structureTensor -- Constructs the structureTensor of the ExteriorExtension

Description

The structure tensor of an algebra is the representative of the bilinear product as a hypermatrix. The matrices constructed by this can get very large, and take a long time to compute. The output can be very large, so we return a hashTable with only the non-zero values.

i1 : printWidth = 450;

i2 : ea = exteriorExtension(3, 6, QQ);

i3 : B = structureTensor ea

o3 = HashTable{(0, 5, 5) => 2    }
               (0, 6, 6) => 1
               (0, 7, 7) => 1
               (0, 8, 8) => 1
               (0, 9, 9) => 1
               (0, 10, 10) => -1
               (0, 11, 11) => -1
               (0, 12, 12) => -1
               (0, 13, 13) => -1
               (0, 20, 20) => -2
               (0, 21, 21) => -1
               (0, 22, 22) => -1
               (0, 23, 23) => -1
               (0, 24, 24) => -1
               (0, 25, 25) => 1
               (0, 26, 26) => 1
               (0, 27, 27) => 1
               (0, 28, 28) => 1
               (0, 39, 39) => 1
               (0, 40, 40) => 1
               (0, 41, 41) => 1
               (0, 42, 42) => 1
               (0, 43, 43) => 1
               (0, 44, 44) => 1
               (0, 45, 45) => -1
               (0, 46, 46) => -1
               (0, 47, 47) => -1
               (0, 48, 48) => -1
               (0, 49, 49) => -1
               (0, 50, 50) => -1
               (1, 5, 5) => -1
               (1, 6, 6) => 1
               (1, 10, 10) => 2
               (1, 11, 11) => 1
               (1, 12, 12) => 1
               (1, 13, 13) => 1
               (1, 14, 14) => -1
               (1, 15, 15) => -1
               (1, 16, 16) => -1
               (1, 20, 20) => 1
               (1, 21, 21) => -1
               (1, 25, 25) => -2
               (1, 26, 26) => -1
               (1, 27, 27) => -1
               (1, 28, 28) => -1
               (1, 29, 29) => 1
               (1, 30, 30) => 1
               (1, 31, 31) => 1
               (1, 36, 36) => 1
               (1, 37, 37) => 1
               (1, 38, 38) => 1
               (1, 39, 39) => -1
               (1, 40, 40) => -1
               (1, 41, 41) => -1
               (1, 48, 48) => 1
               (1, 49, 49) => 1
               (1, 50, 50) => 1
               (1, 51, 51) => -1
               (1, 52, 52) => -1
               (1, 53, 53) => -1
               (2, 6, 6) => -1
               (2, 7, 7) => 1
               (2, 10, 10) => -1
               (2, 11, 11) => 1
               (2, 14, 14) => 2
               (2, 15, 15) => 1
               (2, 16, 16) => 1
               (2, 17, 17) => -1
               (2, 18, 18) => -1
               (2, 21, 21) => 1
               (2, 22, 22) => -1
               (2, 25, 25) => 1
               (2, 26, 26) => -1
               (2, 29, 29) => -2
               (2, 30, 30) => -1
               (2, 31, 31) => -1
               (2, 32, 32) => 1
               (2, 33, 33) => 1
               (2, 35, 35) => 1
               (2, 36, 36) => -1
               (2, 40, 40) => 1
               (2, 41, 41) => 1
               (2, 42, 42) => -1
               (2, 43, 43) => -1
               (2, 46, 46) => 1
               (2, 47, 47) => 1
               (2, 48, 48) => -1
               (2, 49, 49) => -1
               (2, 53, 53) => 1
               (2, 54, 54) => -1
               (3, 7, 7) => -1
               (3, 8, 8) => 1
               (3, 11, 11) => -1
               (3, 12, 12) => 1
               (3, 14, 14) => -1
               (3, 15, 15) => 1
               (3, 17, 17) => 2
               (3, 18, 18) => 1
               (3, 19, 19) => -1
               (3, 22, 22) => 1
               (3, 23, 23) => -1
               (3, 26, 26) => 1
               (3, 27, 27) => -1
