1                INPUTS
                 ******

      MATRIX A OF COEFFICIENTS

       1)             22          10           2           3           7
       2)             14           7          10           0           8
       3)             -1          13          -1         -11           3
       4)             -3          -2          13          -2           4
       5)              9           8           1          -2           4
       6)              9           1          -7           5          -1
       7)              2          -6           6           5           1
       8)              4           5           0          -2           2

      MATRIX B OF RIGHT-HAND SIDES

       1)             12           1
       2)              7           0
       3)            -14           0
       4)             -1           0
       5)              1           0
       6)              8           0
       7)              8           0
       8)             -1           0

      MINPRM =   2     MAXPRM =   3     TR =   1


                 OUTPUTS
                 *******

      IER =   1     NOCOEF =   2

      THE MATRIX A OF COEFFICIENTS HAS RANK R =   3.
      THE ROW SPACE OF A IS SPANNED BY THE LINEAR INDEPENDENT ROWS
          1,  2,  3,
      THE COLUMN SPACE OF A IS SPANNED BY THE LINEAR INDEPENDENT COLUMNS
          1,  2,  3,


      ============================================================================================
      EACH OF THE INTEGERS GIVEN BELOW IS IN FIXED-RADIX FORM. FROM LEFT TO RIGHT, THE NUMBERS ARE 
      COEF(1),COEF(2),...,COEF(L), AND THE VALUE OF THE INTEGER IS
          COEF(1)*BASE**(L-1)+COEF(2)*BASE**(L-2)+...+COEF(L)
      WITH BASE = 10000.
      ============================================================================================


      THE NULL SPACE OF A IS SPANNED BY THE SUBSEQUENT LINEAR INDEPENDENT INTEGER VECTORS

          VECTOR NO.   1

               -1357
                2124
                 413
                2596
                   0

          VECTOR NO.   2

                -413
                -708
               -1003
                   0
                2596


      FOR EACH RIGHT-HAND SIDE OF THE SYSTEM
      THE SOLUTION OR LEAST SQUARES SOLUTION WITH MINIMUM EUCLIDEAN NORM
      WAS COMPUTED.

          RIGHT-HAND SIDE NO.   1

            THE SYSTEM IS CONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

                   1  2263  4240
               -8552 -4480
                1941  5040
                   1  3099    80
                 368  6400

          RIGHT-HAND SIDE NO.   2

            THE SYSTEM IS INCONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

                 405   432
                  88  4736
                 -40 -3968
                 145  7664
                  72  9600

