v0.14.0
test_T3_01.cpp
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1 #include "../../../src/FTensor.hpp"
2 #include "../test_for_zero.hpp"
3 #include <iostream>
4 using namespace FTensor;
5 using namespace std;
6 
7 void test_T3_01(const Tensor1<double, 3> &t1_1, const Tensor1<double, 3> &t1_2,
8  const Tensor2<double, 3, 3> &t2_2,
9  const Tensor2<double, 3, 3> &t2_3,
10  const Tensor2_symmetric<double, 3> &t2s_2,
11  const Tensor2_symmetric<double, 3> &t2s_3,
12  const Dg<double, 3, 3> &t3dg_2)
13 {
14  Index<'i', 3> i;
15  Index<'j', 3> j;
16  Index<'k', 3> k;
17  Index<'l', 3> l;
18 
19  Number<0> N0;
20  Number<1> N1;
21  Number<2> N2;
22 
23  /* Tensor3 tests */
24 
25  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 0, 0)
26  - t2_2(0, 0) * t1_2(0) * 10,
27  "T3*T(0,0,0)");
28  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 0, 1)
29  - t2_2(0, 0) * t1_2(1) * 10,
30  "T3*T(0,0,1)");
31  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 0, 2)
32  - t2_2(0, 0) * t1_2(2) * 10,
33  "T3*T(0,0,2)");
34  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 1, 0)
35  - t2_2(0, 1) * t1_2(0) * 10,
36  "T3*T(0,1,0)");
37  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 1, 1)
38  - t2_2(0, 1) * t1_2(1) * 10,
39  "T3*T(0,1,1)");
40  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 1, 2)
41  - t2_2(0, 1) * t1_2(2) * 10,
42  "T3*T(0,1,2)");
43  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 2, 0)
44  - t2_2(0, 2) * t1_2(0) * 10,
45  "T3*T(0,2,0)");
46  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 2, 1)
47  - t2_2(0, 2) * t1_2(1) * 10,
48  "T3*T(0,2,1)");
49  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(0, 2, 2)
50  - t2_2(0, 2) * t1_2(2) * 10,
51  "T3*T(0,2,2)");
52  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 0, 0)
53  - t2_2(1, 0) * t1_2(0) * 10,
54  "T3*T(1,0,0)");
55  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 0, 1)
56  - t2_2(1, 0) * t1_2(1) * 10,
57  "T3*T(1,0,1)");
58  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 0, 2)
59  - t2_2(1, 0) * t1_2(2) * 10,
60  "T3*T(1,0,2)");
61  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 1, 0)
62  - t2_2(1, 1) * t1_2(0) * 10,
63  "T3*T(1,1,0)");
64  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 1, 1)
65  - t2_2(1, 1) * t1_2(1) * 10,
66  "T3*T(1,1,1)");
67  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 1, 2)
68  - t2_2(1, 1) * t1_2(2) * 10,
69  "T3*T(1,1,2)");
70  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 2, 0)
71  - t2_2(1, 2) * t1_2(0) * 10,
72  "T3*T(1,2,0)");
73  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 2, 1)
74  - t2_2(1, 2) * t1_2(1) * 10,
75  "T3*T(1,2,1)");
76  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(1, 2, 2)
77  - t2_2(1, 2) * t1_2(2) * 10,
78  "T3*T(1,2,2)");
79  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 0, 0)
80  - t2_2(2, 0) * t1_2(0) * 10,
81  "T3*T(2,0,0)");
82  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 0, 1)
83  - t2_2(2, 0) * t1_2(1) * 10,
84  "T3*T(2,0,1)");
85  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 0, 2)
86  - t2_2(2, 0) * t1_2(2) * 10,
87  "T3*T(2,0,2)");
88  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 1, 0)
89  - t2_2(2, 1) * t1_2(0) * 10,
90  "T3*T(2,1,0)");
91  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 1, 1)
92  - t2_2(2, 1) * t1_2(1) * 10,
93  "T3*T(2,1,1)");
94  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 1, 2)
95  - t2_2(2, 1) * t1_2(2) * 10,
96  "T3*T(2,1,2)");
97  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 2, 0)
98  - t2_2(2, 2) * t1_2(0) * 10,
99  "T3*T(2,2,0)");
100  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 2, 1)
101  - t2_2(2, 2) * t1_2(1) * 10,
102  "T3*T(2,2,1)");
103  test_for_zero(((t2_2(i, j) * t1_2(k)) * 10)(2, 2, 2)
104  - t2_2(2, 2) * t1_2(2) * 10,
105  "T3*T(2,2,2)");
106 
107  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 0, 0)
108  - t2_2(0, 0) * t1_2(0) * 10,
109  "T*T3(0,0,0)");
110  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 0, 1)
111  - t2_2(0, 0) * t1_2(1) * 10,
112  "T*T3(0,0,1)");
113  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 0, 2)
114  - t2_2(0, 0) * t1_2(2) * 10,
115  "T*T3(0,0,2)");
116  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 1, 0)
117  - t2_2(0, 1) * t1_2(0) * 10,
118  "T*T3(0,1,0)");
119  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 1, 1)
120  - t2_2(0, 1) * t1_2(1) * 10,
121  "T*T3(0,1,1)");
122  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 1, 2)
123  - t2_2(0, 1) * t1_2(2) * 10,
124  "T*T3(0,1,2)");
125  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 2, 0)
126  - t2_2(0, 2) * t1_2(0) * 10,
127  "T*T3(0,2,0)");
128  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 2, 1)
129  - t2_2(0, 2) * t1_2(1) * 10,
130  "T*T3(0,2,1)");
131  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(0, 2, 2)
132  - t2_2(0, 2) * t1_2(2) * 10,
133  "T*T3(0,2,2)");
134  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 0, 0)
135  - t2_2(1, 0) * t1_2(0) * 10,
136  "T*T3(1,0,0)");
137  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 0, 1)
138  - t2_2(1, 0) * t1_2(1) * 10,
139  "T*T3(1,0,1)");
140  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 0, 2)
141  - t2_2(1, 0) * t1_2(2) * 10,
142  "T*T3(1,0,2)");
143  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 1, 0)
144  - t2_2(1, 1) * t1_2(0) * 10,
145  "T*T3(1,1,0)");
146  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 1, 1)
147  - t2_2(1, 1) * t1_2(1) * 10,
148  "T*T3(1,1,1)");
149  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 1, 2)
150  - t2_2(1, 1) * t1_2(2) * 10,
151  "T*T3(1,1,2)");
152  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 2, 0)
153  - t2_2(1, 2) * t1_2(0) * 10,
154  "T*T3(1,2,0)");
155  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 2, 1)
156  - t2_2(1, 2) * t1_2(1) * 10,
157  "T*T3(1,2,1)");
158  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(1, 2, 2)
159  - t2_2(1, 2) * t1_2(2) * 10,
160  "T*T3(1,2,2)");
161  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 0, 0)
162  - t2_2(2, 0) * t1_2(0) * 10,
163  "T*T3(2,0,0)");
164  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 0, 1)
165  - t2_2(2, 0) * t1_2(1) * 10,
166  "T*T3(2,0,1)");
167  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 0, 2)
168  - t2_2(2, 0) * t1_2(2) * 10,
169  "T*T3(2,0,2)");
170  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 1, 0)
171  - t2_2(2, 1) * t1_2(0) * 10,
172  "T*T3(2,1,0)");
173  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 1, 1)
174  - t2_2(2, 1) * t1_2(1) * 10,
175  "T*T3(2,1,1)");
176  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 1, 2)
177  - t2_2(2, 1) * t1_2(2) * 10,
178  "T*T3(2,1,2)");
179  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 2, 0)
180  - t2_2(2, 2) * t1_2(0) * 10,
181  "T*T3(2,2,0)");
182  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 2, 1)
183  - t2_2(2, 2) * t1_2(1) * 10,
184  "T*T3(2,2,1)");
185  test_for_zero((10 * (t2_2(i, j) * t1_2(k)))(2, 2, 2)
186  - t2_2(2, 2) * t1_2(2) * 10,
187  "T*T3(2,2,2)");
188 
189  Tensor2<double, 3, 3> t2;
190 
191  t2(i, k) = (t2_2(i, j) * t1_2(k)) * t1_1(j);
192 
193  test_for_zero(t2(0, 0)
194  - (t2_2(0, 0) * t1_2(0) * t1_1(0)
195  + t2_2(0, 1) * t1_2(0) * t1_1(1)
196  + t2_2(0, 2) * t1_2(0) * t1_1(2)),
197  "T3(i,j,k)*T1(j)(0,0)");
198  test_for_zero(t2(0, 1)
199  - (t2_2(0, 0) * t1_2(1) * t1_1(0)
200  + t2_2(0, 1) * t1_2(1) * t1_1(1)
201  + t2_2(0, 2) * t1_2(1) * t1_1(2)),
202  "T3(i,j,k)*T1(j)(0,1)");
203  test_for_zero(t2(0, 2)
204  - (t2_2(0, 0) * t1_2(2) * t1_1(0)
205  + t2_2(0, 1) * t1_2(2) * t1_1(1)
206  + t2_2(0, 2) * t1_2(2) * t1_1(2)),
207  "T3(i,j,k)*T1(j)(0,2)");
208  test_for_zero(t2(1, 0)
209  - (t2_2(1, 0) * t1_2(0) * t1_1(0)
210  + t2_2(1, 1) * t1_2(0) * t1_1(1)
211  + t2_2(1, 2) * t1_2(0) * t1_1(2)),
212  "T3(i,j,k)*T1(j)(1,0)");
213  test_for_zero(t2(1, 1)
214  - (t2_2(1, 0) * t1_2(1) * t1_1(0)
215  + t2_2(1, 1) * t1_2(1) * t1_1(1)
216  + t2_2(1, 2) * t1_2(1) * t1_1(2)),
217  "T3(i,j,k)*T1(j)(1,1)");
218  test_for_zero(t2(1, 2)
219  - (t2_2(1, 0) * t1_2(2) * t1_1(0)
220  + t2_2(1, 1) * t1_2(2) * t1_1(1)
221  + t2_2(1, 2) * t1_2(2) * t1_1(2)),
222  "T3(i,j,k)*T1(j)(1,2)");
223  test_for_zero(t2(2, 0)
224  - (t2_2(2, 0) * t1_2(0) * t1_1(0)
225  + t2_2(2, 1) * t1_2(0) * t1_1(1)
226  + t2_2(2, 2) * t1_2(0) * t1_1(2)),
227  "T3(i,j,k)*T1(j)(2,0)");
228  test_for_zero(t2(2, 1)
229  - (t2_2(2, 0) * t1_2(1) * t1_1(0)
230  + t2_2(2, 1) * t1_2(1) * t1_1(1)
231  + t2_2(2, 2) * t1_2(1) * t1_1(2)),
232  "T3(i,j,k)*T1(j)(2,1)");
233  test_for_zero(t2(2, 2)
234  - (t2_2(2, 0) * t1_2(2) * t1_1(0)
235  + t2_2(2, 1) * t1_2(2) * t1_1(1)
236  + t2_2(2, 2) * t1_2(2) * t1_1(2)),
237  "T3(i,j,k)*T1(j)(2,2)");
238 
239  t2(i, k) = t1_2(j) * (t2_2(i, j) * t1_1(k));
240 
241  test_for_zero(t2(0, 0)
242  - (t2_2(0, 0) * t1_1(0) * t1_2(0)
243  + t2_2(0, 1) * t1_1(0) * t1_2(1)
244  + t2_2(0, 2) * t1_1(0) * t1_2(2)),
245  "T1(j)*T3(i,j,k)(0,0)");
246  test_for_zero(t2(0, 1)
247  - (t2_2(0, 0) * t1_1(1) * t1_2(0)
248  + t2_2(0, 1) * t1_1(1) * t1_2(1)
249  + t2_2(0, 2) * t1_1(1) * t1_2(2)),
250  "T1(j)*T3(i,j,k)(0,1)");
251  test_for_zero(t2(0, 2)
252  - (t2_2(0, 0) * t1_1(2) * t1_2(0)
253  + t2_2(0, 1) * t1_1(2) * t1_2(1)
254  + t2_2(0, 2) * t1_1(2) * t1_2(2)),
255  "T1(j)*T3(i,j,k)(0,2)");
256  test_for_zero(t2(1, 0)
257  - (t2_2(1, 0) * t1_1(0) * t1_2(0)
258  + t2_2(1, 1) * t1_1(0) * t1_2(1)
259  + t2_2(1, 2) * t1_1(0) * t1_2(2)),
260  "T1(j)*T3(i,j,k)(1,0)");
261  test_for_zero(t2(1, 1)
262  - (t2_2(1, 0) * t1_1(1) * t1_2(0)
263  + t2_2(1, 1) * t1_1(1) * t1_2(1)
264  + t2_2(1, 2) * t1_1(1) * t1_2(2)),
265  "T1(j)*T3(i,j,k)(1,1)");
266  test_for_zero(t2(1, 2)
267  - (t2_2(1, 0) * t1_1(2) * t1_2(0)
268  + t2_2(1, 1) * t1_1(2) * t1_2(1)
269  + t2_2(1, 2) * t1_1(2) * t1_2(2)),
270  "T1(j)*T3(i,j,k)(1,2)");
271  test_for_zero(t2(2, 0)
272  - (t2_2(2, 0) * t1_1(0) * t1_2(0)
273  + t2_2(2, 1) * t1_1(0) * t1_2(1)
274  + t2_2(2, 2) * t1_1(0) * t1_2(2)),
275  "T1(j)*T3(i,j,k)(2,0)");
276  test_for_zero(t2(2, 1)
277  - (t2_2(2, 0) * t1_1(1) * t1_2(0)
278  + t2_2(2, 1) * t1_1(1) * t1_2(1)
279  + t2_2(2, 2) * t1_1(1) * t1_2(2)),
280  "T1(j)*T3(i,j,k)(2,1)");
281  test_for_zero(t2(2, 2)
282  - (t2_2(2, 0) * t1_1(2) * t1_2(0)
283  + t2_2(2, 1) * t1_1(2) * t1_2(1)
284  + t2_2(2, 2) * t1_1(2) * t1_2(2)),
285  "T1(j)*T3(i,j,k)(2,2)");
286 
287  // T3*T2s double contraction
288  Tensor1<double, 3> t1;
289  for(int ii = 0; ii < 3; ++ii)
290  {
291  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2s_2(j, k))(ii)
292  - (t2_2(ii, 0) * t1_2(0) * t2s_2(0, 0)
293  + t2_2(ii, 0) * t1_2(1) * t2s_2(0, 1)
294  + t2_2(ii, 0) * t1_2(2) * t2s_2(0, 2)
295  + t2_2(ii, 1) * t1_2(0) * t2s_2(1, 0)
296  + t2_2(ii, 1) * t1_2(1) * t2s_2(1, 1)
297  + t2_2(ii, 1) * t1_2(2) * t2s_2(1, 2)
298  + t2_2(ii, 2) * t1_2(0) * t2s_2(2, 0)
299  + t2_2(ii, 2) * t1_2(1) * t2s_2(2, 1)
300  + t2_2(ii, 2) * t1_2(2) * t2s_2(2, 2)),
301  "T3(i,j,k)*T2s(j,k)(" + std::to_string(ii) + ")");
302 
303  test_for_zero((t2s_3(j, k) * (t2_2(i, j) * t1_2(k)))(ii)
304  - (t2_2(ii, 0) * t1_2(0) * t2s_3(0, 0)
305  + t2_2(ii, 0) * t1_2(1) * t2s_3(0, 1)
306  + t2_2(ii, 0) * t1_2(2) * t2s_3(0, 2)
307  + t2_2(ii, 1) * t1_2(0) * t2s_3(1, 0)
308  + t2_2(ii, 1) * t1_2(1) * t2s_3(1, 1)
309  + t2_2(ii, 1) * t1_2(2) * t2s_3(1, 2)
310  + t2_2(ii, 2) * t1_2(0) * t2s_3(2, 0)
311  + t2_2(ii, 2) * t1_2(1) * t2s_3(2, 1)
312  + t2_2(ii, 2) * t1_2(2) * t2s_3(2, 2)),
313  "T2s(j,k)*T3(i,j,k)(" + std::to_string(ii) + ")");