               (3, 29, 29) => 1
               (3, 30, 30) => -1
               (3, 32, 32) => -2
               (3, 33, 33) => -1
               (3, 34, 34) => 1
               (3, 36, 36) => 1
               (3, 37, 37) => -1
               (3, 39, 39) => 1
               (3, 40, 40) => -1
               (3, 43, 43) => 1
               (3, 44, 44) => -1
               (3, 45, 45) => 1
               (3, 46, 46) => -1
               (3, 49, 49) => 1
               (3, 50, 50) => -1
               (3, 52, 52) => 1
               (3, 53, 53) => -1
               (4, 8, 8) => -1
               (4, 9, 9) => 1
               (4, 12, 12) => -1
               (4, 13, 13) => 1
               (4, 15, 15) => -1
               (4, 16, 16) => 1
               (4, 17, 17) => -1
               (4, 18, 18) => 1
               (4, 19, 19) => 2
               (4, 23, 23) => 1
               (4, 24, 24) => -1
               (4, 27, 27) => 1
               (4, 28, 28) => -1
               (4, 30, 30) => 1
               (4, 31, 31) => -1
               (4, 32, 32) => 1
               (4, 33, 33) => -1
               (4, 34, 34) => -2
               (4, 37, 37) => 1
               (4, 38, 38) => -1
               (4, 40, 40) => 1
               (4, 41, 41) => -1
               (4, 42, 42) => 1
               (4, 43, 43) => -1
               (4, 46, 46) => 1
               (4, 47, 47) => -1
               (4, 48, 48) => 1
               (4, 49, 49) => -1
               (4, 51, 51) => 1
               (4, 52, 52) => -1
               (5, 0, 20) => 1
               (5, 5, 0) => -2
               (5, 5, 1) => 1
               (5, 6, 10) => 1
               (5, 7, 11) => 1
               (5, 8, 12) => 1
               (5, 9, 13) => 1
               (5, 25, 21) => -1
               (5, 26, 22) => -1
               (5, 27, 23) => -1
               (5, 28, 24) => -1
               (5, 39, 45) => 1
               (5, 40, 46) => 1
               (5, 41, 47) => 1
               (5, 42, 48) => 1
               (5, 43, 49) => 1
               (5, 44, 50) => 1
               (6, 0, 21) => 1
               (6, 1, 21) => 1
               (6, 5, 25) => 1
               (6, 6, 0) => -1
               (6, 6, 1) => -1
               (6, 6, 2) => 1
               (6, 7, 14) => 1
               (6, 8, 15) => 1
               (6, 9, 16) => 1
               (6, 10, 20) => -1
               (6, 29, 22) => -1
               (6, 30, 23) => -1
               (6, 31, 24) => -1
               (6, 36, 45) => -1
               (6, 37, 46) => -1
               (6, 38, 47) => -1
               (6, 42, 51) => 1
               (6, 43, 52) => 1
               (6, 44, 53) => 1
               (7, 0, 22) => 1
               (7, 1, 22) => 1
               (7, 2, 22) => 1
               (7, 5, 26) => 1
               (7, 6, 29) => 1
               (7, 7, 0) => -1
               (7, 7, 2) => -1
               (7, 7, 3) => 1
               (7, 8, 17) => 1
               (7, 9, 18) => 1
               (7, 11, 20) => -1
               (7, 14, 21) => -1
               (7, 32, 23) => -1
               (7, 33, 24) => -1
               (7, 35, 45) => 1
               (7, 37, 48) => -1
               (7, 38, 49) => -1
               (7, 40, 51) => -1
               (7, 41, 52) => -1
               (7, 44, 54) => 1
               (8, 0, 23) => 1
               (8, 1, 23) => 1
               (8, 2, 23) => 1
               (8, 3, 23) => 1
               (8, 5, 27) => 1
               (8, 6, 30) => 1
               (8, 7, 32) => 1
               (8, 8, 0) => -1
               (8, 8, 3) => -1
               (8, 8, 4) => 1
               (8, 9, 19) => 1
               (8, 12, 20) => -1
               (8, 15, 21) => -1
               (8, 17, 22) => -1
               (8, 34, 24) => -1