          COMMON DENOMINATOR FOR ALL SOLUTIONS

                   1  9169  2800
1                INPUTS
                 ******

      MATRIX A OF COEFFICIENTS

       1)         492087     -709497      187957     -259731     -900605     -245025      214306     -949049      729469
                  744219     -397833       -2970      606256      697417      359680
       2)        -350227     -361288     -216539      164600     -837399      101957     -260009      -20655      337077
                  -74434       23128     -633695     -152083      567074     -283167
       3)         282479     -478604    -1102418      109328      381875     -418832      692579      109496     -369762
                 -543023      745290     -149995     -638732       25778      580502
       4)          91341     -401532     -147343      266670     -310153      538117      171466      437626      -14578
                 -847067     -415763     -241116      554064     -315262     -270857
       5)          99897     -657650     -632981     -160398      241297      387996      307451      219860     -233916
                 -821091      142918     -363595      -56018       89552         378
       6)        -301068      -70933      374333      507914     -394894       18595       38960      177457     -375014
                 -241288    -1313456     -405068     1014990     -470652     -219886
       7)        -615366      562702      684876      494229       80686     -276158     -695252     -131317     -133348
                  575095      274542      472610     -164129      387111     -398100
       8)         508703      561881        1860      267772      848669      159042      214123       -8012      -83117
                  324641      671975      370555     -733148      412712      572533
       9)         720241     -134916      308234     -257128     -744452      -67798      355054    -1269458      573099
                  968986      153335     -169652      902516      545830      359061
      10)        -157890       -4483      130424       90998     -366923      481801       69782      299287     -383766
                 -352561      204854     -308907      -42515     -175646     -603725
      11)         233409      -13077     -291423      481490     1147212      422390      583629     -204427     -472674
                 -582579      466999       23633      -60490      640406      427714
      12)         918902       46783      691388     -644399      218594     1022455      658106      -30196     -136038
                  277270      172579      425328      649680     -627671      645470
      13)         311750       20737     -237472      601304     -239831     -396442      651570     -596281      125793
                  295719      741647       53769     -244240      661274      577991
      14)         191554      234091      268379       50158     -250918     -129758     -159052     -264225      488413
                  759604      753499      495538     -694572      616066      209756
      15)         182191       10115      -32461      375880      -59164       23958     -113900      -19560      108217
                 -221548      207284      242288      524976     -115334     -153142
      16)        -122348     -151131     -155484      483042       14284      309464      275043      -61430     -210491
                 -584856        2568     -362870       41415      470732     -339069
      17)         717504     -149106      505757     -202633      309393      336444      -83013    -1039658      416580
                  656707     -458682      141851     1121306      757765      260048
      18)         362375     -384187     -859582     -303658      431743     -382511      356992     -194016      320219
                 -461458      215142       83803     -386386      194762      186723
      19)          55446      248625       52618      861254      623512    -1335000       92472    -1319502      288512
                  777378     -270360      590661      103096     1306164      424516
      20)         932120     -325993     -623721     -188670     -244095     -382160      713474     -413942       79136
                  101336      751155      111598      187597     -285886      484845
      21)        -350125      -19109      463457     -396770      198772      549338     -193343      896664     -276366
                 -737453     -572295      472391      290185    -1123052     -564571
      22)         -40551      174553      216024      567650      183856       32852     -638864       43472      229986
                  119611     -529480       88563      -66670      665740     -399425
      23)          10999       98144     -279193      -52699     -136987       47828       47830      779035     -147852
                 -390133      -14656      -76321     -166227     -929415       75384
      24)        -318425      -66824     -225986      127704      268559      439151      310059      918952     -719924
                 -881586      723391      131856     -587941     -623020     -104359
      25)        -544900     -219563      677676       64239     -702188      232508     -809728      230537      113145
                   51123     -876125      -21356      562646      -32725     -879899
      26)         149767       73148      610233     -274640      465932     -170888      -74268     -896286      330500
                  996330      134231      643900      103819      816604      620203
      27)         -92822      228283      -69496     -307181      191211       19716      175565      318160     -646743
                  125889     -212430     -522264     -302790     -526335      144904
      28)        -581144     -122653     -225720     -290154      403635     -580239     -592118       -6537      -66192
                  301738     -118623      -33003     -683797      404314        2233
      29)          -1112     -107494     -576317     -519415     -102546      180727      480081      360092      -27089
                 -390767      -74095     -719809     -326443     -509519      421942
      30)        -105312     -260725     -306438      366643      -56987     -619982      -27366     -483587       94019
                  288139     -326606     -292645     -185832      835981      169046

      MATRIX B OF RIGHT-HAND SIDES

       1)            187         499        -239
       2)           -444         255         243
       3)           -585         422        -604
       4)            348         475         579
       5)            333        -560        -327
       6)           -331        -607         141
       7)           -201        -296         571
       8)           -219        -301         226
       9)           -521        -110        -202
      10)           -365        -479         314
      11)            603        -485        -100
      12)            488         239         376
      13)            -67         291         253
      14)            105        -211         251
      15)            -33         163          80
      16)            538         -22        -315
      17)            497        -377         -70
      18)             84        -423         467
      19)             27         592          -7
      20)           -517         166         287
      21)            -23        -384        -553
      22)            156        -403         610
      23)             -2        -172         468
      24)             96         405        -540
      25)           -184        -360        -134
      26)            616         412         -57
      27)           -256        -380        -277
      28)           -592         -61        -532
      29)            368         618         550
      30)           -431         -85         286

      MINPRM =  22     MAXPRM =  42     TR =   4


                 OUTPUTS
                 *******

      IER =   1     NOCOEF =  33

      THE MATRIX A OF COEFFICIENTS HAS RANK R =  12.
      THE ROW SPACE OF A IS SPANNED BY THE LINEAR INDEPENDENT ROWS
          1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12,
      THE COLUMN SPACE OF A IS SPANNED BY THE LINEAR INDEPENDENT COLUMNS
          1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12,


