Bertini(TM) v1.6 (May 22, 2018) D.J. Bates, J.D. Hauenstein, A.J. Sommese, C.W. Wampler (using GMP v6.0.0, MPFR v3.1.2) NOTE: You have requested to use adaptive path tracking. Please make sure that you have setup the following tolerances appropriately: CoeffBound: 6.132263000000e+00, DegreeBound: 1.400000000000e+01 AMPSafetyDigits1: 2, AMPSafetyDigits2: 2, AMPMaxPrec: 2048 Tracking regeneration codim 1 of 4: 14 paths to track. Tracking path 0 of 14 Sorting codimension 1 of 4: 14 paths to sort. Sorting 0 of 14 Preparing regeneration codim 2 of 4: 98 witness points to move. Moving 0 of 98 Moving 20 of 98 Moving 40 of 98 Moving 60 of 98 Moving 80 of 98 Tracking regeneration codim 2 of 4: 112 paths to track. Tracking path 0 of 112 Tracking path 20 of 112 Tracking path 40 of 112 Tracking path 60 of 112 Tracking path 80 of 112 Tracking path 100 of 112 Sorting codimension 2 of 4: 112 paths to sort. Sorting 0 of 112 Sorting 20 of 112 Sorting 40 of 112 Sorting 60 of 112 Sorting 80 of 112 Sorting 100 of 112 Preparing regeneration codim 3 of 4: 552 witness points to move. Moving 0 of 552 Moving 20 of 552 Moving 40 of 552 Moving 60 of 552 Moving 80 of 552 Moving 100 of 552 Moving 120 of 552 Moving 140 of 552 Moving 160 of 552 Moving 180 of 552 Moving 200 of 552 Moving 220 of 552 Moving 240 of 552 Moving 260 of 552 Moving 280 of 552 Moving 300 of 552 Moving 320 of 552 Moving 340 of 552 Moving 360 of 552 Moving 380 of 552 Moving 400 of 552 Moving 420 of 552 Moving 440 of 552 Moving 460 of 552 Moving 480 of 552 Moving 500 of 552 Moving 520 of 552 Moving 540 of 552 Tracking regeneration codim 3 of 4: 644 paths to track. Tracking path 0 of 644 Tracking path 20 of 644 Tracking path 40 of 644 Tracking path 60 of 644 Tracking path 80 of 644 Tracking path 100 of 644 Tracking path 120 of 644 Tracking path 140 of 644 Tracking path 160 of 644 Tracking path 180 of 644 Tracking path 200 of 644 Tracking path 220 of 644 Tracking path 240 of 644 Tracking path 260 of 644 Tracking path 280 of 644 Tracking path 300 of 644 Tracking path 320 of 644 Tracking path 340 of 644 Tracking path 360 of 644 Tracking path 380 of 644 Tracking path 400 of 644 Tracking path 420 of 644 Tracking path 440 of 644 Tracking path 460 of 644 Tracking path 480 of 644 Tracking path 500 of 644 Tracking path 520 of 644 Tracking path 540 of 644 Tracking path 560 of 644 Tracking path 580 of 644 Tracking path 600 of 644 Tracking path 620 of 644 Tracking path 640 of 644 Sorting codimension 3 of 4: 644 paths to sort. Sorting 0 of 644 Sorting 20 of 644 Sorting 40 of 644 Sorting 60 of 644 Sorting 80 of 644 Sorting 100 of 644 Sorting 120 of 644 Sorting 140 of 644 Sorting 160 of 644 Sorting 180 of 644 Sorting 200 of 644 Sorting 220 of 644 Sorting 240 of 644 Sorting 260 of 644 Sorting 280 of 644 Sorting 300 of 644 Sorting 320 of 644 Sorting 340 of 644 Sorting 360 of 644 Sorting 380 of 644 Sorting 400 of 644 Sorting 420 of 644 Sorting 440 of 644 Sorting 460 of 644 Sorting 480 of 644 Sorting 500 of 644 Sorting 520 of 644 Sorting 540 of 644 Sorting 560 of 644 Sorting 580 of 644 Sorting 600 of 644 Sorting 620 of 644 Sorting 640 of 644 Preparing regeneration codim 4 of 4: 2016 witness points to move. Moving 0 of 2016 Moving 20 of 2016 Moving 40 of 2016 Moving 60 of 2016 Moving 80 of 2016 Moving 100 of 2016 Moving 120 of 2016 Moving 140 of 2016 Moving 160 of 2016 Moving 180 of 2016 Moving 200 of 2016 Moving 220 of 2016 Moving 240 of 2016 Moving 260 of 2016 Moving 280 of 2016 Moving 300 of 2016 Moving 320 of 2016 Moving 340 of 2016 Moving 360 of 2016 Moving 380 of 2016 Moving 400 of 2016 Moving 420 of 2016 Moving 440 of 2016 