               (8, 35, 46) => 1
               (8, 36, 48) => 1
               (8, 38, 50) => -1
               (8, 39, 51) => 1
               (8, 41, 53) => -1
               (8, 43, 54) => -1
               (9, 0, 24) => 1
               (9, 1, 24) => 1
               (9, 2, 24) => 1
               (9, 3, 24) => 1
               (9, 4, 24) => 1
               (9, 5, 28) => 1
               (9, 6, 31) => 1
               (9, 7, 33) => 1
               (9, 8, 34) => 1
               (9, 9, 0) => -1
               (9, 9, 4) => -1
               (9, 13, 20) => -1
               (9, 16, 21) => -1
               (9, 18, 22) => -1
               (9, 19, 23) => -1
               (9, 35, 47) => 1
               (9, 36, 49) => 1
               (9, 37, 50) => 1
               (9, 39, 52) => 1
               (9, 40, 53) => 1
               (9, 42, 54) => 1
               (10, 1, 25) => 1
               (10, 6, 5) => -1
               (10, 10, 0) => 1
               (10, 10, 1) => -2
               (10, 10, 2) => 1
               (10, 11, 14) => 1
               (10, 12, 15) => 1
               (10, 13, 16) => 1
               (10, 20, 21) => 1
               (10, 29, 26) => -1
               (10, 30, 27) => -1
               (10, 31, 28) => -1
               (10, 36, 39) => 1
               (10, 37, 40) => 1
               (10, 38, 41) => 1
               (10, 48, 51) => 1
               (10, 49, 52) => 1
               (10, 50, 53) => 1
               (11, 1, 26) => 1
               (11, 2, 26) => 1
               (11, 7, 5) => -1
               (11, 10, 29) => 1
               (11, 11, 0) => 1
               (11, 11, 1) => -1
               (11, 11, 2) => -1
               (11, 11, 3) => 1
               (11, 12, 17) => 1
               (11, 13, 18) => 1
               (11, 14, 25) => -1
               (11, 20, 22) => 1
               (11, 32, 27) => -1
               (11, 33, 28) => -1
               (11, 35, 39) => -1
               (11, 37, 42) => 1
               (11, 38, 43) => 1
               (11, 46, 51) => -1
               (11, 47, 52) => -1
               (11, 50, 54) => 1
               (12, 1, 27) => 1
               (12, 2, 27) => 1
               (12, 3, 27) => 1
               (12, 8, 5) => -1
               (12, 10, 30) => 1
               (12, 11, 32) => 1
               (12, 12, 0) => 1
               (12, 12, 1) => -1
               (12, 12, 3) => -1
               (12, 12, 4) => 1
               (12, 13, 19) => 1
               (12, 15, 25) => -1
               (12, 17, 26) => -1
               (12, 20, 23) => 1
               (12, 34, 28) => -1
               (12, 35, 40) => -1
               (12, 36, 42) => -1
               (12, 38, 44) => 1
               (12, 45, 51) => 1
               (12, 47, 53) => -1
               (12, 49, 54) => -1
               (13, 1, 28) => 1
               (13, 2, 28) => 1
               (13, 3, 28) => 1
               (13, 4, 28) => 1
               (13, 9, 5) => -1
               (13, 10, 31) => 1
               (13, 11, 33) => 1
               (13, 12, 34) => 1
               (13, 13, 0) => 1
               (13, 13, 1) => -1
               (13, 13, 4) => -1
               (13, 16, 25) => -1
               (13, 18, 26) => -1
               (13, 19, 27) => -1
               (13, 20, 24) => 1
               (13, 35, 41) => -1
               (13, 36, 43) => -1
               (13, 37, 44) => -1
               (13, 45, 52) => 1
               (13, 46, 53) => 1
               (13, 48, 54) => 1
               (14, 2, 29) => 1
               (14, 7, 6) => -1
               (14, 11, 10) => -1
               (14, 14, 1) => 1
               (14, 14, 2) => -2
               (14, 14, 3) => 1
               (14, 15, 17) => 1
               (14, 16, 18) => 1
               (14, 21, 22) => 1