      ============================================================================================
      EACH OF THE INTEGERS GIVEN BELOW IS IN FIXED-RADIX FORM. FROM LEFT TO RIGHT, THE NUMBERS ARE 
      COEF(1),COEF(2),...,COEF(L), AND THE VALUE OF THE INTEGER IS
          COEF(1)*BASE**(L-1)+COEF(2)*BASE**(L-2)+...+COEF(L)
      WITH BASE = 10000.
      ============================================================================================


      THE NULL SPACE OF A IS SPANNED BY THE SUBSEQUENT LINEAR INDEPENDENT INTEGER VECTORS

          VECTOR NO.   1

                -190 -7474 -1059 -7409 -4585 -3232 -5525 -9058 -9851 -9916 -5726 -2943 -3311 -4345 -4344 -6155 -9988
                      -316
                 188  8313  6470  7189  6437  2285  4637  7260  3488  1598  6160  4473  3743  4106  1728  9414  2784
                      8740
                -568 -8639 -4035 -4209 -2284 -3290 -9485 -4005 -6756 -5873 -3207 -5211 -9116 -9982 -8685 -1581 -2790
                     -1064
                2521  1130  1344  7124  7493   380   236  6626  8199  7311  2956  5732  6347  2712  5887   684  6260

                -188 -5792 -5340 -5844 -9312 -4792 -4257 -7023 -6861 -3398 -8849 -1516 -8010 -7758 -9016 -3527 -2100
                     -2480
                 378  8224  4140   564  9648  3038  9023  5609  3459  6915  9952  8546  9856  9409  7935  7909   719
                       276
                8571  7842  4572   224  1476  3292   804  6531  1879   858  4052  3490  9580  7222  8016   327  7284

                -187 -8733 -4176 -2079 -7363 -1811 -9193 -6361  -306 -2439 -6377 -5238 -3959 -3986 -5421 -1043 -4183
                     -2952
                -188 -2767 -1984 -4231 -2762 -7800 -7801 -6739 -6909 -1559 -2075 -5968 -9131 -6142 -1761 -2462 -7278
                     -6968
                 190  7474  1059  7409  4585  3232  5525  9058  9851  9916  5726  2943  3311  4345  4344  6155  9988
                       316
                -188 -9322  -922 -7727 -5287 -1282 -6789 -7355  -138 -8878 -5084 -9656   -36 -4645  -813 -9769 -1058
                     -7244
                 378  4190  6331  8413  4248  7050   415  5230  6856  7796  4254  7816  4684  7254  1595  6489  7623
                      6260
                   1  1092  8972  5916  7348  8969  3672  1041  3158    78  8169  7008  9223  5927  9935  3903  1012
                      3544
                   0
                   0

          VECTOR NO.   2

                 126   556  5067  2356  2374  6519    11  8331  3409  9865  5647  8286  6317  3635  6294  3534  2313
                         0
                -124  -387 -6026 -1598 -5376 -6574 -6971 -6438  -395 -4267 -7157 -4634  -456 -2857 -4593 -6437 -6835
                     -9920
                 375  5449  9448  3083  7026  5629  4083  2532  7311   319  4906   111  5332  6895  2672  1377  1818
                      8896
               -9076   -68 -4840 -9649  -974 -9368  -851 -9856 -5519  -320 -6643 -6637 -4850 -1765 -3193 -4464 -6536

                 124  2404  4930  2674  3076  4569  1275  6627  3696  8827  5006  4999  3042  3935  2763  7147  3383
                      6928
                -250 -6994 -7805 -7182  -850 -7076 -9895 -5337 -3709 -7812 -6352 -4016 -4531 -9726 -5398 -2100 -8792
                      -944
               -2016 -8904 -1075 -7699 -7994 -4304  -189 -3301 -4559 -7849  -365 -2586 -1077 -8170  -709 -6547 -7008