314 
315  test_for_zero(((t2_2(j, i) * t1_2(k)) * t2s_2(j, k))(ii)
316  - (t2_2(0, ii) * t1_2(0) * t2s_2(0, 0)
317  + t2_2(0, ii) * t1_2(1) * t2s_2(0, 1)
318  + t2_2(0, ii) * t1_2(2) * t2s_2(0, 2)
319  + t2_2(1, ii) * t1_2(0) * t2s_2(1, 0)
320  + t2_2(1, ii) * t1_2(1) * t2s_2(1, 1)
321  + t2_2(1, ii) * t1_2(2) * t2s_2(1, 2)
322  + t2_2(2, ii) * t1_2(0) * t2s_2(2, 0)
323  + t2_2(2, ii) * t1_2(1) * t2s_2(2, 1)
324  + t2_2(2, ii) * t1_2(2) * t2s_2(2, 2)),
325  "T3(j,i,k)*T2s(j,k)(" + std::to_string(ii) + ")");
326 
327  test_for_zero((t2s_3(j, k) * (t2_2(j, i) * t1_2(k)))(ii)
328  - (t2_2(0, ii) * t1_2(0) * t2s_3(0, 0)
329  + t2_2(0, ii) * t1_2(1) * t2s_3(0, 1)
330  + t2_2(0, ii) * t1_2(2) * t2s_3(0, 2)
331  + t2_2(1, ii) * t1_2(0) * t2s_3(1, 0)
332  + t2_2(1, ii) * t1_2(1) * t2s_3(1, 1)
333  + t2_2(1, ii) * t1_2(2) * t2s_3(1, 2)
334  + t2_2(2, ii) * t1_2(0) * t2s_3(2, 0)
335  + t2_2(2, ii) * t1_2(1) * t2s_3(2, 1)
336  + t2_2(2, ii) * t1_2(2) * t2s_3(2, 2)),
337  "T2s(j,k)*T3(j,i,k)(" + std::to_string(ii) + ")");
338 
339  test_for_zero(((t2_2(j, k) * t1_2(i)) * t2s_2(j, k))(ii)
340  - (t2_2(0, 0) * t1_2(ii) * t2s_2(0, 0)
341  + t2_2(0, 1) * t1_2(ii) * t2s_2(0, 1)
342  + t2_2(0, 2) * t1_2(ii) * t2s_2(0, 2)
343  + t2_2(1, 0) * t1_2(ii) * t2s_2(1, 0)
344  + t2_2(1, 1) * t1_2(ii) * t2s_2(1, 1)
345  + t2_2(1, 2) * t1_2(ii) * t2s_2(1, 2)
346  + t2_2(2, 0) * t1_2(ii) * t2s_2(2, 0)
347  + t2_2(2, 1) * t1_2(ii) * t2s_2(2, 1)
348  + t2_2(2, 2) * t1_2(ii) * t2s_2(2, 2)),
349  "T3(j,k,i)*T2s(j,k)(" + std::to_string(ii) + ")");
350 
351  test_for_zero((t2s_3(j, k) * (t2_2(j, k) * t1_2(i)))(ii)
352  - (t2_2(0, 0) * t1_2(ii) * t2s_3(0, 0)
353  + t2_2(0, 1) * t1_2(ii) * t2s_3(0, 1)
354  + t2_2(0, 2) * t1_2(ii) * t2s_3(0, 2)
355  + t2_2(1, 0) * t1_2(ii) * t2s_3(1, 0)
356  + t2_2(1, 1) * t1_2(ii) * t2s_3(1, 1)
357  + t2_2(1, 2) * t1_2(ii) * t2s_3(1, 2)
358  + t2_2(2, 0) * t1_2(ii) * t2s_3(2, 0)
359  + t2_2(2, 1) * t1_2(ii) * t2s_3(2, 1)
360  + t2_2(2, 2) * t1_2(ii) * t2s_3(2, 2)),
361  "T2s(j,k)*T3(j,k,i)(" + std::to_string(ii) + ")");
362  }
363 
364  // T3*T2 double contraction
365  for(int ii = 0; ii < 3; ++ii)
366  {
367  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_2(j, k))(ii)
368  - (t2_2(ii, 0) * t1_2(0) * t2_2(0, 0)
369  + t2_2(ii, 0) * t1_2(1) * t2_2(0, 1)
370  + t2_2(ii, 0) * t1_2(2) * t2_2(0, 2)
371  + t2_2(ii, 1) * t1_2(0) * t2_2(1, 0)
372  + t2_2(ii, 1) * t1_2(1) * t2_2(1, 1)
373  + t2_2(ii, 1) * t1_2(2) * t2_2(1, 2)
374  + t2_2(ii, 2) * t1_2(0) * t2_2(2, 0)
375  + t2_2(ii, 2) * t1_2(1) * t2_2(2, 1)
376  + t2_2(ii, 2) * t1_2(2) * t2_2(2, 2)),
377  "T3(i,j,k)*T2(j,k)(" + std::to_string(ii) + ")");
378 
379  test_for_zero((t2_2(j, k) * (t2_2(i, j) * t1_2(k)))(ii)
380  - (t2_2(ii, 0) * t1_2(0) * t2_2(0, 0)
381  + t2_2(ii, 0) * t1_2(1) * t2_2(0, 1)
382  + t2_2(ii, 0) * t1_2(2) * t2_2(0, 2)
383  + t2_2(ii, 1) * t1_2(0) * t2_2(1, 0)
384  + t2_2(ii, 1) * t1_2(1) * t2_2(1, 1)
385  + t2_2(ii, 1) * t1_2(2) * t2_2(1, 2)
386  + t2_2(ii, 2) * t1_2(0) * t2_2(2, 0)
387  + t2_2(ii, 2) * t1_2(1) * t2_2(2, 1)
388  + t2_2(ii, 2) * t1_2(2) * t2_2(2, 2)),
389  "T2(j,k)*T3(i,j,k)(" + std::to_string(ii) + ")");
390 
391  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_2(k, j))(ii)
392  - (t2_2(ii, 0) * t1_2(0) * t2_2(0, 0)
393  + t2_2(ii, 0) * t1_2(1) * t2_2(1, 0)
394  + t2_2(ii, 0) * t1_2(2) * t2_2(2, 0)
395  + t2_2(ii, 1) * t1_2(0) * t2_2(0, 1)
396  + t2_2(ii, 1) * t1_2(1) * t2_2(1, 1)
397  + t2_2(ii, 1) * t1_2(2) * t2_2(2, 1)
398  + t2_2(ii, 2) * t1_2(0) * t2_2(0, 2)
399  + t2_2(ii, 2) * t1_2(1) * t2_2(1, 2)
400  + t2_2(ii, 2) * t1_2(2) * t2_2(2, 2)),
401  "T3(i,j,k)*T2(k,j)(" + std::to_string(ii) + ")");
402 
403  test_for_zero((t2_2(k, j) * (t2_2(i, j) * t1_2(k)))(ii)
404  - (t2_2(ii, 0) * t1_2(0) * t2_2(0, 0)
405  + t2_2(ii, 0) * t1_2(1) * t2_2(1, 0)
406  + t2_2(ii, 0) * t1_2(2) * t2_2(2, 0)
407  + t2_2(ii, 1) * t1_2(0) * t2_2(0, 1)
408  + t2_2(ii, 1) * t1_2(1) * t2_2(1, 1)
409  + t2_2(ii, 1) * t1_2(2) * t2_2(2, 1)
410  + t2_2(ii, 2) * t1_2(0) * t2_2(0, 2)
411  + t2_2(ii, 2) * t1_2(1) * t2_2(1, 2)
412  + t2_2(ii, 2) * t1_2(2) * t2_2(2, 2)),
413  "T2(k,j)*T3(i,j,k)(" + std::to_string(ii) + ")");
414 
415  test_for_zero(((t2_2(j, i) * t1_2(k)) * t2_2(j, k))(ii)
416  - (t2_2(0, ii) * t1_2(0) * t2_2(0, 0)
417  + t2_2(0, ii) * t1_2(1) * t2_2(0, 1)
418  + t2_2(0, ii) * t1_2(2) * t2_2(0, 2)
419  + t2_2(1, ii) * t1_2(0) * t2_2(1, 0)
420  + t2_2(1, ii) * t1_2(1) * t2_2(1, 1)
421  + t2_2(1, ii) * t1_2(2) * t2_2(1, 2)
422  + t2_2(2, ii) * t1_2(0) * t2_2(2, 0)
423  + t2_2(2, ii) * t1_2(1) * t2_2(2, 1)
424  + t2_2(2, ii) * t1_2(2) * t2_2(2, 2)),
425  "T3(j,i,k)*T2(j,k)(" + std::to_string(ii) + ")");
426 
427  test_for_zero((t2_2(j, k) * (t2_2(j, i) * t1_2(k)))(ii)
428  - (t2_2(0, ii) * t1_2(0) * t2_2(0, 0)
429  + t2_2(0, ii) * t1_2(1) * t2_2(0, 1)
430  + t2_2(0, ii) * t1_2(2) * t2_2(0, 2)
431  + t2_2(1, ii) * t1_2(0) * t2_2(1, 0)
432  + t2_2(1, ii) * t1_2(1) * t2_2(1, 1)
433  + t2_2(1, ii) * t1_2(2) * t2_2(1, 2)
434  + t2_2(2, ii) * t1_2(0) * t2_2(2, 0)
435  + t2_2(2, ii) * t1_2(1) * t2_2(2, 1)
436  + t2_2(2, ii) * t1_2(2) * t2_2(2, 2)),
437  "T2(j,k)*T3(j,i,k)(" + std::to_string(ii) + ")");
438 
439  test_for_zero(((t2_2(j, i) * t1_2(k)) * t2_2(k, j))(ii)
440  - (t2_2(0, ii) * t1_2(0) * t2_2(0, 0)
441  + t2_2(0, ii) * t1_2(1) * t2_2(1, 0)
442  + t2_2(0, ii) * t1_2(2) * t2_2(2, 0)
443  + t2_2(1, ii) * t1_2(0) * t2_2(0, 1)
444  + t2_2(1, ii) * t1_2(1) * t2_2(1, 1)
445  + t2_2(1, ii) * t1_2(2) * t2_2(2, 1)
446  + t2_2(2, ii) * t1_2(0) * t2_2(0, 2)
447  + t2_2(2, ii) * t1_2(1) * t2_2(1, 2)
448  + t2_2(2, ii) * t1_2(2) * t2_2(2, 2)),
449  "T3(j,i,k)*T2(k,j)(" + std::to_string(ii) + ")");
450 
451  test_for_zero((t2_2(k, j) * (t2_2(j, i) * t1_2(k)))(ii)
452  - (t2_2(0, ii) * t1_2(0) * t2_2(0, 0)
453  + t2_2(0, ii) * t1_2(1) * t2_2(1, 0)
454  + t2_2(0, ii) * t1_2(2) * t2_2(2, 0)
455  + t2_2(1, ii) * t1_2(0) * t2_2(0, 1)
456  + t2_2(1, ii) * t1_2(1) * t2_2(1, 1)
457  + t2_2(1, ii) * t1_2(2) * t2_2(2, 1)
458  + t2_2(2, ii) * t1_2(0) * t2_2(0, 2)
459  + t2_2(2, ii) * t1_2(1) * t2_2(1, 2)
460  + t2_2(2, ii) * t1_2(2) * t2_2(2, 2)),
461  "T2(k,j)*T3(j,i,k)(" + std::to_string(ii) + ")");
462 
463  test_for_zero(((t2_2(j, k) * t1_2(i)) * t2_2(j, k))(ii)
464  - (t2_2(0, 0) * t1_2(ii) * t2_2(0, 0)
465  + t2_2(0, 1) * t1_2(ii) * t2_2(0, 1)
466  + t2_2(0, 2) * t1_2(ii) * t2_2(0, 2)
467  + t2_2(1, 0) * t1_2(ii) * t2_2(1, 0)
468  + t2_2(1, 1) * t1_2(ii) * t2_2(1, 1)
469  + t2_2(1, 2) * t1_2(ii) * t2_2(1, 2)
470  + t2_2(2, 0) * t1_2(ii) * t2_2(2, 0)
471  + t2_2(2, 1) * t1_2(ii) * t2_2(2, 1)
472  + t2_2(2, 2) * t1_2(ii) * t2_2(2, 2)),
473  "T3(j,k,i)*T2(j,k)(" + std::to_string(ii) + ")");
474 
475  test_for_zero((t2_2(j, k) * (t2_2(j, k) * t1_2(i)))(ii)
476  - (t2_2(0, 0) * t1_2(ii) * t2_2(0, 0)
477  + t2_2(0, 1) * t1_2(ii) * t2_2(0, 1)
478  + t2_2(0, 2) * t1_2(ii) * t2_2(0, 2)
479  + t2_2(1, 0) * t1_2(ii) * t2_2(1, 0)
480  + t2_2(1, 1) * t1_2(ii) * t2_2(1, 1)
481  + t2_2(1, 2) * t1_2(ii) * t2_2(1, 2)
482  + t2_2(2, 0) * t1_2(ii) * t2_2(2, 0)
483  + t2_2(2, 1) * t1_2(ii) * t2_2(2, 1)
484  + t2_2(2, 2) * t1_2(ii) * t2_2(2, 2)),
485  "T2(j,k)*T3(j,k,i)(" + std::to_string(ii) + ")");
486 
487  test_for_zero(((t2_2(j, k) * t1_2(i)) * t2_2(k, j))(ii)
488  - (t2_2(0, 0) * t1_2(ii) * t2_2(0, 0)
489  + t2_2(0, 1) * t1_2(ii) * t2_2(1, 0)
490  + t2_2(0, 2) * t1_2(ii) * t2_2(2, 0)
491  + t2_2(1, 0) * t1_2(ii) * t2_2(0, 1)
492  + t2_2(1, 1) * t1_2(ii) * t2_2(1, 1)
493  + t2_2(1, 2) * t1_2(ii) * t2_2(2, 1)
494  + t2_2(2, 0) * t1_2(ii) * t2_2(0, 2)
495  + t2_2(2, 1) * t1_2(ii) * t2_2(1, 2)
496  + t2_2(2, 2) * t1_2(ii) * t2_2(2, 2)),
497  "T3(j,k,i)*T2(k,j)(" + std::to_string(ii) + ")");
498 
499  test_for_zero((t2_2(k, j) * (t2_2(j, k) * t1_2(i)))(ii)
500  - (t2_2(0, 0) * t1_2(ii) * t2_2(0, 0)
501  + t2_2(0, 1) * t1_2(ii) * t2_2(1, 0)
502  + t2_2(0, 2) * t1_2(ii) * t2_2(2, 0)
503  + t2_2(1, 0) * t1_2(ii) * t2_2(0, 1)
504  + t2_2(1, 1) * t1_2(ii) * t2_2(1, 1)
505  + t2_2(1, 2) * t1_2(ii) * t2_2(2, 1)
506  + t2_2(2, 0) * t1_2(ii) * t2_2(0, 2)
507  + t2_2(2, 1) * t1_2(ii) * t2_2(1, 2)
508  + t2_2(2, 2) * t1_2(ii) * t2_2(2, 2)),
509  "T2(k,j)*T3(j,k,i)(" + std::to_string(ii) + ")");
510  }
511 
512  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 0, 0)
513  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 0, 0),
514  "T3(i,j,k)*T2(k,l)(0,0,0)");
515  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 0, 1)
516  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 0, 1),
517  "T3(i,j,k)*T2(k,l)(0,0,1)");
518  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 0, 2)
519  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 0, 2),
520  "T3(i,j,k)*T2(k,l)(0,0,2)");
521  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 1, 0)
522  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 1, 0),
523  "T3(i,j,k)*T2(k,l)(0,1,0)");
524  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 1, 1)
525  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 1, 1),
526  "T3(i,j,k)*T2(k,l)(0,1,1)");
527  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 1, 2)
528  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 1, 2),
529  "T3(i,j,k)*T2(k,l)(0,1,2)");
530  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 2, 0)
531  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 2, 0),
532  "T3(i,j,k)*T2(k,l)(0,2,0)");
533  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 2, 1)
534  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 2, 1),
535  "T3(i,j,k)*T2(k,l)(0,2,1)");
536  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(0, 2, 2)
537  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 2, 2),
538  "T3(i,j,k)*T2(k,l)(0,2,2)");
539  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 0, 0)
540  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 0, 0),
541  "T3(i,j,k)*T2(k,l)(1,0,0)");
542  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 0, 1)
543  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 0, 1),
544  "T3(i,j,k)*T2(k,l)(1,0,1)");
545  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 0, 2)
546  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 0, 2),
547  "T3(i,j,k)*T2(k,l)(1,0,2)");
548  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 1, 0)
549  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 1, 0),
550  "T3(i,j,k)*T2(k,l)(1,1,0)");
551  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 1, 1)
552  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 1, 1),
553  "T3(i,j,k)*T2(k,l)(1,1,1)");
554  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 1, 2)
555  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 1, 2),
556  "T3(i,j,k)*T2(k,l)(1,1,2)");
557  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 2, 0)
558  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 2, 0),
559  "T3(i,j,k)*T2(k,l)(1,2,0)");
560  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 2, 1)
561  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 2, 1),
562  "T3(i,j,k)*T2(k,l)(1,2,1)");
563  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(1, 2, 2)
564  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 2, 2),
565  "T3(i,j,k)*T2(k,l)(1,2,2)");
566  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 0, 0)
567  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 0, 0),
568  "T3(i,j,k)*T2(k,l)(2,0,0)");
569  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 0, 1)
570  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 0, 1),
571  "T3(i,j,k)*T2(k,l)(2,0,1)");