               (14, 25, 26) => 1
               (14, 32, 30) => -1
               (14, 33, 31) => -1
               (14, 35, 36) => 1
               (14, 40, 42) => 1
               (14, 41, 43) => 1
               (14, 46, 48) => 1
               (14, 47, 49) => 1
               (14, 53, 54) => 1
               (15, 2, 30) => 1
               (15, 3, 30) => 1
               (15, 8, 6) => -1
               (15, 12, 10) => -1
               (15, 14, 32) => 1
               (15, 15, 1) => 1
               (15, 15, 2) => -1
               (15, 15, 3) => -1
               (15, 15, 4) => 1
               (15, 16, 19) => 1
               (15, 17, 29) => -1
               (15, 21, 23) => 1
               (15, 25, 27) => 1
               (15, 34, 31) => -1
               (15, 35, 37) => 1
               (15, 39, 42) => -1
               (15, 41, 44) => 1
               (15, 45, 48) => -1
               (15, 47, 50) => 1
               (15, 52, 54) => -1
               (16, 2, 31) => 1
               (16, 3, 31) => 1
               (16, 4, 31) => 1
               (16, 9, 6) => -1
               (16, 13, 10) => -1
               (16, 14, 33) => 1
               (16, 15, 34) => 1
               (16, 16, 1) => 1
               (16, 16, 2) => -1
               (16, 16, 4) => -1
               (16, 18, 29) => -1
               (16, 19, 30) => -1
               (16, 21, 24) => 1
               (16, 25, 28) => 1
               (16, 35, 38) => 1
               (16, 39, 43) => -1
               (16, 40, 44) => -1
               (16, 45, 49) => -1
               (16, 46, 50) => -1
               (16, 51, 54) => 1
               (17, 3, 32) => 1
               (17, 8, 7) => -1
               (17, 12, 11) => -1
               (17, 15, 14) => -1
               (17, 17, 2) => 1
               (17, 17, 3) => -2
               (17, 17, 4) => 1
               (17, 18, 19) => 1
               (17, 22, 23) => 1
               (17, 26, 27) => 1
               (17, 29, 30) => 1
               (17, 34, 33) => -1
               (17, 36, 37) => 1
               (17, 39, 40) => 1
               (17, 43, 44) => 1
               (17, 45, 46) => 1
               (17, 49, 50) => 1
               (17, 52, 53) => 1
               (18, 3, 33) => 1
               (18, 4, 33) => 1
               (18, 9, 7) => -1
               (18, 13, 11) => -1
               (18, 16, 14) => -1
               (18, 17, 34) => 1
               (18, 18, 2) => 1
               (18, 18, 3) => -1
               (18, 18, 4) => -1
               (18, 19, 32) => -1
               (18, 22, 24) => 1
               (18, 26, 28) => 1
               (18, 29, 31) => 1
               (18, 36, 38) => 1
               (18, 39, 41) => 1
               (18, 42, 44) => -1
               (18, 45, 47) => 1
               (18, 48, 50) => -1
               (18, 51, 53) => -1
               (19, 4, 34) => 1
               (19, 9, 8) => -1
               (19, 13, 12) => -1
               (19, 16, 15) => -1
               (19, 18, 17) => -1
               (19, 19, 3) => 1
               (19, 19, 4) => -2
               (19, 23, 24) => 1
               (19, 27, 28) => 1
               (19, 30, 31) => 1
               (19, 32, 33) => 1
               (19, 37, 38) => 1
               (19, 40, 41) => 1
               (19, 42, 43) => 1
               (19, 46, 47) => 1
               (19, 48, 49) => 1
               (19, 51, 52) => 1
               (20, 0, 5) => -1
               (20, 10, 6) => 1
               (20, 11, 7) => 1
               (20, 12, 8) => 1
               (20, 13, 9) => 1
               (20, 20, 0) => 2
               (20, 20, 1) => -1
               (20, 21, 25) => -1
               (20, 22, 26) => -1
               (20, 23, 27) => -1
               (20, 24, 28) => -1
               (20, 45, 39) => 1