                 125  2488  9450  8053  1575  4541  2795  7574   204  1626  4251  6825  5972  9324  3614   695  6122
                      1968
                 124   387  6026  1598  5376  6574  6971  6438   395  4267  7157  4634   456  2857  4593  6437  6835
                      9920
                -126  -556 -5067 -2356 -2374 -6519   -11 -8331 -3409 -9865 -5647 -8286 -6317 -3635 -6294 -3534 -2313
                         0
                 124  8455  1642  5901  6175  8552  4187  7195  3601  2506  8553  6095   800  7168  7273  9276  3026
                      7952
                -249 -6910 -3285 -1803 -2351 -7104 -8375 -4390 -7202 -5013 -7107 -2190 -1601 -4337 -4547 -8552 -6053
                     -5904
                   0
                   1  1092  8972  5916  7348  8969  3672  1041  3158    78  8169  7008  9223  5927  9935  3903  1012
                      3544
                   0

          VECTOR NO.   3

                -123 -8370 -7122  -522 -7676 -8580 -2667 -6248 -7093 -9707 -9308 -4268 -7870 -1779 -6423 -5728  -288
                     -2912
                 124   387  6026  1598  5376  6574  6971  6438   395  4267  7157  4634   456  2857  4593  6437  6835
                      9920
                -371 -1078 -3557 -9416 -7630 -9751 -9394 -8367 -4679    -4 -2227 -2075 -8438 -3183 -2930 -5764 -7769
                     -4720
               -2016 -8904 -1075 -7699 -7994 -4304  -189 -3301 -4559 -7849  -365 -2586 -1077 -8170  -709 -6547 -7008

                -124 -2404 -4930 -2674 -3076 -4569 -1275 -6627 -3696 -8827 -5006 -4999 -3042 -3935 -2763 -7147 -3383
                     -6928
                 247  3716   887  9431  8804   168  8879  2213  4235  7576  1843  2989  6861  1942  5592   391  5755
                       312
               -9076   -68 -4840 -9649  -974 -9368  -851 -9856 -5519  -320 -6643 -6637 -4850 -1765 -3193 -4464 -6536

                -124 -1396  -478 -2136 -4226 -5571 -9123 -6532 -7046 -1547 -6081 -9816 -6749 -3396 -3678 -6792 -5109
                     -8424
                -124  -387 -6026 -1598 -5376 -6574 -6971 -6438  -395 -4267 -7157 -4634  -456 -2857 -4593 -6437 -6835
                     -9920
                 122  7277  8149  4606   327  9610  8995  5207  3935  9629  1138  7259  8646  5851  6488  1824  9275
                      9368
                -123 -7362 -2669 -9984 -8826 -9583  -515 -6154  -443 -2428  -383 -9086 -1577 -1240 -7338 -5373 -2014
                     -4408
                 247  4724  5339  9969  7653  9166  1031  2308   886  4856   767  8172  3154  2481  4677   746  4028
                      8816
                   0
                   0
                   1  1092  8972  5916  7348  8969  3672  1041  3158    78  8169  7008  9223  5927  9935  3903  1012
                      3544


      FOR EACH RIGHT-HAND SIDE OF THE SYSTEM
      THE SOLUTION OR LEAST SQUARES SOLUTION WITH MINIMUM EUCLIDEAN NORM
      WAS COMPUTED.

