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There is an internal testing mode that verifies kspace_t has been built correctly.
./kspace_t -t -n 3 -mpfr_precision=230 --infile=cez.txt
This command yields the output below. The fifth tests tells you that
KSPACE has computed values that are within 3e-69, or 2 bits, of the
rational values contained in the tables listed in cez.txt.
Coprimality tests... pass/fail/total: 4/0/4
Initialisation of preKspace class... pass/fail/total: 2/0/2
I/O tests: pass/fail/total: 4/0/4
<,== tests: pass/fail/total: 75/0/75
CEZTest::test() epsilon=2.31825e-69 2.31825e-69 2.31825e-69 2.31825e-69 2.31825e-69 2.31825e-69
pass/fail/total: 200/0/200
qsort tests... pass/fail/total: 4/0/4
Totals: pass/fail/total: 289/0/289
The file cez.txt contains information on the files to read in
and the tests to perform. The first column specifies the type
of the classification, as specified by the command-line option
--type (see command-line options). The second column
specifies the number of bits of precision that can be lost in
computing the rational Kreck-Stolz invariants. The third column
specifies the name of the text files where the test data is found.
2 2 cez_table4_1.txt 0 2 cez_table4_2.txt 0 2 cez_table4_3.txt 2 2 cez_table4_4.txt 0 2 cez_table4_5.txt 0 2 cez_table4_6.txt
The content of each of the files listed in cez.txt is a table
from Chinburg, Escher and Ziller (2007), up to the addition of the
sign on r and, where noted, the sign on s22 is changed
from that reported. The differences are due to the different ways in
which the invariants are reduced mod 1.
Table 4_1 of Chinburg, Escher and Ziller (2007):
#sum k0 k1 l0 l1 c r s s22 p140 21 21 20 20 0 -43 21 -1/6 26 # sum k0 k1 l0 l1 c r s s22 p1 10 8 7 6 4 0 -43 21 -1/6 13 98 50 50 49 49 0 -101 50 -1/6 55 14 12 10 9 5 0 -101 50 -1/6 21 134 68 68 67 67 0 -137 68 -1/6 73 29 19 17 16 13 0 -137 68 -1/6 23 22 16 16 13 9 0 -181 -26 -1/6 85 50 30 26 25 25 0 -181 26 1/6 164 84 45 43 42 42 0 -181 43 0/1 89 18 15 14 12 6 0 -181 43 0/1 35 # end of table 4.1 (sign of r corrected 18-10-2008)
Table 4_2 of Chinburg, Escher and Ziller (2007):
#sum k0 k1 l0 l1 c r s p1 s1 s278 79 49 46 32 0 -4001 -1502 3336 49741/112028 -1043/8002 78 75 54 46 32 0 -4001 1502 3336 1877/8002 1043/8002 36 71 59 34 2 0 -8099 3085 2184 -1055/9968 -6975/32396 54 92 47 38 16 0 -8099 -3085 2184 -4285/9968 6975/32396 30 83 43 24 6 0 -8671 4216 936 -941/10672 -11343/34684 42 97 33 24 18 0 -8671 -4216 936 -1417/74704 11343/34684 114 104 96 81 33 0 -9889 1719 65 2961/79112 9505/39556 129 109 101 81 48 0 -9889 -1719 65 275943/553784 -9505/39556 204 144 136 135 69 0 -11011 -1899 5320 31695/176176 -6767/22022 228 152 144 129 99 0 -11011 -1899 5320 12819/176176 -6767/22022 # CEZ table 4.2 (sign of r corrected 18-10-2008)
Table 4_3 of Chinburg, Escher and Ziller (2007):
#sum k0 k1 l0 l1 c r s p1 s1 s2177 145 121 113 64 0 -13361 1732 5905 -272959/748216 6839/53444 195 151 127 104 91 0 -13361 -1732 5905 272959/748216 -6839/53444 150 154 154 135 15 0 -26973 2119 5877 -6131/18648 123965/323676 705 389 383 357 348 0 -26973 -2119 5877 6131/18648 -123965/323676 114 185 115 102 12 0 -35749 10989 18648 -9018/35749 8920/35749 186 230 111 108 78 0 -35749 10989 18648 -9018/35749 8920/35749 153 205 141 114 39 0 -42319 7443 20142 -73317/677104 4123/84638 153 191 157 114 39 0 -42319 -7443 20142 73317/677104 -4123/84638 # CEZ table 4.3 (sign of r corrected 18-10-2008)
Table 4_4 of Chinburg, Escher and Ziller (2007):
#sum k0 k1 l0 l1 c r s s22 p1320 316 3 320 0 0 1267 -319 -1/3 813 # CEZ table 4.4 (sign of s22 corrected 18-10-2008) on lines with # 62 25 19 62 0 0 1267 -319 -1/3 86 # 188 181 5 188 0 0 1277 533 -1/6 453 # 70 44 19 70 0 0 1277 -533 1/6 861 # 780 778 1 780 0 0 1557 778 -1/6 783 # 150 139 7 150 0 0 1557 778 -1/6 1404 # 402 398 3 402 0 0 1595 -401 0/1 1018 72 36 23 72 0 0 1595 -401 0/1 798 120 105 11 120 0 0 1619 -237 0/1 1277 144 132 7 144 0 0 1619 -237 0/1 997 ## sum k0 k1 l0 l1 absr s s22 p1
Table 4_5 of Chinburg, Escher and Ziller (2007):
#sum k0 k1 l0 l1 c r s p1 s1 s2336 171 164 336 0 0 28379 -335 27139 -82869/3178448 -2393/56758 336 223 60 336 0 0 28379 -335 27139 -1104513/3178448 -2393/56758 690 362 291 690 0 0 129503 12564 45679 69409/14504336 -80901/259006 690 423 169 690 0 0 129503 12564 45679 5767541/14504336 -80901/259006 1092 717 362 1092 0 0 273581 91230 196280 -393315/1094324 370663/1094324 1092 761 241 1092 0 0 273581 91230 196280 310179/1094324 370663/1094324 1302 891 368 1302 0 0 382025 -35741 334208 -74669/436600 -294993/1528100 1302 928 191 1302 0 0 382025 -35741 334208 1442017/3056200 -294993/1528100 1614 1265 347 1614 0 0 442179 -6448 346023 -173889/611408 115166/1326537 1614 1274 311 1614 0 0 442179 -6448 346023 -21037/611408 115166/1326537
Table 4_6 of Chinburg, Escher and Ziller (2007):
#sum k0 k1 l0 l1 c r s p1 s1 s24266 2279 1603 4266 0 0 5143925 -1448517 390037 -37291099/144029900 36777/4115140 4266 2528 939 4266 0 0 5143925 -1448517 390037 -37291099/144029900 36777/4115140