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>