          RIGHT-HAND SIDE NO.   1

            THE SYSTEM IS INCONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

               -1045 -1811 -7529 -3857 -2963 -3613 -2539 -5372  -996 -1914 -7322 -3686 -9141 -1969  -133  -125 -4756
                     -6222 -6852 -8146 -2068 -1987 -6771 -6564 -5614 -9115   -14  -219 -9105 -6269 -2549   -61 -6671
                     -9333 -4609 -1822 -5356
                 614  7039  8945  6819  4575  6260  8831  1257  4153  6119  2000  6476  8324  3310  7573  1088  1052
                       563  9517   595  5593  7807  2935  3057  5445  5414  5713  5460  6569  8376  4440  8300  8397
                       415  6331  8247  6170
                 518  3544  5507  4700  7152  9505  4827  2859  2773  4633  8870  5282  9852   535   763  2030  3498
                      3879  9564   799  2941   576  9012  5149   309  5314  7311  8478  9750  5905  6831  8904  3845
                      2442  3865  5274  3616
                -262 -5166 -4468  -806 -6794 -9187 -2957 -9997 -9224 -4290 -5145 -2406 -2647 -8530 -8041 -4328 -1331
                        -4 -4622 -6743 -1245 -6228 -8433 -4626 -2087 -2410 -3606  -263 -6489 -1204 -2890 -7859 -9970
                     -4761 -5662  -631 -7170
                 484  5712  5181  5821  5207  5602  1212  2149  8413  7763  7780  3931  9048  4219   503  9728  5831
                       962  2561  8615  6935  9579  2618   624  5859  5514  9406  9135  4992  4530  9799  6550  8701
                        48  7467  4043  3356
                 977  5341  4806  7648  3801  6720  3438  8120  6478  6111  5405  3683  7112  6419  7117  5264  4642
                      8981  1650  5485  6277  4592  4256  1396   687  7110  3809  8465  3876  3201  7990  2084  3651
                      5516  3004  4858  5280
                 793  6726  4999  8526  6538  8253  5918  8912  5992  5724  3436  9955  6968  7169  4948  1923   855
                      8814  3942  7723   829  7793  3074  9589  2080  3039  9215  1179  2775  6387   782  6694   662
                      8990  2276   123  8744
                -206 -6765 -4672 -3386 -6943 -9827 -6007 -5972 -1360 -4433 -2328 -8530 -4207 -6683 -7131 -5204 -8857
                      -694  -670 -9969 -5471  -663 -4602 -8148 -2523  -365 -5656 -5937 -4065 -2331 -4370 -7450 -2225
                      -622 -3356  -648  -660
                1621  6073  7697  5917   747  6400   395  9434  2418  5769  7827    29  4766  9104  9112  2000  2621
                      1121  6651   278  1884  3396  7270  8835  2541  3665  4660   347  2133  7555  4141  5756  5874
                      4267  6531  6813  3384
               -1143 -7258 -8027 -5319 -3956 -3332 -2738 -1537 -3160 -1869 -4237 -2747 -5217 -4713 -3202 -5711  -912
                     -9637 -6905 -7588 -1673  -478 -6619 -4957 -8515 -4096 -8267 -4576 -5903 -7905 -9819 -5205 -6565
                      -678  -810 -4667 -5832
                -315   -27 -7185 -8909 -5830 -4505  -630 -8001 -2712   -65 -8955 -3083 -9196 -9687 -4650 -7993 -4164
                     -3560  -459 -8398 -2314 -9451 -9972 -9596 -9952 -3856 -7317 -5335 -4487 -1766 -9799 -6962 -4875
                     -5685 -8914 -1909 -4836
                 330  1491  5504  6852  1335  5139  5462  4166   110   477  1644   793  6410  8454  8750  3207   273
                      9782  9172   894  1675  1192  3833  4497  7741  2674  9333  5147  9365  1312  1495  7121  5268
                      7595  7849  2306  4396
                  73  9115  3949  9594  3003  9357  1699  9519   611  6567  5171  1798  2218  9992  6976  4512  1925
                      3003  3771  7778  2389  2260  8935  8854  3318  7892  5223  2957  4792  6567  6669  2650  9582
                      6348  7150  6976  8818
                 406  7070  2465  7328  7822   826  6195  8473  9941  2735   801  7294  1885  5254  7221  2059  9002
                      5221  3499  1089  5793  3223  9566  8471  9265  2749  7456  2165  6605  9334  7989  4441  8304
                      4874  8995   653  3766
                 824  7959  4300  2290  4218  2220  2200  1803  1973  2172  4729  2507  3221  3581  7926  5937   801
                      2364  4979  6834  1112  4849  7720  5079  5194  3463  7201  8509    89  7373  9346  8189  9248
                      4265  5925  9129  6688