               (20, 46, 40) => 1
               (20, 47, 41) => 1
               (20, 48, 42) => 1
               (20, 49, 43) => 1
               (20, 50, 44) => 1
               (21, 0, 6) => -1
               (21, 1, 6) => -1
               (21, 14, 7) => 1
               (21, 15, 8) => 1
               (21, 16, 9) => 1
               (21, 20, 10) => -1
               (21, 21, 0) => 1
               (21, 21, 1) => 1
               (21, 21, 2) => -1
               (21, 22, 29) => -1
               (21, 23, 30) => -1
               (21, 24, 31) => -1
               (21, 25, 5) => 1
               (21, 45, 36) => -1
               (21, 46, 37) => -1
               (21, 47, 38) => -1
               (21, 51, 42) => 1
               (21, 52, 43) => 1
               (21, 53, 44) => 1
               (22, 0, 7) => -1
               (22, 1, 7) => -1
               (22, 2, 7) => -1
               (22, 17, 8) => 1
               (22, 18, 9) => 1
               (22, 20, 11) => -1
               (22, 21, 14) => -1
               (22, 22, 0) => 1
               (22, 22, 2) => 1
               (22, 22, 3) => -1
               (22, 23, 32) => -1
               (22, 24, 33) => -1
               (22, 26, 5) => 1
               (22, 29, 6) => 1
               (22, 45, 35) => 1
               (22, 48, 37) => -1
               (22, 49, 38) => -1
               (22, 51, 40) => -1
               (22, 52, 41) => -1
               (22, 54, 44) => 1
               (23, 0, 8) => -1
               (23, 1, 8) => -1
               (23, 2, 8) => -1
               (23, 3, 8) => -1
               (23, 19, 9) => 1
               (23, 20, 12) => -1
               (23, 21, 15) => -1
               (23, 22, 17) => -1
               (23, 23, 0) => 1
               (23, 23, 3) => 1
               (23, 23, 4) => -1
               (23, 24, 34) => -1
               (23, 27, 5) => 1
               (23, 30, 6) => 1
               (23, 32, 7) => 1
               (23, 46, 35) => 1
               (23, 48, 36) => 1
               (23, 50, 38) => -1
               (23, 51, 39) => 1
               (23, 53, 41) => -1
               (23, 54, 43) => -1
               (24, 0, 9) => -1
               (24, 1, 9) => -1
               (24, 2, 9) => -1
               (24, 3, 9) => -1
               (24, 4, 9) => -1
               (24, 20, 13) => -1
               (24, 21, 16) => -1
               (24, 22, 18) => -1
               (24, 23, 19) => -1
               (24, 24, 0) => 1
               (24, 24, 4) => 1
               (24, 28, 5) => 1
               (24, 31, 6) => 1
               (24, 33, 7) => 1
               (24, 34, 8) => 1
               (24, 47, 35) => 1
               (24, 49, 36) => 1
               (24, 50, 37) => 1
               (24, 52, 39) => 1
               (24, 53, 40) => 1
               (24, 54, 42) => 1
               (25, 1, 10) => -1
               (25, 5, 6) => -1
               (25, 14, 11) => 1
               (25, 15, 12) => 1
               (25, 16, 13) => 1
               (25, 21, 20) => 1
               (25, 25, 0) => -1
               (25, 25, 1) => 2
               (25, 25, 2) => -1
               (25, 26, 29) => -1
               (25, 27, 30) => -1
               (25, 28, 31) => -1
               (25, 39, 36) => 1
               (25, 40, 37) => 1
               (25, 41, 38) => 1
               (25, 51, 48) => 1
               (25, 52, 49) => 1
               (25, 53, 50) => 1
               (26, 1, 11) => -1
               (26, 2, 11) => -1
               (26, 5, 7) => -1
               (26, 17, 12) => 1
               (26, 18, 13) => 1
               (26, 22, 20) => 1
               (26, 25, 14) => -1
               (26, 26, 0) => -1
               (26, 26, 1) => 1
               (26, 26, 2) => 1
               (26, 26, 3) => -1
