|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U4>+<sqrt|2>*<with|math-font-family|rm|S1>*<with|math-font-family|rm|U3>+<sqrt|2>*<with|math-font-family|rm|S3>*<with|math-font-family|rm|U0>|)>*<with|math-font-family|rm|U5>+<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4><rsup|2>+<around*|(|<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S2>*<with|math-font-family|rm|U2>+2*<with|math-font-family|rm|S0>*<with|math-font-family|rm|U0>|)>*<with|math-font-family|rm|U4>+<sqrt|2>*<with|math-font-family|rm|S5>*<with|math-font-family|rm|U2>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S4>*<with|math-font-family|rm|U0>*<with|math-font-family|rm|U2>|2>>>|<row|<cell|<frac|<with|math-font-family|rm|S5>*<with|math-font-family|rm|U5><rsup|2>+<around*|(|<with|math-font-family|rm|S4>*<with|math-font-family|rm|U4>+<with|math-font-family|rm|S3>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S2>*<with|math-font-family|rm|U2>+2*<with|math-font-family|rm|S1>*<with|math-font-family|rm|U1>|)>*<with|math-font-family|rm|U5>+<around*|(|<sqrt|2>*<with|math-font-family|rm|S0>*<with|math-font-family|rm|U3>+<sqrt|2>*<with|math-font-family|rm|S3>*<with|math-font-family|rm|U1>|)>*<with|math-font-family|rm|U4>+<sqrt|2>*<with|math-font-family|rm|S4>*<with|math-font-family|rm|U2>*<with|math-font-family|rm|U3>+2*<with|math-font-family|rm|S5>*<with|math-font-family|rm|U1>*<with|math-font-family|rm|U2>|2>>>>>>>>
57    </unfolded-io>
58
59    <\input>
60      <with|color|red|(<with|math-font-family|rm|%i>19) >
61    <|input>
62      \;
63    </input>
64  </session>
65</body>