572  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 0, 2)
573  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 0, 2),
574  "T3(i,j,k)*T2(k,l)(2,0,2)");
575  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 1, 0)
576  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 1, 0),
577  "T3(i,j,k)*T2(k,l)(2,1,0)");
578  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 1, 1)
579  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 1, 1),
580  "T3(i,j,k)*T2(k,l)(2,1,1)");
581  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 1, 2)
582  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 1, 2),
583  "T3(i,j,k)*T2(k,l)(2,1,2)");
584  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 2, 0)
585  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 2, 0),
586  "T3(i,j,k)*T2(k,l)(2,2,0)");
587  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 2, 1)
588  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 2, 1),
589  "T3(i,j,k)*T2(k,l)(2,2,1)");
590  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(k, l))(2, 2, 2)
591  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 2, 2),
592  "T3(i,j,k)*T2(k,l)(2,2,2)");
593 
594  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 0, 0)
595  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 0, 0),
596  "T3(i,j,k)*T2(l,k)(0,0,0)");
597  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 0, 1)
598  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 0, 1),
599  "T3(i,j,k)*T2(l,k)(0,0,1)");
600  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 0, 2)
601  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 0, 2),
602  "T3(i,j,k)*T2(l,k)(0,0,2)");
603  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 1, 0)
604  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 1, 0),
605  "T3(i,j,k)*T2(l,k)(0,1,0)");
606  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 1, 1)
607  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 1, 1),
608  "T3(i,j,k)*T2(l,k)(0,1,1)");
609  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 1, 2)
610  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 1, 2),
611  "T3(i,j,k)*T2(l,k)(0,1,2)");
612  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 2, 0)
613  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 2, 0),
614  "T3(i,j,k)*T2(l,k)(0,2,0)");
615  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 2, 1)
616  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 2, 1),
617  "T3(i,j,k)*T2(l,k)(0,2,1)");
618  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(0, 2, 2)
619  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 2, 2),
620  "T3(i,j,k)*T2(l,k)(0,2,2)");
621  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 0, 0)
622  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 0, 0),
623  "T3(i,j,k)*T2(l,k)(1,0,0)");
624  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 0, 1)
625  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 0, 1),
626  "T3(i,j,k)*T2(l,k)(1,0,1)");
627  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 0, 2)
628  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 0, 2),
629  "T3(i,j,k)*T2(l,k)(1,0,2)");
630  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 1, 0)
631  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 1, 0),
632  "T3(i,j,k)*T2(l,k)(1,1,0)");
633  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 1, 1)
634  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 1, 1),
635  "T3(i,j,k)*T2(l,k)(1,1,1)");
636  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 1, 2)
637  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 1, 2),
638  "T3(i,j,k)*T2(l,k)(1,1,2)");
639  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 2, 0)
640  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 2, 0),
641  "T3(i,j,k)*T2(l,k)(1,2,0)");
642  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 2, 1)
643  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 2, 1),
644  "T3(i,j,k)*T2(l,k)(1,2,1)");
645  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(1, 2, 2)
646  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 2, 2),
647  "T3(i,j,k)*T2(l,k)(1,2,2)");
648  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 0, 0)
649  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 0, 0),
650  "T3(i,j,k)*T2(l,k)(2,0,0)");
651  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 0, 1)
652  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 0, 1),
653  "T3(i,j,k)*T2(l,k)(2,0,1)");
654  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 0, 2)
655  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 0, 2),
656  "T3(i,j,k)*T2(l,k)(2,0,2)");
657  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 1, 0)
658  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 1, 0),
659  "T3(i,j,k)*T2(l,k)(2,1,0)");
660  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 1, 1)
661  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 1, 1),
662  "T3(i,j,k)*T2(l,k)(2,1,1)");
663  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 1, 2)
664  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 1, 2),
665  "T3(i,j,k)*T2(l,k)(2,1,2)");
666  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 2, 0)
667  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 2, 0),
668  "T3(i,j,k)*T2(l,k)(2,2,0)");
669  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 2, 1)
670  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 2, 1),
671  "T3(i,j,k)*T2(l,k)(2,2,1)");
672  test_for_zero(((t2_2(i, j) * t1_2(k)) * t2_3(l, k))(2, 2, 2)
673  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 2, 2),
674  "T3(i,j,k)*T2(l,k)(2,2,2)");
675 
676  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 0, 0)
677  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 0, 0),
678  "T2(k,l)*T3(i,j,k)(0,0,0)");
679  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 0, 1)
680  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 0, 1),
681  "T2(k,l)*T3(i,j,k)(0,0,1)");
682  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 0, 2)
683  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 0, 2),
684  "T2(k,l)*T3(i,j,k)(0,0,2)");
685  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 1, 0)
686  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 1, 0),
687  "T2(k,l)*T3(i,j,k)(0,1,0)");
688  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 1, 1)
689  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 1, 1),
690  "T2(k,l)*T3(i,j,k)(0,1,1)");
691  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 1, 2)
692  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 1, 2),
693  "T2(k,l)*T3(i,j,k)(0,1,2)");
694  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 2, 0)
695  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 2, 0),
696  "T2(k,l)*T3(i,j,k)(0,2,0)");
697  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 2, 1)
698  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 2, 1),
699  "T2(k,l)*T3(i,j,k)(0,2,1)");
700  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(0, 2, 2)
701  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(0, 2, 2),
702  "T2(k,l)*T3(i,j,k)(0,2,2)");
703  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 0, 0)
704  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 0, 0),
705  "T2(k,l)*T3(i,j,k)(1,0,0)");
706  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 0, 1)
707  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 0, 1),
708  "T2(k,l)*T3(i,j,k)(1,0,1)");
709  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 0, 2)
710  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 0, 2),
711  "T2(k,l)*T3(i,j,k)(1,0,2)");
712  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 1, 0)
713  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 1, 0),
714  "T2(k,l)*T3(i,j,k)(1,1,0)");
715  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 1, 1)
716  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 1, 1),
717  "T2(k,l)*T3(i,j,k)(1,1,1)");
718  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 1, 2)
719  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 1, 2),
720  "T2(k,l)*T3(i,j,k)(1,1,2)");
721  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 2, 0)
722  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 2, 0),
723  "T2(k,l)*T3(i,j,k)(1,2,0)");
724  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 2, 1)
725  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 2, 1),
726  "T2(k,l)*T3(i,j,k)(1,2,1)");
727  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(1, 2, 2)
728  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(1, 2, 2),
729  "T2(k,l)*T3(i,j,k)(1,2,2)");
730  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 0, 0)
731  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 0, 0),
732  "T2(k,l)*T3(i,j,k)(2,0,0)");
733  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 0, 1)
734  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 0, 1),
735  "T2(k,l)*T3(i,j,k)(2,0,1)");
736  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 0, 2)
737  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 0, 2),
738  "T2(k,l)*T3(i,j,k)(2,0,2)");
739  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 1, 0)
740  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 1, 0),
741  "T2(k,l)*T3(i,j,k)(2,1,0)");
742  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 1, 1)
743  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 1, 1),
744  "T2(k,l)*T3(i,j,k)(2,1,1)");
745  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 1, 2)
746  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 1, 2),
747  "T2(k,l)*T3(i,j,k)(2,1,2)");
748  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 2, 0)
749  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 2, 0),
750  "T2(k,l)*T3(i,j,k)(2,2,0)");
751  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 2, 1)
752  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 2, 1),
753  "T2(k,l)*T3(i,j,k)(2,2,1)");
754  test_for_zero((t2_3(k, l) * (t2_2(i, j) * t1_2(k)))(2, 2, 2)
755  - (t2_2(i, j) * (t1_2(k) * t2_3(k, l)))(2, 2, 2),
756  "T2(k,l)*T3(i,j,k)(2,2,2)");
757 
758  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 0, 0)
759  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 0, 0),
760  "T2(l,k)*T3(i,j,k)(0,0,0)");
761  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 0, 1)
762  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 0, 1),
763  "T2(l,k)*T3(i,j,k)(0,0,1)");
764  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 0, 2)
765  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 0, 2),
766  "T2(l,k)*T3(i,j,k)(0,0,2)");
767  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 1, 0)
768  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 1, 0),
769  "T2(l,k)*T3(i,j,k)(0,1,0)");
770  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 1, 1)
771  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 1, 1),
772  "T2(l,k)*T3(i,j,k)(0,1,1)");
773  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 1, 2)
774  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 1, 2),
775  "T2(l,k)*T3(i,j,k)(0,1,2)");
776  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 2, 0)
777  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 2, 0),
778  "T2(l,k)*T3(i,j,k)(0,2,0)");
779  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 2, 1)
780  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 2, 1),
781  "T2(l,k)*T3(i,j,k)(0,2,1)");
782  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(0, 2, 2)
783  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(0, 2, 2),