               (26, 27, 32) => -1
               (26, 28, 33) => -1
               (26, 29, 10) => 1
               (26, 39, 35) => -1
               (26, 42, 37) => 1
               (26, 43, 38) => 1
               (26, 51, 46) => -1
               (26, 52, 47) => -1
               (26, 54, 50) => 1
               (27, 1, 12) => -1
               (27, 2, 12) => -1
               (27, 3, 12) => -1
               (27, 5, 8) => -1
               (27, 19, 13) => 1
               (27, 23, 20) => 1
               (27, 25, 15) => -1
               (27, 26, 17) => -1
               (27, 27, 0) => -1
               (27, 27, 1) => 1
               (27, 27, 3) => 1
               (27, 27, 4) => -1
               (27, 28, 34) => -1
               (27, 30, 10) => 1
               (27, 32, 11) => 1
               (27, 40, 35) => -1
               (27, 42, 36) => -1
               (27, 44, 38) => 1
               (27, 51, 45) => 1
               (27, 53, 47) => -1
               (27, 54, 49) => -1
               (28, 1, 13) => -1
               (28, 2, 13) => -1
               (28, 3, 13) => -1
               (28, 4, 13) => -1
               (28, 5, 9) => -1
               (28, 24, 20) => 1
               (28, 25, 16) => -1
               (28, 26, 18) => -1
               (28, 27, 19) => -1
               (28, 28, 0) => -1
               (28, 28, 1) => 1
               (28, 28, 4) => 1
               (28, 31, 10) => 1
               (28, 33, 11) => 1
               (28, 34, 12) => 1
               (28, 41, 35) => -1
               (28, 43, 36) => -1
               (28, 44, 37) => -1
               (28, 52, 45) => 1
               (28, 53, 46) => 1
               (28, 54, 48) => 1
               (29, 2, 14) => -1
               (29, 6, 7) => -1
               (29, 10, 11) => -1
               (29, 17, 15) => 1
               (29, 18, 16) => 1
               (29, 22, 21) => 1
               (29, 26, 25) => 1
               (29, 29, 1) => -1
               (29, 29, 2) => 2
               (29, 29, 3) => -1
               (29, 30, 32) => -1
               (29, 31, 33) => -1
               (29, 36, 35) => 1
               (29, 42, 40) => 1
               (29, 43, 41) => 1
               (29, 48, 46) => 1
               (29, 49, 47) => 1
               (29, 54, 53) => 1
               (30, 2, 15) => -1
               (30, 3, 15) => -1
               (30, 6, 8) => -1
               (30, 10, 12) => -1
               (30, 19, 16) => 1
               (30, 23, 21) => 1
               (30, 27, 25) => 1
               (30, 29, 17) => -1
               (30, 30, 1) => -1
               (30, 30, 2) => 1
               (30, 30, 3) => 1
               (30, 30, 4) => -1
               (30, 31, 34) => -1
               (30, 32, 14) => 1
               (30, 37, 35) => 1
               (30, 42, 39) => -1
               (30, 44, 41) => 1
               (30, 48, 45) => -1
               (30, 50, 47) => 1
               (30, 54, 52) => -1
               (31, 2, 16) => -1
               (31, 3, 16) => -1
               (31, 4, 16) => -1
               (31, 6, 9) => -1
               (31, 10, 13) => -1
               (31, 24, 21) => 1
               (31, 28, 25) => 1
               (31, 29, 18) => -1
               (31, 30, 19) => -1
               (31, 31, 1) => -1
               (31, 31, 2) => 1
               (31, 31, 4) => 1
               (31, 33, 14) => 1
               (31, 34, 15) => 1
               (31, 38, 35) => 1
               (31, 43, 39) => -1
               (31, 44, 40) => -1
               (31, 49, 45) => -1
               (31, 50, 46) => -1
               (31, 54, 51) => 1
               (32, 3, 17) => -1
               (32, 7, 8) => -1
               (32, 11, 12) => -1
               (32, 14, 15) => -1
               (32, 19, 18) => 1