          RIGHT-HAND SIDE NO.   2

            THE SYSTEM IS INCONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

               -1747 -3031 -4985 -7472 -9700 -7471 -2823  -630 -4299 -1502  -592 -8514 -6912 -7347 -4334 -3049 -2316
                      -483 -2954 -8726  -850 -9949 -8729 -4311 -2186 -9936 -1358 -5371 -1646 -1201  -491 -9089 -7906
                     -7928   -34 -3664 -7752
                 -98 -1979 -2993 -6958 -4364 -7849 -5657 -1030 -5322 -8220 -9536 -9367 -4528 -5676  -714 -8470 -3162
                     -3138 -7029 -5049 -6681 -6455 -9304 -3685 -3285 -5861 -6014 -6072  -699 -4152 -6191 -4149 -8856
                     -3582 -7291 -1301  -680
                 171  7585   523  5775  3700  5655  5938  4259  4587  7312  1574  9409  6137  4482  1260  1416  2597
                      1338  1828  2174  6605  5966  9296  6964  7707  6808  7131  8077  8608  6051  6161  7853  3305
                      2707  4700  7306  4802
                 165  7782  8572  4494   384   467  1573  4874   289   668  1334  7265  7055  9807  9517   433  5060
                       790  5032  5996  4624  5782   617  1372  5796  6223  3298  4719  7339  2302  4905  9667   665
                      2633  6335  1473  8820
                -543 -8070 -7933 -9104 -1205 -1670 -8832 -1499 -5046 -8421 -8024 -6897 -9532 -7564  -157 -9938 -9384
                     -8890 -6435 -2123 -5883 -7373 -5563 -7667 -1402 -6729 -6512  -846 -6898 -3709 -6019  -896 -8219
                     -6038  -923 -2823  -748
                -130 -3606 -5221 -7188 -3582 -6754 -8881 -2486 -7382 -2588 -2628 -3904 -5215 -4324  -706 -4331 -2522
                     -6322 -2877 -9787 -6972 -4158 -1625  -296 -5229 -2704  -186 -8036 -9714 -4603 -7801  -557 -3144
                     -4435 -6164 -9997 -6655
                 446  7126  1757  3888  8900   637  4770  8856  9946  7600     6  6125  3582  5110  8702  4997   103
                       673  2363  9523  6177  9578  4888  9946  1326  6254  3813  5275   754   746  2346  9426  5935
                      2553  2599  3531  9143
                  97  8490  2249  3605  3979   263  2319  6060  4693   917  7038  3394  5458  1251  2628  8852  7234
                      9056  9754  3624   820  2286  9452  4617  2764  6230  5042  1553  1914  8322  5048  5475  3345
                      5978  1597  2180  4395
                1214  9167  1341  6935  7410  3992  6856  7337  2313  9304  3775  8669  3638   810  2005  5352  2402
                      3924  2190  1925  8400  4687  7019  7453  6572  2424  8599  4101  3962  4144   887  9157  3982
                      7859  3317  2774  7248
                -549 -9080 -8774 -8288 -9625  -527 -6344 -7377 -5200 -6712 -9329 -7508 -4216 -6584 -2157 -9892 -9704
                     -7817 -9409  -527 -6823 -9628 -4369 -8482 -4444 -3012 -4430 -9797 -9742 -4792 -8455 -7231 -3277
                     -2023 -1445 -3733  -509
                 421  7075    28  5159  3355  5219  3017  8741  8745  4540  6869  4768  3548   582  6806  4833  7954
                      4559  9340  7911  5173  4089  2529  7857  2717   506   215  5988  2605  1107  5462  6383  8659
                      6184  5225  6920  5313
                 424  4016  4576  6846  7634  9475  6389  8715  6087  1149  5610   782  6854  7966  2680  8741  3490
                      2695  5232    12  6693  4539  2671  5926  7336  8823  4528  8551  5222  6097  8701  4864  1429
                      6145  1269  6851  2952
                 409  6090  4433  2316   217  5179  8052  7375  8294  6359  7009  3726   848  4651  6811  5014  1816
                      8964  7433   710  1690  4639  3293  4161  8235   889   991  1975  5973  7404   679  3009  4445
                      4375  4777  1211  1696
                -229 -1439 -4706 -3240  -202 -7566 -6221 -8290 -3718 -5692 -4742 -1899   -26 -4432 -3689 -6830 -5184
                     -3128 -5188 -1585 -9777 -1922 -6998  -741  -769 -7635 -6787 -4686 -5355 -1166 -7823  -490 -8434
                     -4587 -4865 -6878  -218
                1937  6476  7799  1964  2398  2612  6222  9280  5188  6653  2407  3844  6347  7491  2870  3817  9699
                      9559  5689  3403  1863  4657  8152  5865  1607  6511  8035  9168  9860  6986  9534   853  9216
                      5551  7951  3396  9181