784  "T2(l,k)*T3(i,j,k)(0,2,2)");
785  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 0, 0)
786  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 0, 0),
787  "T2(l,k)*T3(i,j,k)(1,0,0)");
788  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 0, 1)
789  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 0, 1),
790  "T2(l,k)*T3(i,j,k)(1,0,1)");
791  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 0, 2)
792  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 0, 2),
793  "T2(l,k)*T3(i,j,k)(1,0,2)");
794  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 1, 0)
795  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 1, 0),
796  "T2(l,k)*T3(i,j,k)(1,1,0)");
797  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 1, 1)
798  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 1, 1),
799  "T2(l,k)*T3(i,j,k)(1,1,1)");
800  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 1, 2)
801  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 1, 2),
802  "T2(l,k)*T3(i,j,k)(1,1,2)");
803  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 2, 0)
804  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 2, 0),
805  "T2(l,k)*T3(i,j,k)(1,2,0)");
806  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 2, 1)
807  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 2, 1),
808  "T2(l,k)*T3(i,j,k)(1,2,1)");
809  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(1, 2, 2)
810  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(1, 2, 2),
811  "T2(l,k)*T3(i,j,k)(1,2,2)");
812  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 0, 0)
813  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 0, 0),
814  "T2(l,k)*T3(i,j,k)(2,0,0)");
815  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 0, 1)
816  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 0, 1),
817  "T2(l,k)*T3(i,j,k)(2,0,1)");
818  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 0, 2)
819  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 0, 2),
820  "T2(l,k)*T3(i,j,k)(2,0,2)");
821  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 1, 0)
822  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 1, 0),
823  "T2(l,k)*T3(i,j,k)(2,1,0)");
824  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 1, 1)
825  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 1, 1),
826  "T2(l,k)*T3(i,j,k)(2,1,1)");
827  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 1, 2)
828  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 1, 2),
829  "T2(l,k)*T3(i,j,k)(2,1,2)");
830  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 2, 0)
831  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 2, 0),
832  "T2(l,k)*T3(i,j,k)(2,2,0)");
833  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 2, 1)
834  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 2, 1),
835  "T2(l,k)*T3(i,j,k)(2,2,1)");
836  test_for_zero((t2_3(l, k) * (t2_2(i, j) * t1_2(k)))(2, 2, 2)
837  - (t2_2(i, j) * (t1_2(k) * t2_3(l, k)))(2, 2, 2),
838  "T2(l,k)*T3(i,j,k)(2,2,2)");
839 
840  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 0, 0)
841  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 0, 0),
842  "T3(i,j,l)*T2(j,k)(0,0,0)");
843  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 0, 1)
844  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 0, 1),
845  "T3(i,j,l)*T2(j,k)(0,0,1)");
846  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 0, 2)
847  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 0, 2),
848  "T3(i,j,l)*T2(j,k)(0,0,2)");
849  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 1, 0)
850  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 1, 0),
851  "T3(i,j,l)*T2(j,k)(0,1,0)");
852  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 1, 1)
853  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 1, 1),
854  "T3(i,j,l)*T2(j,k)(0,1,1)");
855  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 1, 2)
856  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 1, 2),
857  "T3(i,j,l)*T2(j,k)(0,1,2)");
858  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 2, 0)
859  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 2, 0),
860  "T3(i,j,l)*T2(j,k)(0,2,0)");
861  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 2, 1)
862  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 2, 1),
863  "T3(i,j,l)*T2(j,k)(0,2,1)");
864  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(0, 2, 2)
865  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 2, 2),
866  "T3(i,j,l)*T2(j,k)(0,2,2)");
867  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 0, 0)
868  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 0, 0),
869  "T3(i,j,l)*T2(j,k)(1,0,0)");
870  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 0, 1)
871  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 0, 1),
872  "T3(i,j,l)*T2(j,k)(1,0,1)");
873  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 0, 2)
874  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 0, 2),
875  "T3(i,j,l)*T2(j,k)(1,0,2)");
876  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 1, 0)
877  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 1, 0),
878  "T3(i,j,l)*T2(j,k)(1,1,0)");
879  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 1, 1)
880  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 1, 1),
881  "T3(i,j,l)*T2(j,k)(1,1,1)");
882  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 1, 2)
883  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 1, 2),
884  "T3(i,j,l)*T2(j,k)(1,1,2)");
885  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 2, 0)
886  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 2, 0),
887  "T3(i,j,l)*T2(j,k)(1,2,0)");
888  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 2, 1)
889  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 2, 1),
890  "T3(i,j,l)*T2(j,k)(1,2,1)");
891  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(1, 2, 2)
892  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 2, 2),
893  "T3(i,j,l)*T2(j,k)(1,2,2)");
894  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 0, 0)
895  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 0, 0),
896  "T3(i,j,l)*T2(j,k)(2,0,0)");
897  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 0, 1)
898  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 0, 1),
899  "T3(i,j,l)*T2(j,k)(2,0,1)");
900  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 0, 2)
901  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 0, 2),
902  "T3(i,j,l)*T2(j,k)(2,0,2)");
903  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 1, 0)
904  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 1, 0),
905  "T3(i,j,l)*T2(j,k)(2,1,0)");
906  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 1, 1)
907  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 1, 1),
908  "T3(i,j,l)*T2(j,k)(2,1,1)");
909  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 1, 2)
910  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 1, 2),
911  "T3(i,j,l)*T2(j,k)(2,1,2)");
912  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 2, 0)
913  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 2, 0),
914  "T3(i,j,l)*T2(j,k)(2,2,0)");
915  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 2, 1)
916  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 2, 1),
917  "T3(i,j,l)*T2(j,k)(2,2,1)");
918  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(j, k))(2, 2, 2)
919  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 2, 2),
920  "T3(i,j,l)*T2(j,k)(2,2,2)");
921 
922  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 0, 0)
923  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 0, 0),
924  "T3(i,j,l)*T2(k,j)(0,0,0)");
925  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 0, 1)
926  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 0, 1),
927  "T3(i,j,l)*T2(k,j)(0,0,1)");
928  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 0, 2)
929  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 0, 2),
930  "T3(i,j,l)*T2(k,j)(0,0,2)");
931  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 1, 0)
932  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 1, 0),
933  "T3(i,j,l)*T2(k,j)(0,1,0)");
934  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 1, 1)
935  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 1, 1),
936  "T3(i,j,l)*T2(k,j)(0,1,1)");
937  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 1, 2)
938  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 1, 2),
939  "T3(i,j,l)*T2(k,j)(0,1,2)");
940  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 2, 0)
941  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 2, 0),
942  "T3(i,j,l)*T2(k,j)(0,2,0)");
943  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 2, 1)
944  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 2, 1),
945  "T3(i,j,l)*T2(k,j)(0,2,1)");
946  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(0, 2, 2)
947  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 2, 2),
948  "T3(i,j,l)*T2(k,j)(0,2,2)");
949  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 0, 0)
950  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 0, 0),
951  "T3(i,j,l)*T2(k,j)(1,0,0)");
952  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 0, 1)
953  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 0, 1),
954  "T3(i,j,l)*T2(k,j)(1,0,1)");
955  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 0, 2)
956  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 0, 2),
957  "T3(i,j,l)*T2(k,j)(1,0,2)");
958  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 1, 0)
959  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 1, 0),
960  "T3(i,j,l)*T2(k,j)(1,1,0)");
961  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 1, 1)
962  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 1, 1),
963  "T3(i,j,l)*T2(k,j)(1,1,1)");
964  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 1, 2)
965  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 1, 2),
966  "T3(i,j,l)*T2(k,j)(1,1,2)");
967  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 2, 0)
968  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 2, 0),
969  "T3(i,j,l)*T2(k,j)(1,2,0)");
970  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 2, 1)
971  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 2, 1),
972  "T3(i,j,l)*T2(k,j)(1,2,1)");
973  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(1, 2, 2)
974  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 2, 2),
975  "T3(i,j,l)*T2(k,j)(1,2,2)");
976  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 0, 0)
977  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 0, 0),
978  "T3(i,j,l)*T2(k,j)(2,0,0)");
979  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 0, 1)
980  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 0, 1),
981  "T3(i,j,l)*T2(k,j)(2,0,1)");
982  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 0, 2)
983  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 0, 2),
984  "T3(i,j,l)*T2(k,j)(2,0,2)");
985  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 1, 0)
986  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 1, 0),
987  "T3(i,j,l)*T2(k,j)(2,1,0)");
988  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 1, 1)
989  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 1, 1),
990  "T3(i,j,l)*T2(k,j)(2,1,1)");
991  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 1, 2)
992  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 1, 2),
993  "T3(i,j,l)*T2(k,j)(2,1,2)");
994  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 2, 0)
