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
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
|
/* Copyright (C) 2004 Viktor T. Toth <http://www.vttoth.com/>
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation; either version 2 of
* the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be
* useful, but WITHOUT ANY WARRANTY; without even the implied
* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
* PURPOSE. See the GNU General Public License for more details.
*
* The main MAXIMA tensor demo
*
*/
done,
block(
[sel:false],
print("This is the main demonstration program for MAXIMA tensors."),
print("The following demos are available:"),
while sel#x and sel#X do
(
/* This block of code restores trigonometric
simplification properties that are removed
when a kill(all) is executed. */
kill(all),
put('sin,'cos,'complement_function),
put('cos,'sin,'complement_function),
put('sinh,'cosh,'complement_function),
put('cosh,'sinh,'complement_function),
put('cos,1,'unitcof),
put('sin,1,'unitcof),
put('cosh,1,'unitcof),
put('sinh,-1,'unitcof),
put('cos,-1,'complement_cof),
put('sin,-1,'complement_cof),
put('cosh,1,'complement_cof),
put('sinh,1,'complement_cof),
put('sin,'trigonometric,'type),
put('cos,'trigonometric,'type),
put('sinh,'hyper_trigonometric,'type),
put('cosh,'hyper_trigonometric,'type),
print(""),
print("INDICIAL TENSOR MANIPULATION COMPONENT TENSOR MANIPULATION"),
print("1. Basics 11. Initialization"),
print("2. Index contraction 12. Differential geometry"),
print("3. Simplification and symmetries 13. Gravitational theory"),
print("4. Special tensors 14. Frame fields"),
print("5. Coordinate differentiation 15. Torsion and nonmetricity"),
print("6. Covariant derivatives, curvature 16. Algebraic classification"),
print("7. Exterior algebra 17. Differential equations"),
print("8. Generating CTENSOR programs 18. Using Taylor series"),
print("9. Frames, torsion, nonmetricity"),
print(""),
print("A. Algebraic tensor manipulation"),
print("E. Complete examples"),
print("X. Exit this demo"),
print(""),
sel:read("Select an option by its number followed by a semicolon (;)"),
if sel=1 then demo(itensor1)
else if sel=2 then demo(itensor2)
else if sel=3 then demo(itensor3)
else if sel=4 then demo(itensor4)
else if sel=5 then demo(itensor5)
else if sel=6 then demo(itensor6)
else if sel=7 then demo(ex_calc)
else if sel=8 then demo(itensor8)
else if sel=9 then demo(itensor9)
else if sel=11 then demo(ctensor1)
else if sel=12 then demo(ctensor2)
else if sel=13 then demo(ctensor3)
else if sel=14 then demo(ctensor4)
else if sel=15 then demo(ctensor5)
else if sel=16 then demo(ctensor6)
else if sel=17 then demo(ctensor7)
else if sel=18 then demo(ctensor8)
else if sel=a then demo(atensor)
else if sel=E or sel=e then
(
print("The following specific examples demonstrate practical applications:"),
print(""),
print("INDICIAL TENSOR MANIPULATION COMPONENT TENSOR MANIPULATION"),
print("1. Proving the Bianchi-identities 11. Deriving Schwarzschild's metric"),
print("2. Proving Cartan's identities 12. Verifying Reissner-Nordstrom"),
print("3. The Kaluza-Klein metric 13. Petrov classification of metrics"),
print("4. The double divergence of R 14. Using a tetrad base"),
print("5. Helicity in hydrodynamics 15. The Friedmann equations"),
print("6. Magnetic field in plasma 16. Papapetrou's nonsymmetric metric"),
print("7. Spinor algebra 17. The Kruskal extension"),
print("8. The EM field tensor 18. Hydrostatic equilibrium"),
print("9. The Hodge star operator"),
print("A. The Riemann and Weyl tensors"),
print("B. The Rainich conditions"),
print("C. The Einstein-Hilbert action"),
print("D. Brans-Dicke cosmology"),
print(""),
print("X. Return to main menu"),
print(""),
sel:read("Select an option by its number followed by a semicolon (;)"),
if sel=1 then demo(bianchi)
else if sel=2 then demo(car_iden)
else if sel=3 then demo(kaluza)
else if sel=4 then demo(ademo)
else if sel=5 then demo(helicity)
else if sel=6 then demo(plasma)
else if sel=7 then demo(spinor)
else if sel=8 then demo(maxwell)
else if sel=9 then demo(hodge)
else if sel=a or sel=A then demo(weyl)
else if sel=b or sel=B then demo(rainich)
else if sel=c or sel=C then demo(einhil)
else if sel=d or sel=D then demo(bradic)
else if sel=11 then demo(schwarz)
else if sel=12 then demo(reissner)
else if sel=13 then
(
print("Choose from the following metrics"),
print(""),
print("1. The Schwarschild metric (type D)"),
print("2. The Kerr metric (type D)"),
print("3. The anti-deSitter metric (type 0)"),
print("4. Godel's universe (type D)"),
print("5. Taub-Nut plane vacuum (type D)"),
print("6. Allnutt's perfect fluid metric (type III)"),
print(""),
print("X. Return to main menu"),
print(""),
sel:read("Select an option by its number followed by a semicolon (;)"),
if sel=1 then demo("ctensor6")
else if sel=2 then demo("petrov")
else if sel=3 then demo("adsitter")
else if sel=4 then demo("godel")
else if sel=5 then demo("taubnut")
else if sel=6 then demo("allnutt")
else if sel#X and sel#x then print("*** Invalid entry, please try again")
else sel:0
)
else if sel=14 then demo(tetrad)
else if sel=15 then demo(friedmann)
else if sel=16 then demo(papapetrou)
else if sel=17 then demo(kruskal)
else if sel=18 then demo(hydro)
else if sel#X and sel#x then print("*** Invalid entry, please try again")
else sel:0
)
else if sel#X and sel#x then print("*** Invalid entry, please try again")
))$
|
