1<TeXmacs|1.0.7.15> 2 3<style|<tuple|generic|maxima>> 4 5<\body> 6 Compute deformation tensors from the\ 7 8 <\session|maxima|default> 9 <\output> 10 Maxima 5.27.0 http://maxima.sourceforge.net 11 12 using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (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>37) > 23 <|unfolded-io> 24 F:matrix([F0,F3,0],[F4,F1,0],[0,0,F2]) 25 <|unfolded-io> 26 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o37>) 27 >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F0>>|<cell|<with|math-font-family|rm|F3>>|<cell|0>>|<row|<cell|<with|math-font-family|rm|F4>>|<cell|<with|math-font-family|rm|F1>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|F2>>>>>>>> 28 </unfolded-io> 29 30 <\unfolded-io> 31 <with|color|red|(<with|math-font-family|rm|%i>38) > 32 <|unfolded-io> 33 transpose(F).F /* right cauchy green tensor */ 34 <|unfolded-io> 35 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o38>) 36 >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F4><rsup|2>+<with|math-font-family|rm|F0><rsup|2>>|<cell|<with|math-font-family|rm|F1>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F0>*<with|math-font-family|rm|F3>>|<cell|0>>|<row|<cell|<with|math-font-family|rm|F1>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F0>*<with|math-font-family|rm|F3>>|<cell|<with|math-font-family|rm|F3><rsup|2>+<with|math-font-family|rm|F1><rsup|2>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|F2><rsup|2>>>>>>>> 37 </unfolded-io> 38 39 <\unfolded-io> 40 <with|color|red|(<with|math-font-family|rm|%i>39) > 41 <|unfolded-io> 42 F.transpose(F) /* left cauchy green tensor */ 43 <|unfolded-io> 44 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o39>) 45 >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F3><rsup|2>+<with|math-font-family|rm|F0><rsup|2>>|<cell|<with|math-font-family|rm|F0>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F1>*<with|math-font-family|rm|F3>>|<cell|0>>|<row|<cell|<with|math-font-family|rm|F0>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F1>*<with|math-font-family|rm|F3>>|<cell|<with|math-font-family|rm|F4><rsup|2>+<with|math-font-family|rm|F1><rsup|2>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|F2><rsup|2>>>>>>>> 46 </unfolded-io> 47 48 <\unfolded-io> 49 <with|color|red|(<with|math-font-family|rm|%i>40) > 50 <|unfolded-io> 51 p:matrix([p0,p3/sqrt(2),0],[p3/sqrt(2),p1,0],[0,0,p2]) 52 <|unfolded-io> 53 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o40>) 54 >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|p0>>|<cell|<frac|<with|math-font-family|rm|p3>|<sqrt|2>>>|<cell|0>>|<row|<cell|<frac|<with|math-font-family|rm|p3>|<sqrt|2>>>|<cell|<with|math-font-family|rm|p1>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|p2>>>>>>>> 55 </unfolded-io> 56 57 <\unfolded-io> 58 <with|color|red|(<with|math-font-family|rm|%i>41) > 59 <|unfolded-io> 60 s:F.p.transpose(F) 61 <|unfolded-io> 62 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o41>) 63 >><matrix|<tformat|<table|<row|<cell|<with|math-font-family|rm|F0>*<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F3>|<sqrt|2>>+<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0>|)>+<with|math-font-family|rm|F3>*<around*|(|<with|math-font-family|rm|p1>*<with|math-font-family|rm|F3>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>|<sqrt|2>>|)>>|<cell|<with|math-font-family|rm|F3>*<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F4>|<sqrt|2>>+<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1>|)>+<with|math-font-family|rm|F0>*<around*|(|<with|math-font-family|rm|p0>*<with|math-font-family|rm|F4>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F1>|<sqrt|2>>|)>>|<cell|0>>|<row|<cell|<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F3>|<sqrt|2>>+<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0>|)>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|F1>*<around*|(|<with|math-font-family|rm|p1>*<with|math-font-family|rm|F3>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>|<sqrt|2>>|)>>|<cell|<with|math-font-family|rm|F1>*<around*|(|<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F4>|<sqrt|2>>+<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1>|)>+<with|math-font-family|rm|F4>*<around*|(|<with|math-font-family|rm|p0>*<with|math-font-family|rm|F4>+<frac|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F1>|<sqrt|2>>|)>>|<cell|0>>|<row|<cell|0>|<cell|0>|<cell|<with|math-font-family|rm|p2>*<with|math-font-family|rm|F2><rsup|2>>>>>>>> 64 </unfolded-io> 65 66 <\unfolded-io> 67 <with|color|red|(<with|math-font-family|rm|%i>42) > 68 <|unfolded-io> 69 fullratsimp(s[1,1]) 70 <|unfolded-io> 71 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o42>) 72 >><with|math-font-family|rm|p1>*<with|math-font-family|rm|F3><rsup|2>+<sqrt|2>*<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>*<with|math-font-family|rm|F3>+<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0><rsup|2>>> 73 </unfolded-io> 74 75 <\unfolded-io> 76 <with|color|red|(<with|math-font-family|rm|%i>43) > 77 <|unfolded-io> 78 fullratsimp(s[2,2]) 79 <|unfolded-io> 80 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o43>) 81 >><with|math-font-family|rm|p0>*<with|math-font-family|rm|F4><rsup|2>+<sqrt|2>*<with|math-font-family|rm|p3>*<with|math-font-family|rm|F1>*<with|math-font-family|rm|F4>+<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1><rsup|2>>> 82 </unfolded-io> 83 84 <\unfolded-io> 85 <with|color|red|(<with|math-font-family|rm|%i>44) > 86 <|unfolded-io> 87 fullratsimp(s[3,3]) 88 <|unfolded-io> 89 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o44>) 90 >><with|math-font-family|rm|p2>*<with|math-font-family|rm|F2><rsup|2>>> 91 </unfolded-io> 92 93 <\unfolded-io> 94 <with|color|red|(<with|math-font-family|rm|%i>45) > 95 <|unfolded-io> 96 fullratsimp(s[1,2]*sqrt(2)) 97 <|unfolded-io> 98 <math|<with|math-display|true|<text|<with|font-family|tt|color|red|(<with|math-font-family|rm|%o45>) 99 >><around*|(|<with|math-font-family|rm|p3>*<with|math-font-family|rm|F3>+<sqrt|2>*<with|math-font-family|rm|p0>*<with|math-font-family|rm|F0>|)>*<with|math-font-family|rm|F4>+<sqrt|2>*<with|math-font-family|rm|p1>*<with|math-font-family|rm|F1>*<with|math-font-family|rm|F3>+<with|math-font-family|rm|p3>*<with|math-font-family|rm|F0>*<with|math-font-family|rm|F1>>> 100 </unfolded-io> 101 102 <\input> 103 <with|color|red|(<with|math-font-family|rm|%i>46) > 104 <|input> 105 \; 106 </input> 107 </session> 108</body> 109 110<\initial> 111 <\collection> 112 <associate|language|french> 113 <associate|page-type|a3> 114 </collection> 115</initial>