995  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 2, 0),
996  "T3(i,j,l)*T2(k,j)(2,2,0)");
997  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 2, 1)
998  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 2, 1),
999  "T3(i,j,l)*T2(k,j)(2,2,1)");
1000  test_for_zero(((t2_2(i, j) * t1_2(l)) * t2_3(k, j))(2, 2, 2)
1001  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 2, 2),
1002  "T3(i,j,l)*T2(k,j)(2,2,2)");
1003 
1004  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 0, 0)
1005  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 0, 0),
1006  "T2(j,k)*T3(i,j,l)(0,0,0)");
1007  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 0, 1)
1008  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 0, 1),
1009  "T2(j,k)*T3(i,j,l)(0,0,1)");
1010  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 0, 2)
1011  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 0, 2),
1012  "T2(j,k)*T3(i,j,l)(0,0,2)");
1013  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 1, 0)
1014  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 1, 0),
1015  "T2(j,k)*T3(i,j,l)(0,1,0)");
1016  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 1, 1)
1017  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 1, 1),
1018  "T2(j,k)*T3(i,j,l)(0,1,1)");
1019  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 1, 2)
1020  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 1, 2),
1021  "T2(j,k)*T3(i,j,l)(0,1,2)");
1022  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 2, 0)
1023  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 2, 0),
1024  "T2(j,k)*T3(i,j,l)(0,2,0)");
1025  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 2, 1)
1026  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 2, 1),
1027  "T2(j,k)*T3(i,j,l)(0,2,1)");
1028  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(0, 2, 2)
1029  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(0, 2, 2),
1030  "T2(j,k)*T3(i,j,l)(0,2,2)");
1031  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 0, 0)
1032  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 0, 0),
1033  "T2(j,k)*T3(i,j,l)(1,0,0)");
1034  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 0, 1)
1035  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 0, 1),
1036  "T2(j,k)*T3(i,j,l)(1,0,1)");
1037  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 0, 2)
1038  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 0, 2),
1039  "T2(j,k)*T3(i,j,l)(1,0,2)");
1040  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 1, 0)
1041  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 1, 0),
1042  "T2(j,k)*T3(i,j,l)(1,1,0)");
1043  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 1, 1)
1044  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 1, 1),
1045  "T2(j,k)*T3(i,j,l)(1,1,1)");
1046  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 1, 2)
1047  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 1, 2),
1048  "T2(j,k)*T3(i,j,l)(1,1,2)");
1049  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 2, 0)
1050  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 2, 0),
1051  "T2(j,k)*T3(i,j,l)(1,2,0)");
1052  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 2, 1)
1053  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 2, 1),
1054  "T2(j,k)*T3(i,j,l)(1,2,1)");
1055  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(1, 2, 2)
1056  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(1, 2, 2),
1057  "T2(j,k)*T3(i,j,l)(1,2,2)");
1058  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 0, 0)
1059  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 0, 0),
1060  "T2(j,k)*T3(i,j,l)(2,0,0)");
1061  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 0, 1)
1062  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 0, 1),
1063  "T2(j,k)*T3(i,j,l)(2,0,1)");
1064  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 0, 2)
1065  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 0, 2),
1066  "T2(j,k)*T3(i,j,l)(2,0,2)");
1067  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 1, 0)
1068  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 1, 0),
1069  "T2(j,k)*T3(i,j,l)(2,1,0)");
1070  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 1, 1)
1071  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 1, 1),
1072  "T2(j,k)*T3(i,j,l)(2,1,1)");
1073  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 1, 2)
1074  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 1, 2),
1075  "T2(j,k)*T3(i,j,l)(2,1,2)");
1076  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 2, 0)
1077  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 2, 0),
1078  "T2(j,k)*T3(i,j,l)(2,2,0)");
1079  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 2, 1)
1080  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 2, 1),
1081  "T2(j,k)*T3(i,j,l)(2,2,1)");
1082  test_for_zero((t2_3(j, k) * (t2_2(i, j) * t1_2(l)))(2, 2, 2)
1083  - ((t2_2(i, j) * t2_3(j, k)) * t1_2(l))(2, 2, 2),
1084  "T2(j,k)*T3(i,j,l)(2,2,2)");
1085 
1086  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 0, 0)
1087  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 0, 0),
1088  "T2(k,j)*T3(i,j,l)(0,0,0)");
1089  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 0, 1)
1090  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 0, 1),
1091  "T2(k,j)*T3(i,j,l)(0,0,1)");
1092  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 0, 2)
1093  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 0, 2),
1094  "T2(k,j)*T3(i,j,l)(0,0,2)");
1095  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 1, 0)
1096  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 1, 0),
1097  "T2(k,j)*T3(i,j,l)(0,1,0)");
1098  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 1, 1)
1099  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 1, 1),
1100  "T2(k,j)*T3(i,j,l)(0,1,1)");
1101  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 1, 2)
1102  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 1, 2),
1103  "T2(k,j)*T3(i,j,l)(0,1,2)");
1104  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 2, 0)
1105  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 2, 0),
1106  "T2(k,j)*T3(i,j,l)(0,2,0)");
1107  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 2, 1)
1108  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 2, 1),
1109  "T2(k,j)*T3(i,j,l)(0,2,1)");
1110  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(0, 2, 2)
1111  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(0, 2, 2),
1112  "T2(k,j)*T3(i,j,l)(0,2,2)");
1113  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 0, 0)
1114  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 0, 0),
1115  "T2(k,j)*T3(i,j,l)(1,0,0)");
1116  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 0, 1)
1117  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 0, 1),
1118  "T2(k,j)*T3(i,j,l)(1,0,1)");
1119  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 0, 2)
1120  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 0, 2),
1121  "T2(k,j)*T3(i,j,l)(1,0,2)");
1122  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 1, 0)
1123  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 1, 0),
1124  "T2(k,j)*T3(i,j,l)(1,1,0)");
1125  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 1, 1)
1126  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 1, 1),
1127  "T2(k,j)*T3(i,j,l)(1,1,1)");
1128  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 1, 2)
1129  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 1, 2),
1130  "T2(k,j)*T3(i,j,l)(1,1,2)");
1131  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 2, 0)
1132  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 2, 0),
1133  "T2(k,j)*T3(i,j,l)(1,2,0)");
1134  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 2, 1)
1135  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 2, 1),
1136  "T2(k,j)*T3(i,j,l)(1,2,1)");
1137  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(1, 2, 2)
1138  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(1, 2, 2),
1139  "T2(k,j)*T3(i,j,l)(1,2,2)");
1140  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 0, 0)
1141  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 0, 0),
1142  "T2(k,j)*T3(i,j,l)(2,0,0)");
1143  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 0, 1)
1144  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 0, 1),
1145  "T2(k,j)*T3(i,j,l)(2,0,1)");
1146  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 0, 2)
1147  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 0, 2),
1148  "T2(k,j)*T3(i,j,l)(2,0,2)");
1149  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 1, 0)
1150  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 1, 0),
1151  "T2(k,j)*T3(i,j,l)(2,1,0)");
1152  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 1, 1)
1153  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 1, 1),
1154  "T2(k,j)*T3(i,j,l)(2,1,1)");
1155  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 1, 2)
1156  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 1, 2),
1157  "T2(k,j)*T3(i,j,l)(2,1,2)");
1158  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 2, 0)
1159  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 2, 0),
1160  "T2(k,j)*T3(i,j,l)(2,2,0)");
1161  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 2, 1)
1162  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 2, 1),
1163  "T2(k,j)*T3(i,j,l)(2,2,1)");
1164  test_for_zero((t2_3(k, j) * (t2_2(i, j) * t1_2(l)))(2, 2, 2)
1165  - ((t2_2(i, j) * t2_3(k, j)) * t1_2(l))(2, 2, 2),
1166  "T2(k,j)*T3(i,j,l)(2,2,2)");
1167 
1168  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 0, 0)
1169  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 0, 0),
1170  "T3(i,k,l)*T2(i,j)(0,0,0)");
1171  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 0, 1)
1172  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 0, 1),
1173  "T3(i,k,l)*T2(i,j)(0,0,1)");
1174  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 0, 2)
1175  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 0, 2),
1176  "T3(i,k,l)*T2(i,j)(0,0,2)");
1177  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 1, 0)
1178  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 1, 0),
1179  "T3(i,k,l)*T2(i,j)(0,1,0)");
1180  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 1, 1)
1181  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 1, 1),
1182  "T3(i,k,l)*T2(i,j)(0,1,1)");
1183  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 1, 2)
1184  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 1, 2),
1185  "T3(i,k,l)*T2(i,j)(0,1,2)");
1186  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 2, 0)
1187  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 2, 0),
1188  "T3(i,k,l)*T2(i,j)(0,2,0)");
1189  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 2, 1)
1190  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 2, 1),
1191  "T3(i,k,l)*T2(i,j)(0,2,1)");
1192  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(0, 2, 2)
1193  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 2, 2),
1194  "T3(i,k,l)*T2(i,j)(0,2,2)");
1195  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 0, 0)
1196  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 0, 0),
1197  "T3(i,k,l)*T2(i,j)(1,0,0)");
1198  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 0, 1)
1199  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 0, 1),
1200  "T3(i,k,l)*T2(i,j)(1,0,1)");
1201  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 0, 2)
1202  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 0, 2),