Moving 460 of 2016 Moving 480 of 2016 Moving 500 of 2016 Moving 520 of 2016 Moving 540 of 2016 Moving 560 of 2016 Moving 580 of 2016 Moving 600 of 2016 Moving 620 of 2016 Moving 640 of 2016 Moving 660 of 2016 Moving 680 of 2016 Moving 700 of 2016 Moving 720 of 2016 Moving 740 of 2016 Moving 760 of 2016 Moving 780 of 2016 Moving 800 of 2016 Moving 820 of 2016 Moving 840 of 2016 Moving 860 of 2016 Moving 880 of 2016 Moving 900 of 2016 Moving 920 of 2016 Moving 940 of 2016 Moving 960 of 2016 Moving 980 of 2016 Moving 1000 of 2016 Moving 1020 of 2016 Moving 1040 of 2016 Moving 1060 of 2016 Moving 1080 of 2016 Moving 1100 of 2016 Moving 1120 of 2016 Moving 1140 of 2016 Moving 1160 of 2016 Moving 1180 of 2016 Moving 1200 of 2016 Moving 1220 of 2016 Moving 1240 of 2016 Moving 1260 of 2016 Moving 1280 of 2016 Moving 1300 of 2016 Moving 1320 of 2016 Moving 1340 of 2016 Moving 1360 of 2016 Moving 1380 of 2016 Moving 1400 of 2016 Moving 1420 of 2016 Moving 1440 of 2016 Moving 1460 of 2016 Moving 1480 of 2016 Moving 1500 of 2016 Moving 1520 of 2016 Moving 1540 of 2016 Moving 1560 of 2016 Moving 1580 of 2016 Moving 1600 of 2016 Moving 1620 of 2016 Moving 1640 of 2016 Moving 1660 of 2016 Moving 1680 of 2016 Moving 1700 of 2016 Moving 1720 of 2016 Moving 1740 of 2016 Moving 1760 of 2016 Moving 1780 of 2016 Moving 1800 of 2016 Moving 1820 of 2016 Moving 1840 of 2016 Moving 1860 of 2016 Moving 1880 of 2016 Moving 1900 of 2016 Moving 1920 of 2016 Moving 1940 of 2016 Moving 1960 of 2016 Moving 1980 of 2016 Moving 2000 of 2016 Tracking regeneration codim 4 of 4: 2352 paths to track. Tracking path 0 of 2352 Tracking path 20 of 2352 Tracking path 40 of 2352 Tracking path 60 of 2352 Tracking path 80 of 2352 Tracking path 100 of 2352 Tracking path 120 of 2352 Tracking path 140 of 2352 Tracking path 160 of 2352 Tracking path 180 of 2352 Tracking path 200 of 2352 Tracking path 220 of 2352 Tracking path 240 of 2352 Tracking path 260 of 2352 Tracking path 280 of 2352 Tracking path 300 of 2352 Tracking path 320 of 2352 Tracking path 340 of 2352 Tracking path 360 of 2352 Tracking path 380 of 2352 Tracking path 400 of 2352 Tracking path 420 of 2352 Tracking path 440 of 2352 Tracking path 460 of 2352 Tracking path 480 of 2352 Tracking path 500 of 2352 Tracking path 520 of 2352 Tracking path 540 of 2352 Tracking path 560 of 2352 Tracking path 580 of 2352 Tracking path 600 of 2352 Tracking path 620 of 2352 Tracking path 640 of 2352 Tracking path 660 of 2352 Tracking path 680 of 2352 Tracking path 700 of 2352 Tracking path 720 of 2352 Tracking path 740 of 2352 Tracking path 760 of 2352 Tracking path 780 of 2352 Tracking path 800 of 2352 Tracking path 820 of 2352 Tracking path 840 of 2352 Tracking path 860 of 2352 Tracking path 880 of 2352 Tracking path 900 of 2352 Tracking path 920 of 2352 Tracking path 940 of 2352 Tracking path 960 of 2352 Tracking path 980 of 2352 Tracking path 1000 of 2352 Tracking path 1020 of 2352 Tracking path 1040 of 2352 Tracking path 1060 of 2352 Tracking path 1080 of 2352 Tracking path 1100 of 2352 Tracking path 1120 of 2352 Tracking path 1140 of 2352 Tracking path 1160 of 2352 Tracking path 1180 of 2352 Tracking path 1200 of 2352 Tracking path 1220 of 2352 Tracking path 1240 of 2352 Tracking path 1260 of 2352 Tracking path 1280 of 2352 Tracking path 1300 of 2352 Tracking path 1320 of 2352 Tracking path 1340 of 2352 Tracking path 1360 of 2352 Tracking path 1380 of 2352 Tracking path 1400 of 2352 Tracking path 1420 of 2352 Tracking path 1440 of 2352 Tracking path 1460 of 2352 Tracking path 1480 of 2352 Tracking path 1500 of 2352 Tracking path 1520 of 2352 Tracking