          RIGHT-HAND SIDE NO.   3

            THE SYSTEM IS INCONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

                 795   360  6712  9810  2798  2980  5124  7682  8784  1684  4454  8399  2126  8861  3550  1169  2452
                      6693  7793  6072  4504  5427   883  3429  7423  9711  3939  5356  7633  8941  3520  4798  9811
                      4568  7482  6577  5118
                1336  7723  4924  2011  8808  6382  1756  7218  3545  6569  8351  6970  5711  4523  9313  2549  6314
                      9925  4866   327  8593  5037  7043  7142  8916  1345  4119  9843  8847  1897  4070  5673  7703
                      5949  3802  4409  9860
                -291 -9215 -2430 -1774 -3873 -2987 -9668 -5795 -5184 -4210  -523  -588 -5197 -7566  -132 -3913  -627
                      -709 -7212 -7791 -3152 -4198 -7295 -3318 -8314 -2518 -1032 -5715 -4309 -4752 -4179 -3398 -6391
                     -5249 -7377  -186 -9618
                 846  5995  1397  3919  2521  8368  5937  7652   493  5466  8880   435  6622  5862  7985  3635  2682
                      4436  7832  7752  4926  5263  2492  3022  2379  9158  6844  2388   565   237  5636    77  8178
                      2438  8972  9276  8960
                -262  -316 -7775 -3049 -7619 -1399 -3496  -518 -5076 -9636 -2164 -5689  -981 -2525  -948 -8051 -8888
                     -8439 -5970 -7165 -1102 -7173 -4628 -4240 -9650 -2911 -5491 -6333 -7743 -5976 -2105 -7604   -99
                      -642 -7066 -9947 -1588
                 350  9948  4213  4109   755   419  4345  7362  5780  6425  4193  3473  3990  5636  4196   796  2696
                      2961  5702  5587  5830  8512   508  6217  3899  7662  6234  8426  6168  4815   215  1056  5968
                      9850  3946  9012  6850
                -105 -7943 -9788 -6594 -4767 -9332  -554 -9529 -3745 -2177  -544 -9884 -8276 -2651 -4419  -536 -5918
                     -4929 -6173 -2736 -6657 -9065 -5376 -4307 -1704 -9714 -1434 -3368 -2274  -577 -9858 -4909 -6177
                     -9778 -9372  -596 -9492
                 469   222  5792  5786  2262  1339  4990  8659   355  8886  8010  1988  2791  1817  9955  8132  2320
                      9232  3952  4772  2010  8956  8608  8064  2994  1360  5379  7975  3589  6021  8091  2180  3155
                      7410   800  3653  9670
                1385   859  3548  4459  5805  8743  5072  3021  5626  5777  2706  5242  1882  7251  6122  6052  6872
                      8203  5766  9929  7201  1730  7077  2153  7869  6256  6254  7627   700  3454  8010  1535  8840
                      7345  2583  5109  5398
                 -99 -1294 -4905 -5701 -6039 -4736 -5877 -1285 -6397 -4553 -2635 -3245 -8186 -9023 -5828 -3132 -2613
                     -9430 -8494 -5599 -1102  -488 -2907 -2102 -8947 -5010  -912 -6667 -7012 -2696  -736 -4502 -5683
                     -4692 -9462 -6959 -7854
                -356 -1620 -5454 -1517 -2111 -8460 -9132 -2758 -9265  -390 -5302 -4642 -6996 -1270 -6358 -7616 -1651
                     -2103   -53 -6946  -874 -2330 -1856  -351 -8379 -5060 -8897 -1941 -6967 -8587 -2743 -8797 -9276
                     -4871 -9483 -4823 -8992
                -392 -6964 -5863   -86 -1621 -3681 -9244 -8839 -6437 -4251  -334 -3860 -7377 -3931 -1684 -5911 -2469
                     -3159 -6699 -5825  -646 -5026 -4123 -5560 -4890 -9580   -88   -79 -3043 -5718 -5377 -2006 -6040
                      -113 -8401 -4562 -7398
                -198 -3924 -6035 -1979 -5466 -2574 -8386 -7295  -508 -8331 -8545 -8501 -1542 -5634 -5814 -2312 -1618
                     -7085 -4895 -3467 -4695 -6483 -4643 -8846 -1046 -2688 -6851 -2961 -4155 -5783 -5066 -9796 -1468
                     -6833 -5238 -6459 -2454
                -102 -3900 -7569 -7243 -3844 -3250  -455 -3639 -2571 -8479 -7562 -4700 -6893 -4849 -5101 -9996 -9113
                      -106 -6185 -2101 -1542 -4335 -8867 -5276 -2524 -9130  -580 -2821   -96 -9790 -5386 -7232  -301
                     -4132  -486 -6061 -6148
                 278  1522  1332  2826  2248  5083  5320  4229  6673  3859   377  6422  8638  2031   234  7062  8118
                      6208  5434  6626  5168  3866  1202  3917  2069  1722  1549  3073  5117  8062  3174  8663  3142
                      1359  9963   537  5366