1203  "T3(i,k,l)*T2(i,j)(1,0,2)");
1204  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 1, 0)
1205  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 1, 0),
1206  "T3(i,k,l)*T2(i,j)(1,1,0)");
1207  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 1, 1)
1208  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 1, 1),
1209  "T3(i,k,l)*T2(i,j)(1,1,1)");
1210  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 1, 2)
1211  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 1, 2),
1212  "T3(i,k,l)*T2(i,j)(1,1,2)");
1213  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 2, 0)
1214  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 2, 0),
1215  "T3(i,k,l)*T2(i,j)(1,2,0)");
1216  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 2, 1)
1217  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 2, 1),
1218  "T3(i,k,l)*T2(i,j)(1,2,1)");
1219  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(1, 2, 2)
1220  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 2, 2),
1221  "T3(i,k,l)*T2(i,j)(1,2,2)");
1222  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 0, 0)
1223  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 0, 0),
1224  "T3(i,k,l)*T2(i,j)(2,0,0)");
1225  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 0, 1)
1226  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 0, 1),
1227  "T3(i,k,l)*T2(i,j)(2,0,1)");
1228  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 0, 2)
1229  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 0, 2),
1230  "T3(i,k,l)*T2(i,j)(2,0,2)");
1231  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 1, 0)
1232  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 1, 0),
1233  "T3(i,k,l)*T2(i,j)(2,1,0)");
1234  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 1, 1)
1235  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 1, 1),
1236  "T3(i,k,l)*T2(i,j)(2,1,1)");
1237  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 1, 2)
1238  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 1, 2),
1239  "T3(i,k,l)*T2(i,j)(2,1,2)");
1240  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 2, 0)
1241  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 2, 0),
1242  "T3(i,k,l)*T2(i,j)(2,2,0)");
1243  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 2, 1)
1244  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 2, 1),
1245  "T3(i,k,l)*T2(i,j)(2,2,1)");
1246  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(i, j))(2, 2, 2)
1247  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 2, 2),
1248  "T3(i,k,l)*T2(i,j)(2,2,2)");
1249 
1250  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 0, 0)
1251  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 0, 0),
1252  "T3(i,k,l)*T2(j,i)(0,0,0)");
1253  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 0, 1)
1254  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 0, 1),
1255  "T3(i,k,l)*T2(j,i)(0,0,1)");
1256  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 0, 2)
1257  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 0, 2),
1258  "T3(i,k,l)*T2(j,i)(0,0,2)");
1259  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 1, 0)
1260  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 1, 0),
1261  "T3(i,k,l)*T2(j,i)(0,1,0)");
1262  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 1, 1)
1263  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 1, 1),
1264  "T3(i,k,l)*T2(j,i)(0,1,1)");
1265  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 1, 2)
1266  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 1, 2),
1267  "T3(i,k,l)*T2(j,i)(0,1,2)");
1268  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 2, 0)
1269  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 2, 0),
1270  "T3(i,k,l)*T2(j,i)(0,2,0)");
1271  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 2, 1)
1272  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 2, 1),
1273  "T3(i,k,l)*T2(j,i)(0,2,1)");
1274  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(0, 2, 2)
1275  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 2, 2),
1276  "T3(i,k,l)*T2(j,i)(0,2,2)");
1277  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 0, 0)
1278  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 0, 0),
1279  "T3(i,k,l)*T2(j,i)(1,0,0)");
1280  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 0, 1)
1281  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 0, 1),
1282  "T3(i,k,l)*T2(j,i)(1,0,1)");
1283  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 0, 2)
1284  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 0, 2),
1285  "T3(i,k,l)*T2(j,i)(1,0,2)");
1286  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 1, 0)
1287  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 1, 0),
1288  "T3(i,k,l)*T2(j,i)(1,1,0)");
1289  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 1, 1)
1290  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 1, 1),
1291  "T3(i,k,l)*T2(j,i)(1,1,1)");
1292  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 1, 2)
1293  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 1, 2),
1294  "T3(i,k,l)*T2(j,i)(1,1,2)");
1295  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 2, 0)
1296  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 2, 0),
1297  "T3(i,k,l)*T2(j,i)(1,2,0)");
1298  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 2, 1)
1299  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 2, 1),
1300  "T3(i,k,l)*T2(j,i)(1,2,1)");
1301  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(1, 2, 2)
1302  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 2, 2),
1303  "T3(i,k,l)*T2(j,i)(1,2,2)");
1304  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 0, 0)
1305  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 0, 0),
1306  "T3(i,k,l)*T2(j,i)(2,0,0)");
1307  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 0, 1)
1308  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 0, 1),
1309  "T3(i,k,l)*T2(j,i)(2,0,1)");
1310  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 0, 2)
1311  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 0, 2),
1312  "T3(i,k,l)*T2(j,i)(2,0,2)");
1313  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 1, 0)
1314  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 1, 0),
1315  "T3(i,k,l)*T2(j,i)(2,1,0)");
1316  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 1, 1)
1317  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 1, 1),
1318  "T3(i,k,l)*T2(j,i)(2,1,1)");
1319  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 1, 2)
1320  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 1, 2),
1321  "T3(i,k,l)*T2(j,i)(2,1,2)");
1322  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 2, 0)
1323  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 2, 0),
1324  "T3(i,k,l)*T2(j,i)(2,2,0)");
1325  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 2, 1)
1326  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 2, 1),
1327  "T3(i,k,l)*T2(j,i)(2,2,1)");
1328  test_for_zero(((t2_2(i, k) * t1_2(l)) * t2_3(j, i))(2, 2, 2)
1329  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 2, 2),
1330  "T3(i,k,l)*T2(j,i)(2,2,2)");
1331 
1332  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 0, 0)
1333  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 0, 0),
1334  "T2(i,j)*T3(i,k,l)(0,0,0)");
1335  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 0, 1)
1336  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 0, 1),
1337  "T2(i,j)*T3(i,k,l)(0,0,1)");
1338  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 0, 2)
1339  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 0, 2),
1340  "T2(i,j)*T3(i,k,l)(0,0,2)");
1341  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 1, 0)
1342  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 1, 0),
1343  "T2(i,j)*T3(i,k,l)(0,1,0)");
1344  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 1, 1)
1345  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 1, 1),
1346  "T2(i,j)*T3(i,k,l)(0,1,1)");
1347  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 1, 2)
1348  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 1, 2),
1349  "T2(i,j)*T3(i,k,l)(0,1,2)");
1350  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 2, 0)
1351  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 2, 0),
1352  "T2(i,j)*T3(i,k,l)(0,2,0)");
1353  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 2, 1)
1354  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 2, 1),
1355  "T2(i,j)*T3(i,k,l)(0,2,1)");
1356  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(0, 2, 2)
1357  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(0, 2, 2),
1358  "T2(i,j)*T3(i,k,l)(0,2,2)");
1359  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 0, 0)
1360  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 0, 0),
1361  "T2(i,j)*T3(i,k,l)(1,0,0)");
1362  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 0, 1)
1363  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 0, 1),
1364  "T2(i,j)*T3(i,k,l)(1,0,1)");
1365  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 0, 2)
1366  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 0, 2),
1367  "T2(i,j)*T3(i,k,l)(1,0,2)");
1368  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 1, 0)
1369  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 1, 0),
1370  "T2(i,j)*T3(i,k,l)(1,1,0)");
1371  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 1, 1)
1372  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 1, 1),
1373  "T2(i,j)*T3(i,k,l)(1,1,1)");
1374  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 1, 2)
1375  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 1, 2),
1376  "T2(i,j)*T3(i,k,l)(1,1,2)");
1377  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 2, 0)
1378  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 2, 0),
1379  "T2(i,j)*T3(i,k,l)(1,2,0)");
1380  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 2, 1)
1381  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 2, 1),
1382  "T2(i,j)*T3(i,k,l)(1,2,1)");
1383  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(1, 2, 2)
1384  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(1, 2, 2),
1385  "T2(i,j)*T3(i,k,l)(1,2,2)");
1386  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 0, 0)
1387  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 0, 0),
1388  "T2(i,j)*T3(i,k,l)(2,0,0)");
1389  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 0, 1)
1390  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 0, 1),
1391  "T2(i,j)*T3(i,k,l)(2,0,1)");
1392  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 0, 2)
1393  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 0, 2),
1394  "T2(i,j)*T3(i,k,l)(2,0,2)");
1395  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 1, 0)
1396  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 1, 0),
1397  "T2(i,j)*T3(i,k,l)(2,1,0)");
1398  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 1, 1)
1399  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 1, 1),
1400  "T2(i,j)*T3(i,k,l)(2,1,1)");
1401  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 1, 2)
1402  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 1, 2),
1403  "T2(i,j)*T3(i,k,l)(2,1,2)");
1404  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 2, 0)
1405  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 2, 0),
1406  "T2(i,j)*T3(i,k,l)(2,2,0)");
1407  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 2, 1)
1408  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 2, 1),
1409  "T2(i,j)*T3(i,k,l)(2,2,1)");