path 1540 of 2352 Tracking path 1560 of 2352 Tracking path 1580 of 2352 Tracking path 1600 of 2352 Tracking path 1620 of 2352 Tracking path 1640 of 2352 Tracking path 1660 of 2352 Tracking path 1680 of 2352 Tracking path 1700 of 2352 Tracking path 1720 of 2352 Tracking path 1740 of 2352 Tracking path 1760 of 2352 Tracking path 1780 of 2352 Tracking path 1800 of 2352 Tracking path 1820 of 2352 Tracking path 1840 of 2352 Tracking path 1860 of 2352 Tracking path 1880 of 2352 Tracking path 1900 of 2352 Tracking path 1920 of 2352 Tracking path 1940 of 2352 Tracking path 1960 of 2352 Tracking path 1980 of 2352 Tracking path 2000 of 2352 Tracking path 2020 of 2352 Tracking path 2040 of 2352 Tracking path 2060 of 2352 Tracking path 2080 of 2352 Tracking path 2100 of 2352 Tracking path 2120 of 2352 Tracking path 2140 of 2352 Tracking path 2160 of 2352 Tracking path 2180 of 2352 Tracking path 2200 of 2352 Tracking path 2220 of 2352 Tracking path 2240 of 2352 Tracking path 2260 of 2352 Tracking path 2280 of 2352 Tracking path 2300 of 2352 Tracking path 2320 of 2352 Tracking path 2340 of 2352 Sorting codimension 4 of 4: 2352 paths to sort. Sorting 0 of 2352 Sorting 20 of 2352 Sorting 40 of 2352 Sorting 60 of 2352 Sorting 80 of 2352 Sorting 100 of 2352 Sorting 120 of 2352 Sorting 140 of 2352 Sorting 160 of 2352 Sorting 180 of 2352 Sorting 200 of 2352 Sorting 220 of 2352 Sorting 240 of 2352 Sorting 260 of 2352 Sorting 280 of 2352 Sorting 300 of 2352 Sorting 320 of 2352 Sorting 340 of 2352 Sorting 360 of 2352 Sorting 380 of 2352 Sorting 400 of 2352 Sorting 420 of 2352 Sorting 440 of 2352 Sorting 460 of 2352 Sorting 480 of 2352 Sorting 500 of 2352 Sorting 520 of 2352 Sorting 540 of 2352 Sorting 560 of 2352 Sorting 580 of 2352 Sorting 600 of 2352 Sorting 620 of 2352 Sorting 640 of 2352 Sorting 660 of 2352 Sorting 680 of 2352 Sorting 700 of 2352 Sorting 720 of 2352 Sorting 740 of 2352 Sorting 760 of 2352 Sorting 780 of 2352 Sorting 800 of 2352 Sorting 820 of 2352 Sorting 840 of 2352 Sorting 860 of 2352 Sorting 880 of 2352 Sorting 900 of 2352 Sorting 920 of 2352 Sorting 940 of 2352 Sorting 960 of 2352 Sorting 980 of 2352 Sorting 1000 of 2352 Sorting 1020 of 2352 Sorting 1040 of 2352 Sorting 1060 of 2352 Sorting 1080 of 2352 Sorting 1100 of 2352 Sorting 1120 of 2352 Sorting 1140 of 2352 Sorting 1160 of 2352 Sorting 1180 of 2352 Sorting 1200 of 2352 Sorting 1220 of 2352 Sorting 1240 of 2352 Sorting 1260 of 2352 Sorting 1280 of 2352 Sorting 1300 of 2352 Sorting 1320 of 2352 Sorting 1340 of 2352 Sorting 1360 of 2352 Sorting 1380 of 2352 Sorting 1400 of 2352 Sorting 1420 of 2352 Sorting 1440 of 2352 Sorting 1460 of 2352 Sorting 1480 of 2352 Sorting 1500 of 2352 Sorting 1520 of 2352 Sorting 1540 of 2352 Sorting 1560 of 2352 Sorting 1580 of 2352 Sorting 1600 of 2352 Sorting 1620 of 2352 Sorting 1640 of 2352 Sorting 1660 of 2352 Sorting 1680 of 2352 Sorting 1700 of 2352 Sorting 1720 of 2352 Sorting 1740 of 2352 Sorting 1760 of 2352 Sorting 1780 of 2352 Sorting 1800 of 2352 Sorting 1820 of 2352 Sorting 1840 of 2352 Sorting 1860 of 2352 Sorting 1880 of 2352 Sorting 1900 of 2352 Sorting 1920 of 2352 Sorting 1940 of 2352 Sorting 1960 of 2352 Sorting 1980 of 2352 Sorting 2000 of 2352 Sorting 2020 of 2352 Sorting 2040 of 2352 Sorting 2060 of 2352 Sorting 2080 of 2352 Sorting 2100 of 2352 Sorting 2120 of 2352 Sorting 2140 of 2352 Sorting 2160 of 2352 Sorting 2180 of 2352 Sorting 2200 of 2352 Sorting 2220 of 2352 Sorting 2240 of 2352 Sorting 2260 of 2352 Sorting 2280 of 2352 Sorting 2300 of 2352 Sorting 2320 of 2352 Sorting 2340 of 2352 ************ Regenerative Cascade Summary ************ NOTE: nonsingular vs singular is based on rank deficiency and identical endpoints |codim| paths |witness superset| nonsingular | singular |nonsolutions| inf endpoints | other bad endpoints ---------------------------------------------------------------------------------------------------------------- | 1 | 14 | 0 | 0 | 0 | 14 | 0 | 0 | 2 | 112 | 0 | 0 | 0 | 92 | 20 | 0 | 3 | 644 | 20 | 16 | 4 | 336 | 288 | 0 | 4 | 2352 | 938 | 760 | 178 | 0 | 1408 | 6 ---------------------------------------------------------------------------------------------------------------- |total| 3122 **************************************************** Removing junk points from codimension 4: 94 endpoints to check. Checking 0 of 94 Checking 20 of 94 Checking 40 of 94 Checking 60 of 94 Checking 80 of 94 *************** Witness Set Summary **************** NOTE: nonsingular vs singular is based on rank deficiency and identical endpoints |codim| witness points | nonsingular | singular ------------------------------------------------- | 3 | 18 | 16 | 2 | 4 | 775 | 760 | 15 ------------------------------------------------- **************************************************** Calculating traces for codimension 3. Calculating 0 of 18 Using monodromy to decompose codimension 3. Performing monodromy loops: 18 points left to classify Performing monodromy loops: 18 points left to classify Performing monodromy loops: 18 points left to classify Using combinatorial trace test to decompose codimension 3. Calculating traces for codimension 4. Calculating 0 of 775 Calculating 20 of 775 Calculating 40 of 775 Calculating 60 of 775 Calculating 80 of 775 Calculating 100 of 775 Calculating 120 of 775 Calculating 140 of 775 Calculating 160 of 775 Calculating 180 of 775 Calculating 200 of 775 Calculating 220 of 775 Calculating 240 of 775 Calculating 260 of 775 Calculating 280 of 775 Calculating 300 of 775 Calculating 320 of 775 Calculating 340 of 775 Calculating 360 of 775 Calculating 380 of 775 Calculating 400 of 775 Calculating 420 of 775 Calculating 440 of 775 Calculating 460 of 775 Calculating 480 of 775 Calculating 500 of 775 Calculating 520 of 775 Calculating 540 of 775 Calculating 560 of 775 Calculating 580 of 775 Calculating 600 of 775 Calculating 620 of 775 Calculating 640 of 775 Calculating 660 of 775 Calculating 680 of 775 Calculating 700 of 775 Calculating 720 of 775 Calculating 740 of 775 Calculating 760 of 775 Using monodromy to decompose codimension 4. Performing monodromy loops: 774 points left to classify Performing monodromy loops: 771 points left to classify Performing monodromy loops: 771 points left to classify Performing monodromy loops: 752 points left to classify Performing monodromy loops: 752 points left to classify Performing monodromy loops: 752 points left to classify Performing monodromy loops: 752 points left to classify Using combinatorial trace test to decompose codimension 4. ************* Witness Set Decomposition ************* | dimension | components | classified | unclassified ----------------------------------------------------- | 9 | 3 | 18 | 0 | 8 | 7 | 775 | 0 ----------------------------------------------------- ************** Decomposition by Degree ************** Dimension 9: 3 classified components ----------------------------------------------------- degree 2: 1 component degree 8: 2 components Dimension 8: 7 classified components ----------------------------------------------------- degree 1: 1 component degree 3: 2 components degree 8: 3 components degree 744: 1 component ***************************************************** Witness Points Deflated: 17