          COMMON DENOMINATOR FOR ALL SOLUTIONS

                 199  1748  2753  3640  7141  7342  8611  8319  2513  2089  5841  7655  6712  2873    91  1622  8842
                      3141  3700  7482  8862  7682  4478  7293  3299  8954  1400  1950  5216  7529  6100  9959  3033
                      6250  9289  2771  5592  1310
1                INPUTS
                 ******

      MATRIX A OF COEFFICIENTS

       1)         100006      100005      100004      100003      100002      100001
       2)         100005      100005      100004      100003      100002      100001
       3)         100004      100004      100004      100003      100002      100001
       4)         100003      100003      100003      100003      100002      100001
       5)         100002      100002      100002      100002      100001      100000
       6)         100001      100001      100001      100001      100000       99999
       7)         100000      100000      100000      100000       99999       99998

      MATRIX B OF RIGHT-HAND SIDES

       1)              1           1
       2)              1           2
       3)              1           3
       4)              1           4
       5)              1           5
       6)              1           6
       7)              1           7

      MINPRM =   8     MAXPRM =  15     TR =   3


                 OUTPUTS
                 *******

      IER =   0     NOCOEF =   2

      THE MATRIX A OF COEFFICIENTS HAS RANK R =   5.
      THE ROW SPACE OF A IS SPANNED BY THE LINEAR INDEPENDENT ROWS
          1,  2,  3,  4,  5,
      THE COLUMN SPACE OF A IS SPANNED BY THE LINEAR INDEPENDENT COLUMNS
          1,  2,  3,  4,  5,


      ============================================================================================
      EACH OF THE INTEGERS GIVEN BELOW IS IN FIXED-RADIX FORM. FROM LEFT TO RIGHT, THE NUMBERS ARE 
      COEF(1),COEF(2),...,COEF(L), AND THE VALUE OF THE INTEGER IS
          COEF(1)*BASE**(L-1)+COEF(2)*BASE**(L-2)+...+COEF(L)
      WITH BASE = 10000.
      ============================================================================================


      THE NULL SPACE OF A IS SPANNED BY THE SUBSEQUENT LINEAR INDEPENDENT INTEGER VECTORS

          VECTOR NO.   1

                   0
                   0
                   0
                   1
                  -2
                   1


      FOR EACH RIGHT-HAND SIDE OF THE SYSTEM
      THE SOLUTION OR LEAST SQUARES SOLUTION WITH MINIMUM EUCLIDEAN NORM
      WAS COMPUTED.

          RIGHT-HAND SIDE NO.   1

            THE SYSTEM IS CONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

                   0
                   0
                   0
                  60
                   0
                 -60

          RIGHT-HAND SIDE NO.   2

            THE SYSTEM IS CONSISTENT.
            NUMERATORS OF THE ELEMENTS OF THE SOLUTION

                -120
                   0
                   0
                 600   420
                   0
                -600  -420

          COMMON DENOMINATOR FOR ALL SOLUTIONS

                 120