1410  test_for_zero((t2_3(i, j) * (t2_2(i, k) * t1_2(l)))(2, 2, 2)
1411  - ((t2_3(i, j) * t2_2(i, k)) * t1_2(l))(2, 2, 2),
1412  "T2(i,j)*T3(i,k,l)(2,2,2)");
1413 
1414  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 0, 0)
1415  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 0, 0),
1416  "T2(j,i)*T3(i,k,l)(0,0,0)");
1417  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 0, 1)
1418  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 0, 1),
1419  "T2(j,i)*T3(i,k,l)(0,0,1)");
1420  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 0, 2)
1421  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 0, 2),
1422  "T2(j,i)*T3(i,k,l)(0,0,2)");
1423  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 1, 0)
1424  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 1, 0),
1425  "T2(j,i)*T3(i,k,l)(0,1,0)");
1426  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 1, 1)
1427  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 1, 1),
1428  "T2(j,i)*T3(i,k,l)(0,1,1)");
1429  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 1, 2)
1430  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 1, 2),
1431  "T2(j,i)*T3(i,k,l)(0,1,2)");
1432  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 2, 0)
1433  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 2, 0),
1434  "T2(j,i)*T3(i,k,l)(0,2,0)");
1435  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 2, 1)
1436  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 2, 1),
1437  "T2(j,i)*T3(i,k,l)(0,2,1)");
1438  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(0, 2, 2)
1439  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(0, 2, 2),
1440  "T2(j,i)*T3(i,k,l)(0,2,2)");
1441  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 0, 0)
1442  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 0, 0),
1443  "T2(j,i)*T3(i,k,l)(1,0,0)");
1444  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 0, 1)
1445  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 0, 1),
1446  "T2(j,i)*T3(i,k,l)(1,0,1)");
1447  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 0, 2)
1448  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 0, 2),
1449  "T2(j,i)*T3(i,k,l)(1,0,2)");
1450  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 1, 0)
1451  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 1, 0),
1452  "T2(j,i)*T3(i,k,l)(1,1,0)");
1453  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 1, 1)
1454  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 1, 1),
1455  "T2(j,i)*T3(i,k,l)(1,1,1)");
1456  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 1, 2)
1457  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 1, 2),
1458  "T2(j,i)*T3(i,k,l)(1,1,2)");
1459  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 2, 0)
1460  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 2, 0),
1461  "T2(j,i)*T3(i,k,l)(1,2,0)");
1462  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 2, 1)
1463  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 2, 1),
1464  "T2(j,i)*T3(i,k,l)(1,2,1)");
1465  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(1, 2, 2)
1466  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(1, 2, 2),
1467  "T2(j,i)*T3(i,k,l)(1,2,2)");
1468  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 0, 0)
1469  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 0, 0),
1470  "T2(j,i)*T3(i,k,l)(2,0,0)");
1471  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 0, 1)
1472  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 0, 1),
1473  "T2(j,i)*T3(i,k,l)(2,0,1)");
1474  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 0, 2)
1475  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 0, 2),
1476  "T2(j,i)*T3(i,k,l)(2,0,2)");
1477  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 1, 0)
1478  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 1, 0),
1479  "T2(j,i)*T3(i,k,l)(2,1,0)");
1480  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 1, 1)
1481  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 1, 1),
1482  "T2(j,i)*T3(i,k,l)(2,1,1)");
1483  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 1, 2)
1484  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 1, 2),
1485  "T2(j,i)*T3(i,k,l)(2,1,2)");
1486  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 2, 0)
1487  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 2, 0),
1488  "T2(j,i)*T3(i,k,l)(2,2,0)");
1489  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 2, 1)
1490  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 2, 1),
1491  "T2(j,i)*T3(i,k,l)(2,2,1)");
1492  test_for_zero((t2_3(j, i) * (t2_2(i, k) * t1_2(l)))(2, 2, 2)
1493  - ((t2_3(j, i) * t2_2(i, k)) * t1_2(l))(2, 2, 2),
1494  "T2(j,i)*T3(i,k,l)(2,2,2)");
1495 
1496  test_for_zero((t2_2(i, j) * t1_2(k)) * (t2_3(i, j) * t1_1(k))
1497  - (t2_2(0, 0) * t1_2(0) * t2_3(0, 0) * t1_1(0)
1498  + t2_2(1, 0) * t1_2(0) * t2_3(1, 0) * t1_1(0)
1499  + t2_2(2, 0) * t1_2(0) * t2_3(2, 0) * t1_1(0)
1500  + t2_2(0, 1) * t1_2(0) * t2_3(0, 1) * t1_1(0)
1501  + t2_2(1, 1) * t1_2(0) * t2_3(1, 1) * t1_1(0)
1502  + t2_2(2, 1) * t1_2(0) * t2_3(2, 1) * t1_1(0)
1503  + t2_2(0, 2) * t1_2(0) * t2_3(0, 2) * t1_1(0)
1504  + t2_2(1, 2) * t1_2(0) * t2_3(1, 2) * t1_1(0)
1505  + t2_2(2, 2) * t1_2(0) * t2_3(2, 2) * t1_1(0)
1506  + t2_2(0, 0) * t1_2(1) * t2_3(0, 0) * t1_1(1)
1507  + t2_2(1, 0) * t1_2(1) * t2_3(1, 0) * t1_1(1)
1508  + t2_2(2, 0) * t1_2(1) * t2_3(2, 0) * t1_1(1)
1509  + t2_2(0, 1) * t1_2(1) * t2_3(0, 1) * t1_1(1)
1510  + t2_2(1, 1) * t1_2(1) * t2_3(1, 1) * t1_1(1)
1511  + t2_2(2, 1) * t1_2(1) * t2_3(2, 1) * t1_1(1)
1512  + t2_2(0, 2) * t1_2(1) * t2_3(0, 2) * t1_1(1)
1513  + t2_2(1, 2) * t1_2(1) * t2_3(1, 2) * t1_1(1)
1514  + t2_2(2, 2) * t1_2(1) * t2_3(2, 2) * t1_1(1)
1515  + t2_2(0, 0) * t1_2(2) * t2_3(0, 0) * t1_1(2)
1516  + t2_2(1, 0) * t1_2(2) * t2_3(1, 0) * t1_1(2)
1517  + t2_2(2, 0) * t1_2(2) * t2_3(2, 0) * t1_1(2)
1518  + t2_2(0, 1) * t1_2(2) * t2_3(0, 1) * t1_1(2)
1519  + t2_2(1, 1) * t1_2(2) * t2_3(1, 1) * t1_1(2)
1520  + t2_2(2, 1) * t1_2(2) * t2_3(2, 1) * t1_1(2)
1521  + t2_2(0, 2) * t1_2(2) * t2_3(0, 2) * t1_1(2)
1522  + t2_2(1, 2) * t1_2(2) * t2_3(1, 2) * t1_1(2)
1523  + t2_2(2, 2) * t1_2(2) * t2_3(2, 2) * t1_1(2)),
1524  "T3(i,j,k)*T3(i,j,k)");
1525 
1526  test_for_zero((t2_2(i, j) * t1_2(k)) * (t2_3(j, i) * t1_1(k))
1527  - (t2_2(0, 0) * t1_2(0) * t2_3(0, 0) * t1_1(0)
1528  + t2_2(1, 0) * t1_2(0) * t2_3(0, 1) * t1_1(0)
1529  + t2_2(2, 0) * t1_2(0) * t2_3(0, 2) * t1_1(0)
1530  + t2_2(0, 1) * t1_2(0) * t2_3(1, 0) * t1_1(0)
1531  + t2_2(1, 1) * t1_2(0) * t2_3(1, 1) * t1_1(0)
1532  + t2_2(2, 1) * t1_2(0) * t2_3(1, 2) * t1_1(0)
1533  + t2_2(0, 2) * t1_2(0) * t2_3(2, 0) * t1_1(0)
1534  + t2_2(1, 2) * t1_2(0) * t2_3(2, 1) * t1_1(0)
1535  + t2_2(2, 2) * t1_2(0) * t2_3(2, 2) * t1_1(0)
1536  + t2_2(0, 0) * t1_2(1) * t2_3(0, 0) * t1_1(1)
1537  + t2_2(1, 0) * t1_2(1) * t2_3(0, 1) * t1_1(1)
1538  + t2_2(2, 0) * t1_2(1) * t2_3(0, 2) * t1_1(1)
1539  + t2_2(0, 1) * t1_2(1) * t2_3(1, 0) * t1_1(1)
1540  + t2_2(1, 1) * t1_2(1) * t2_3(1, 1) * t1_1(1)
1541  + t2_2(2, 1) * t1_2(1) * t2_3(1, 2) * t1_1(1)
1542  + t2_2(0, 2) * t1_2(1) * t2_3(2, 0) * t1_1(1)
1543  + t2_2(1, 2) * t1_2(1) * t2_3(2, 1) * t1_1(1)
1544  + t2_2(2, 2) * t1_2(1) * t2_3(2, 2) * t1_1(1)
1545  + t2_2(0, 0) * t1_2(2) * t2_3(0, 0) * t1_1(2)
1546  + t2_2(1, 0) * t1_2(2) * t2_3(0, 1) * t1_1(2)
1547  + t2_2(2, 0) * t1_2(2) * t2_3(0, 2) * t1_1(2)
1548  + t2_2(0, 1) * t1_2(2) * t2_3(1, 0) * t1_1(2)
1549  + t2_2(1, 1) * t1_2(2) * t2_3(1, 1) * t1_1(2)
1550  + t2_2(2, 1) * t1_2(2) * t2_3(1, 2) * t1_1(2)
1551  + t2_2(0, 2) * t1_2(2) * t2_3(2, 0) * t1_1(2)
1552  + t2_2(1, 2) * t1_2(2) * t2_3(2, 1) * t1_1(2)
1553  + t2_2(2, 2) * t1_2(2) * t2_3(2, 2) * t1_1(2)),
1554  "T3(i,j,k)*T3(j,i,k)");
1555 
1556  test_for_zero((t2_2(i, j) * t1_2(k)) * (t2_3(i, k) * t1_1(j))
1557  - (t2_2(0, 0) * t1_2(0) * t2_3(0, 0) * t1_1(0)
1558  + t2_2(1, 0) * t1_2(0) * t2_3(1, 0) * t1_1(0)
1559  + t2_2(2, 0) * t1_2(0) * t2_3(2, 0) * t1_1(0)
1560  + t2_2(0, 1) * t1_2(0) * t2_3(0, 0) * t1_1(1)
1561  + t2_2(1, 1) * t1_2(0) * t2_3(1, 0) * t1_1(1)
1562  + t2_2(2, 1) * t1_2(0) * t2_3(2, 0) * t1_1(1)
1563  + t2_2(0, 2) * t1_2(0) * t2_3(0, 0) * t1_1(2)
1564  + t2_2(1, 2) * t1_2(0) * t2_3(1, 0) * t1_1(2)
1565  + t2_2(2, 2) * t1_2(0) * t2_3(2, 0) * t1_1(2)
1566  + t2_2(0, 0) * t1_2(1) * t2_3(0, 1) * t1_1(0)
1567  + t2_2(1, 0) * t1_2(1) * t2_3(1, 1) * t1_1(0)
1568  + t2_2(2, 0) * t1_2(1) * t2_3(2, 1) * t1_1(0)
1569  + t2_2(0, 1) * t1_2(1) * t2_3(0, 1) * t1_1(1)
1570  + t2_2(1, 1) * t1_2(1) * t2_3(1, 1) * t1_1(1)
1571  + t2_2(2, 1) * t1_2(1) * t2_3(2, 1) * t1_1(1)
1572  + t2_2(0, 2) * t1_2(1) * t2_3(0, 1) * t1_1(2)
1573  + t2_2(1, 2) * t1_2(1) * t2_3(1, 1) * t1_1(2)
1574  + t2_2(2, 2) * t1_2(1) * t2_3(2, 1) * t1_1(2)
1575  + t2_2(0, 0) * t1_2(2) * t2_3(0, 2) * t1_1(0)
1576  + t2_2(1, 0) * t1_2(2) * t2_3(1, 2) * t1_1(0)
1577  + t2_2(2, 0) * t1_2(2) * t2_3(2, 2) * t1_1(0)
1578  + t2_2(0, 1) * t1_2(2) * t2_3(0, 2) * t1_1(1)
1579  + t2_2(1, 1) * t1_2(2) * t2_3(1, 2) * t1_1(1)
1580  + t2_2(2, 1) * t1_2(2) * t2_3(2, 2) * t1_1(1)
1581  + t2_2(0, 2) * t1_2(2) * t2_3(0, 2) * t1_1(2)
1582  + t2_2(1, 2) * t1_2(2) * t2_3(1, 2) * t1_1(2)
1583  + t2_2(2, 2) * t1_2(2) * t2_3(2, 2) * t1_1(2)),
1584  "T3(i,j,k)*T3(i,k,j)");
1585 
1586  test_for_zero((t2_2(i, j) * t1_2(k)) * (t2_3(j, k) * t1_1(i))
1587  - (t2_2(0, 0) * t1_2(0) * t2_3(0, 0) * t1_1(0)
1588  + t2_2(1, 0) * t1_2(0) * t2_3(0, 0) * t1_1(1)
1589  + t2_2(2, 0) * t1_2(0) * t2_3(0, 0) * t1_1(2)
1590  + t2_2(0, 1) * t1_2(0) * t2_3(1, 0) * t1_1(0)
1591  + t2_2(1, 1) * t1_2(0) * t2_3(1, 0) * t1_1(1)
1592  + t2_2(2, 1) * t1_2(0) * t2_3(1, 0) * t1_1(2)
1593  + t2_2(0, 2) * t1_2(0) * t2_3(2, 0) * t1_1(0)
1594  + t2_2(1, 2) * t1_2(0) * t2_3(2, 0) * t1_1(1)
1595  + t2_2(2, 2) * t1_2(0) * t2_3(2, 0) * t1_1(2)
1596  + t2_2(0, 0) * t1_2(1) * t2_3(0, 1) * t1_1(0)
1597  + t2_2(1, 0) * t1_2(1) * t2_3(0, 1) * t1_1(1)
1598  + t2_2(2, 0) * t1_2(1) * t2_3(0, 1) * t1_1(2)
1599  + t2_2(0, 1) * t1_2(1) * t2_3(1, 1) * t1_1(0)
1600  + t2_2(1, 1) * t1_2(1) * t2_3(1, 1) * t1_1(1)
1601  + t2_2(2, 1) * t1_2(1) * t2_3(1, 1) * t1_1(2)
1602  + t2_2(0, 2) * t1_2(1) * t2_3(2, 1) * t1_1(0)
1603  + t2_2(1, 2) * t1_2(1) * t2_3(2, 1) * t1_1(1)
1604  + t2_2(2, 2) * t1_2(1) * t2_3(2, 1) * t1_1(2)
1605  + t2_2(0, 0) * t1_2(2) * t2_3(0, 2) * t1_1(0)
1606  + t2_2(1, 0) * t1_2(2) * t2_3(0, 2) * t1_1(1)
1607  + t2_2(2, 0) * t1_2(2) * t2_3(0, 2) * t1_1(2)
1608  + t2_2(0, 1) * t1_2(2) * t2_3(1, 2) * t1_1(0)
1609  + t2_2(1, 1) * t1_2(2) * t2_3(1, 2) * t1_1(1)
1610  + t2_2(2, 1) * t1_2(2) * t2_3(1, 2) * t1_1(2)
1611  + t2_2(0, 2) * t1_2(2) * t2_3(2, 2) * t1_1(0)
1612  + t2_2(1, 2) * t1_2(2) * t2_3(2, 2) * t1_1(1)
1613  + t2_2(2, 2) * t1_2(2) * t2_3(2, 2) * t1_1(2)),
1614  "T3(i,j,k)*T3(j,k,i)");
1615 
1616  test_for_zero((t2_2(i, j) * t1_2(k)) * (t2_3(k, j) * t1_1(i))
1617  - (t2_2(0, 0) * t1_2(0) * t2_3(0, 0) * t1_1(0)
1618  + t2_2(1, 0) * t1_2(0) * t2_3(0, 0) * t1_1(1)
1619  + t2_2(2, 0) * t1_2(0) * t2_3(0, 0) * t1_1(2)
1620  + t2_2(0, 1) * t1_2(0) * t2_3(0, 1) * t1_1(0)
1621  + t2_2(1, 1) * t1_2(0) * t2_3(0, 1) * t1_1(1)
1622  + t2_2(2, 1) * t1_2(0) * t2_3(0, 1) * t1_1(2)
1623  + t2_2(0, 2) * t1_2(0) * t2_3(0, 2) * t1_1(0)
1624  + t2_2(1, 2) * t1_2(0) * t2_3(0, 2) * t1_1(1)
1625  + t2_2(2, 2) * t1_2(0) * t2_3(0, 2) * t1_1(2)
1626  + t2_2(0, 0) * t1_2(1) * t2_3(1, 0) * t1_1(0)
1627  + t2_2(1, 0) * t1_2(1) * t2_3(1, 0) * t1_1(1)
1628  + t2_2(2, 0) * t1_2(1) * t2_3(1, 0) * t1_1(2)
1629  + t2_2(0, 1) * t1_2(1) * t2_3(1, 1) * t1_1(0)
1630  + t2_2(1, 1) * t1_2(1) * t2_3(1, 1) * t1_1(1)
1631  + t2_2(2, 1) * t1_2(1) * t2_3(1, 1) * t1_1(2)
1632  + t2_2(0, 2) * t1_2(1) * t2_3(1, 2) * t1_1(0)
1633  + t2_2(1, 2) * t1_2(1) * t2_3(1, 2) * t1_1(1)
1634  + t2_2(2, 2) * t1_2(1) * t2_3(1, 2) * t1_1(2)
1635  + t2_2(0, 0) * t1_2(2) * t2_3(2, 0) * t1_1(0)
1636  + t2_2(1, 0) * t1_2(2) * t2_3(2, 0) * t1_1(1)
1637  + t2_2(2, 0) * t1_2(2) * t2_3(2, 0) * t1_1(2)
1638  + t2_2(0, 1) * t1_2(2) * t2_3(2, 1) * t1_1(0)
1639  + t2_2(1, 1) * t1_2(2) * t2_3(2, 1) * t1_1(1)
1640  + t2_2(2, 1) * t1_2(2) * t2_3(2, 1) * t1_1(2)
1641  + t2_2(0, 2) * t1_2(2) * t2_3(2, 2) * t1_1(0)
1642  + t2_2(1, 2) * t1_2(2) * t2_3(2, 2) * t1_1(1)
1643  + t2_2(2, 2) * t1_2(2) * t2_3(2, 2) * t1_1(2)),
1644  "T3(i,j,k)*T3(k,j,i)");
1645 
1646  test_for_zero((t2_2(i, j) * t1_2(k)) * (t2_3(k, i) * t1_1(j))
1647  - (t2_2(0, 0) * t1_2(0) * t2_3(0, 0) * t1_1(0)
1648  + t2_2(1, 0) * t1_2(0) * t2_3(0, 1) * t1_1(0)
1649  + t2_2(2, 0) * t1_2(0) * t2_3(0, 2) * t1_1(0)
1650  + t2_2(0, 1) * t1_2(0) * t2_3(0, 0) * t1_1(1)
1651  + t2_2(1, 1) * t1_2(0) * t2_3(0, 1) * t1_1(1)
1652  + t2_2(2, 1) * t1_2(0) * t2_3(0, 2) * t1_1(1)
1653  + t2_2(0, 2) * t1_2(0) * t2_3(0, 0) * t1_1(2)
1654  + t2_2(1, 2) * t1_2(0) * t2_3(0, 1) * t1_1(2)
1655  + t2_2(2, 2) * t1_2(0) * t2_3(0, 2) * t1_1(2)
1656  + t2_2(0, 0) * t1_2(1) * t2_3(1, 0) * t1_1(0)
1657  + t2_2(1, 0) * t1_2(1) * t2_3(1, 1) * t1_1(0)
1658  + t2_2(2, 0) * t1_2(1) * t2_3(1, 2) * t1_1(0)
1659  + t2_2(0, 1) * t1_2(1) * t2_3(1, 0) * t1_1(1)
1660  + t2_2(1, 1) * t1_2(1) * t2_3(1, 1) * t1_1(1)
1661  + t2_2(2, 1) * t1_2(1) * t2_3(1, 2) * t1_1(1)
1662  + t2_2(0, 2) * t1_2(1) * t2_3(1, 0) * t1_1(2)
1663  + t2_2(1, 2) * t1_2(1) * t2_3(1, 1) * t1_1(2)
1664  + t2_2(2, 2) * t1_2(1) * t2_3(1, 2) * t1_1(2)
1665  + t2_2(0, 0) * t1_2(2) * t2_3(2, 0) * t1_1(0)
1666  + t2_2(1, 0) * t1_2(2) * t2_3(2, 1) * t1_1(0)
1667  + t2_2(2, 0) * t1_2(2) * t2_3(2, 2) * t1_1(0)
1668  + t2_2(0, 1) * t1_2(2) * t2_3(2, 0) * t1_1(1)
1669  + t2_2(1, 1) * t1_2(2) * t2_3(2, 1) * t1_1(1)
1670  + t2_2(2, 1) * t1_2(2) * t2_3(2, 2) * t1_1(1)
1671  + t2_2(0, 2) * t1_2(2) * t2_3(2, 0) * t1_1(2)
1672  + t2_2(1, 2) * t1_2(2) * t2_3(2, 1) * t1_1(2)
1673  + t2_2(2, 2) * t1_2(2) * t2_3(2, 2) * t1_1(2)),
1674  "T3(i,j,k)*T3(k,i,j)");
1675 
1676  test_for_zero((t2_2(i, j) * t1_2(k)) * (t3dg_2(i, j, k))
1677  - (t2_2(0, 0) * t1_2(0) * t3dg_2(0, 0, 0)
1678  + t2_2(1, 0) * t1_2(0) * t3dg_2(1, 0, 0)
1679  + t2_2(2, 0) * t1_2(0) * t3dg_2(2, 0, 0)
1680  + t2_2(0, 1) * t1_2(0) * t3dg_2(0, 1, 0)
1681  + t2_2(1, 1) * t1_2(0) * t3dg_2(1, 1, 0)
1682  + t2_2(2, 1) * t1_2(0) * t3dg_2(2, 1, 0)
1683  + t2_2(0, 2) * t1_2(0) * t3dg_2(0, 2, 0)
1684  + t2_2(1, 2) * t1_2(0) * t3dg_2(1, 2, 0)
1685  + t2_2(2, 2) * t1_2(0) * t3dg_2(2, 2, 0)
1686  + t2_2(0, 0) * t1_2(1) * t3dg_2(0, 0, 1)
1687  + t2_2(1, 0) * t1_2(1) * t3dg_2(1, 0, 1)
1688  + t2_2(2, 0) * t1_2(1) * t3dg_2(2, 0, 1)
1689  + t2_2(0, 1) * t1_2(1) * t3dg_2(0, 1, 1)
1690  + t2_2(1, 1) * t1_2(1) * t3dg_2(1, 1, 1)
1691  + t2_2(2, 1) * t1_2(1) * t3dg_2(2, 1, 1)
1692  + t2_2(0, 2) * t1_2(1) * t3dg_2(0, 2, 1)
1693  + t2_2(1, 2) * t1_2(1) * t3dg_2(1, 2, 1)
1694  + t2_2(2, 2) * t1_2(1) * t3dg_2(2, 2, 1)
1695  + t2_2(0, 0) * t1_2(2) * t3dg_2(0, 0, 2)
1696  + t2_2(1, 0) * t1_2(2) * t3dg_2(1, 0, 2)
1697  + t2_2(2, 0) * t1_2(2) * t3dg_2(2, 0, 2)
1698  + t2_2(0, 1) * t1_2(2) * t3dg_2(0, 1, 2)
1699  + t2_2(1, 1) * t1_2(2) * t3dg_2(1, 1, 2)
1700  + t2_2(2, 1) * t1_2(2) * t3dg_2(2, 1, 2)
1701  + t2_2(0, 2) * t1_2(2) * t3dg_2(0, 2, 2)
1702  + t2_2(1, 2) * t1_2(2) * t3dg_2(1, 2, 2)
1703  + t2_2(2, 2) * t1_2(2) * t3dg_2(2, 2, 2)),
1704  "T3(i,j,k)*T3dg(i,j,k)");
1705 
1706  test_for_zero((t2_2(i, j) * t1_2(k)) * (t3dg_2(j, i, k))
1707  - (t2_2(0, 0) * t1_2(0) * t3dg_2(0, 0, 0)
1708  + t2_2(1, 0) * t1_2(0) * t3dg_2(0, 1, 0)
1709  + t2_2(2, 0) * t1_2(0) * t3dg_2(0, 2, 0)
1710  + t2_2(0, 1) * t1_2(0) * t3dg_2(1, 0, 0)
1711  + t2_2(1, 1) * t1_2(0) * t3dg_2(1, 1, 0)
1712  + t2_2(2, 1) * t1_2(0) * t3dg_2(1, 2, 0)
1713  + t2_2(0, 2) * t1_2(0) * t3dg_2(2, 0, 0)
1714  + t2_2(1, 2) * t1_2(0) * t3dg_2(2, 1, 0)
1715  + t2_2(2, 2) * t1_2(0) * t3dg_2(2, 2, 0)
1716  + t2_2(0, 0) * t1_2(1) * t3dg_2(0, 0, 1)
1717  + t2_2(1, 0) * t1_2(1) * t3dg_2(0, 1, 1)
1718  + t2_2(2, 0) * t1_2(1) * t3dg_2(0, 2, 1)
1719  + t2_2(0, 1) * t1_2(1) * t3dg_2(1, 0, 1)
1720  + t2_2(1, 1) * t1_2(1) * t3dg_2(1, 1, 1)
1721  + t2_2(2, 1) * t1_2(1) * t3dg_2(1, 2, 1)
1722  + t2_2(0, 2) * t1_2(1) * t3dg_2(2, 0, 1)
1723  + t2_2(1, 2) * t1_2(1) * t3dg_2(2, 1, 1)
1724  + t2_2(2, 2) * t1_2(1) * t3dg_2(2, 2, 1)
1725  + t2_2(0, 0) * t1_2(2) * t3dg_2(0, 0, 2)
1726  + t2_2(1, 0) * t1_2(2) * t3dg_2(0, 1, 2)
1727  + t2_2(2, 0) * t1_2(2) * t3dg_2(0, 2, 2)
1728  + t2_2(0, 1) * t1_2(2) * t3dg_2(1, 0, 2)
1729  + t2_2(1, 1) * t1_2(2) * t3dg_2(1, 1, 2)
1730  + t2_2(2, 1) * t1_2(2) * t3dg_2(1, 2, 2)
1731  + t2_2(0, 2) * t1_2(2) * t3dg_2(2, 0, 2)
1732  + t2_2(1, 2) * t1_2(2) * t3dg_2(2, 1, 2)
1733  + t2_2(2, 2) * t1_2(2) * t3dg_2(2, 2, 2)),
1734  "T3(i,j,k)*T3dg(j,i,k)");
1735 
1736  test_for_zero((t2_2(i, j) * t1_2(k)) * (t3dg_2(i, k, j))
1737  - (t2_2(0, 0) * t1_2(0) * t3dg_2(0, 0, 0)
1738  + t2_2(1, 0) * t1_2(0) * t3dg_2(1, 0, 0)
1739  + t2_2(2, 0) * t1_2(0) * t3dg_2(2, 0, 0)
1740  + t2_2(0, 1) * t1_2(0) * t3dg_2(0, 0, 1)
1741  + t2_2(1, 1) * t1_2(0) * t3dg_2(1, 0, 1)
1742  + t2_2(2, 1) * t1_2(0) * t3dg_2(2, 0, 1)
1743  + t2_2(0, 2) * t1_2(0) * t3dg_2(0, 0, 2)
1744  + t2_2(1, 2) * t1_2(0) * t3dg_2(1, 0, 2)
1745  + t2_2(2, 2) * t1_2(0) * t3dg_2(2, 0, 2)
1746  + t2_2(0, 0) * t1_2(1) * t3dg_2(0, 1, 0)
1747  + t2_2(1, 0) * t1_2(1) * t3dg_2(1, 1, 0)
1748  + t2_2(2, 0) * t1_2(1) * t3dg_2(2, 1, 0)
1749  + t2_2(0, 1) * t1_2(1) * t3dg_2(0, 1, 1)
1750  + t2_2(1, 1) * t1_2(1) * t3dg_2(1, 1, 1)
1751  + t2_2(2, 1) * t1_2(1) * t3dg_2(2, 1, 1)
1752  + t2_2(0, 2) * t1_2(1) * t3dg_2(0, 1, 2)
1753  + t2_2(1, 2) * t1_2(1) * t3dg_2(1, 1, 2)
1754  + t2_2(2, 2) * t1_2(1) * t3dg_2(2, 1, 2)
1755  + t2_2(0, 0) * t1_2(2) * t3dg_2(0, 2, 0)
1756  + t2_2(1, 0) * t1_2(2) * t3dg_2(1, 2, 0)
1757  + t2_2(2, 0) * t1_2(2) * t3dg_2(2, 2, 0)
1758  + t2_2(0, 1) * t1_2(2) * t3dg_2(0, 2, 1)
1759  + t2_2(1, 1) * t1_2(2) * t3dg_2(1, 2, 1)
1760  + t2_2(2, 1) * t1_2(2) * t3dg_2(2, 2, 1)
1761  + t2_2(0, 2) * t1_2(2) * t3dg_2(0, 2, 2)
1762  + t2_2(1, 2) * t1_2(2) * t3dg_2(1, 2, 2)
1763  + t2_2(2, 2) * t1_2(2) * t3dg_2(2, 2, 2)),
1764  "T3(i,j,k)*T3dg(i,k,j)");
1765 
1766  test_for_zero((t2_2(i, j) * t1_2(k)) * (t3dg_2(j, k, i))
1767  - (t2_2(0, 0) * t1_2(0) * t3dg_2(0, 0, 0)
1768  + t2_2(1, 0) * t1_2(0) * t3dg_2(0, 0, 1)
1769  + t2_2(2, 0) * t1_2(0) * t3dg_2(0, 0, 2)
1770  + t2_2(0, 1) * t1_2(0) * t3dg_2(1, 0, 0)
1771  + t2_2(1, 1) * t1_2(0) * t3dg_2(1, 0, 1)
1772  + t2_2(2, 1) * t1_2(0) * t3dg_2(1, 0, 2)
1773  + t2_2(0, 2) * t1_2(0) * t3dg_2(2, 0, 0)
1774  + t2_2(1, 2) * t1_2(0) * t3dg_2(2, 0, 1)
1775  + t2_2(2, 2) * t1_2(0) * t3dg_2(2, 0, 2)
1776  + t2_2(0, 0) * t1_2(1) * t3dg_2(0, 1, 0)
1777  + t2_2(1, 0) * t1_2(1) * t3dg_2(0, 1, 1)
1778  + t2_2(2, 0) * t1_2(1) * t3dg_2(0, 1, 2)
1779  + t2_2(0, 1) * t1_2(1) * t3dg_2(1, 1, 0)
1780  + t2_2(1, 1) * t1_2(1) * t3dg_2(1, 1, 1)
1781  + t2_2(2, 1) * t1_2(1) * t3dg_2(1, 1, 2)
1782  + t2_2(0, 2) * t1_2(1) * t3dg_2(2, 1, 0)
1783  + t2_2(1, 2) * t1_2(1) * t3dg_2(2, 1, 1)
1784  + t2_2(2, 2) * t1_2(1) * t3dg_2(2, 1, 2)
1785  + t2_2(0, 0) * t1_2(2) * t3dg_2(0, 2, 0)
1786  + t2_2(1, 0) * t1_2(2) * t3dg_2(0, 2, 1)
1787  + t2_2(2, 0) * t1_2(2) * t3dg_2(0, 2, 2)
1788  + t2_2(0, 1) * t1_2(2) * t3dg_2(1, 2, 0)
1789  + t2_2(1, 1) * t1_2(2) * t3dg_2(1, 2, 1)
1790  + t2_2(2, 1) * t1_2(2) * t3dg_2(1, 2, 2)
1791  + t2_2(0, 2) * t1_2(2) * t3dg_2(2, 2, 0)
1792  + t2_2(1, 2) * t1_2(2) * t3dg_2(2, 2, 1)
1793  + t2_2(2, 2) * t1_2(2) * t3dg_2(2, 2, 2)),
1794  "T3(i,j,k)*T3dg(j,k,i)");
1795 
1796  test_for_zero((t2_2(i, j) * t1_2(k)) * (t3dg_2(k, j, i))
1797  - (t2_2(0, 0) * t1_2(0) * t3dg_2(0, 0, 0)
1798  + t2_2(1, 0) * t1_2(0) * t3dg_2(0, 0, 1)
1799  + t2_2(2, 0) * t1_2(0) * t3dg_2(0, 0, 2)
1800  + t2_2(0, 1) * t1_2(0) * t3dg_2(0, 1, 0)
1801  + t2_2(1, 1) * t1_2(0) * t3dg_2(0, 1, 1)
1802  + t2_2(2, 1) * t1_2(0) * t3dg_2(0, 1, 2)
1803  + t2_2(0, 2) * t1_2(0) * t3dg_2(0, 2, 0)
1804  + t2_2(1, 2) * t1_2(0) * t3dg_2(0, 2, 1)
1805  + t2_2(2, 2) * t1_2(0) * t3dg_2(0, 2, 2)
1806  + t2_2(0, 0) * t1_2(1) * t3dg_2(1, 0, 0)
1807  + t2_2(1, 0) * t1_2(1) * t3dg_2(1, 0, 1)
1808  + t2_2(2, 0) * t1_2(1) * t3dg_2(1, 0, 2)
1809  + t2_2(0, 1) * t1_2(1) * t3dg_2(1, 1, 0)
1810  + t2_2(1, 1) * t1_2(1) * t3dg_2(1, 1, 1)
1811  + t2_2(2, 1) * t1_2(1) * t3dg_2(1, 1, 2)
1812  + t2_2(0, 2) * t1_2(1) * t3dg_2(1, 2, 0)
1813  + t2_2(1, 2) * t1_2(1) * t3dg_2(1, 2, 1)
1814  + t2_2(2, 2) * t1_2(1) * t3dg_2(1, 2, 2)
1815  + t2_2(0, 0) * t1_2(2) * t3dg_2(2, 0, 0)
1816  + t2_2(1, 0) * t1_2(2) * t3dg_2(2, 0, 1)
1817  + t2_2(2, 0) * t1_2(2) * t3dg_2(2, 0, 2)
1818  + t2_2(0, 1) * t1_2(2) * t3dg_2(2, 1, 0)
1819  + t2_2(1, 1) * t1_2(2) * t3dg_2(2, 1, 1)
1820  + t2_2(2, 1) * t1_2(2) * t3dg_2(2, 1, 2)
1821  + t2_2(0, 2) * t1_2(2) * t3dg_2(2, 2, 0)
1822  + t2_2(1, 2) * t1_2(2) * t3dg_2(2, 2, 1)
1823  + t2_2(2, 2) * t1_2(2) * t3dg_2(2, 2, 2)),
1824  "T3(i,j,k)*T3dg(k,j,i)");
1825 
1826  test_for_zero((t2_2(i, j) * t1_2(k)) * (t3dg_2(k, i, j))
1827  - (t2_2(0, 0) * t1_2(0) * t3dg_2(0, 0, 0)
1828  + t2_2(1, 0) * t1_2(0) * t3dg_2(0, 1, 0)
1829  + t2_2(2, 0) * t1_2(0) * t3dg_2(0, 2, 0)
1830  + t2_2(0, 1) * t1_2(0) * t3dg_2(0, 0, 1)
1831  + t2_2(1, 1) * t1_2(0) * t3dg_2(0, 1, 1)
1832  + t2_2(2, 1) * t1_2(0) * t3dg_2(0, 2, 1)
1833  + t2_2(0, 2) * t1_2(0) * t3dg_2(0, 0, 2)
1834  + t2_2(1, 2) * t1_2(0) * t3dg_2(0, 1, 2)
1835  + t2_2(2, 2) * t1_2(0) * t3dg_2(0, 2, 2)
1836  + t2_2(0, 0) * t1_2(1) * t3dg_2(1, 0, 0)
1837  + t2_2(1, 0) * t1_2(1) * t3dg_2(1, 1, 0)
1838  + t2_2(2, 0) * t1_2(1) * t3dg_2(1, 2, 0)
1839  + t2_2(0, 1) * t1_2(1) * t3dg_2(1, 0, 1)
1840  + t2_2(1, 1) * t1_2(1) * t3dg_2(1, 1, 1)
1841  + t2_2(2, 1) * t1_2(1) * t3dg_2(1, 2, 1)
1842  + t2_2(0, 2) * t1_2(1) * t3dg_2(1, 0, 2)
1843  + t2_2(1, 2) * t1_2(1) * t3dg_2(1, 1, 2)
1844  + t2_2(2, 2) * t1_2(1) * t3dg_2(1, 2, 2)
1845  + t2_2(0, 0) * t1_2(2) * t3dg_2(2, 0, 0)
1846  + t2_2(1, 0) * t1_2(2) * t3dg_2(2, 1, 0)
1847  + t2_2(2, 0) * t1_2(2) * t3dg_2(2, 2, 0)
1848  + t2_2(0, 1) * t1_2(2) * t3dg_2(2, 0, 1)
1849  + t2_2(1, 1) * t1_2(2) * t3dg_2(2, 1, 1)
1850  + t2_2(2, 1) * t1_2(2) * t3dg_2(2, 2, 1)
1851  + t2_2(0, 2) * t1_2(2) * t3dg_2(2, 0, 2)
1852  + t2_2(1, 2) * t1_2(2) * t3dg_2(2, 1, 2)
1853  + t2_2(2, 2) * t1_2(2) * t3dg_2(2, 2, 2)),
1854  "T3(i,j,k)*T3dg(k,i,j)");
1855 }
FTensor
JSON compatible output.
Definition: Christof_constructor.hpp:6
FTensor::Tensor1< double, 3 >
test_T3_01
void test_T3_01(const Tensor1< double, 3 > &t1_1, const Tensor1< double, 3 > &t1_2, const Tensor2< double, 3, 3 > &t2_2, const Tensor2< double, 3, 3 > &t2_3, const Tensor2_symmetric< double, 3 > &t2s_2, const Tensor2_symmetric< double, 3 > &t2s_3, const Dg< double, 3, 3 > &t3dg_2)
Definition: test_T3_01.cpp:7
FTensor::Tensor2_symmetric
Definition: Tensor2_symmetric_value.hpp:13
FTensor::Tensor2< double, 3, 3 >
FTensor::Number< 0 >
test_for_zero
void test_for_zero(const T &t, const std::string &s)
Definition: test_for_zero.hpp:7
i
FTensor::Index< 'i', SPACE_DIM > i
Definition: hcurl_divergence_operator_2d.cpp:27
FTensor::Index< 'i', 3 >
FTensor::Dg
Definition: Dg_value.hpp:9
std
Definition: enable_if.hpp:5
j
FTensor::Index< 'j', 3 > j
Definition: matrix_function.cpp:19
k
FTensor::Index< 'k', 3 > k
Definition: matrix_function.cpp:20
l
FTensor::Index< 'l', 3 > l
Definition: matrix_function.cpp:21
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