               (32, 23, 22) => 1
               (32, 27, 26) => 1
               (32, 30, 29) => 1
               (32, 32, 2) => -1
               (32, 32, 3) => 2
               (32, 32, 4) => -1
               (32, 33, 34) => -1
               (32, 37, 36) => 1
               (32, 40, 39) => 1
               (32, 44, 43) => 1
               (32, 46, 45) => 1
               (32, 50, 49) => 1
               (32, 53, 52) => 1
               (33, 3, 18) => -1
               (33, 4, 18) => -1
               (33, 7, 9) => -1
               (33, 11, 13) => -1
               (33, 14, 16) => -1
               (33, 24, 22) => 1
               (33, 28, 26) => 1
               (33, 31, 29) => 1
               (33, 32, 19) => -1
               (33, 33, 2) => -1
               (33, 33, 3) => 1
               (33, 33, 4) => 1
               (33, 34, 17) => 1
               (33, 38, 36) => 1
               (33, 41, 39) => 1
               (33, 44, 42) => -1
               (33, 47, 45) => 1
               (33, 50, 48) => -1
               (33, 53, 51) => -1
               (34, 4, 19) => -1
               (34, 8, 9) => -1
               (34, 12, 13) => -1
               (34, 15, 16) => -1
               (34, 17, 18) => -1
               (34, 24, 23) => 1
               (34, 28, 27) => 1
               (34, 31, 30) => 1
               (34, 33, 32) => 1
               (34, 34, 3) => -1
               (34, 34, 4) => 2
               (34, 38, 37) => 1
               (34, 41, 40) => 1
               (34, 43, 42) => 1
               (34, 47, 46) => 1
               (34, 49, 48) => 1
               (34, 52, 51) => 1
                              1
               (35, 0, 54) => -
                              2
               (35, 1, 54) => 1
                              3
               (35, 2, 54) => -
                              2
               (35, 3, 54) => 1
                              1
               (35, 4, 54) => -
                              2
               (35, 7, 44) => -1
               (35, 8, 43) => 1
               (35, 9, 42) => -1
               (35, 11, 50) => -1
               (35, 12, 49) => 1
               (35, 13, 48) => -1
               (35, 14, 53) => -1
               (35, 15, 52) => 1
               (35, 16, 51) => -1
               (35, 35, 2) => -1
               (35, 36, 29) => -1
               (35, 37, 30) => -1
               (35, 38, 31) => -1
               (35, 39, 26) => 1
               (35, 40, 27) => 1
               (35, 41, 28) => 1
               (35, 45, 22) => -1
               (35, 46, 23) => -1
               (35, 47, 24) => -1
                                1
               (36, 0, 53) => - -
                                2
               (36, 1, 53) => -1
                                1
               (36, 2, 53) => - -
                                2
               (36, 3, 53) => -1
                                1
               (36, 4, 53) => - -
                                2
               (36, 6, 44) => 1
               (36, 8, 41) => -1
               (36, 9, 40) => 1
               (36, 10, 50) => 1
               (36, 12, 47) => -1
               (36, 13, 46) => 1
               (36, 17, 52) => 1
               (36, 18, 51) => -1
               (36, 29, 54) => 1
               (36, 35, 14) => -1
               (36, 36, 1) => -1
               (36, 36, 2) => 1
               (36, 36, 3) => -1
               (36, 37, 32) => -1
               (36, 38, 33) => -1
               (36, 39, 25) => -1
               (36, 42, 27) => 1
               (36, 43, 28) => 1
               (36, 45, 21) => 1
               (36, 48, 23) => -1
               (36, 49, 24) => -1
                              1
               (37, 0, 52) => -
                              2
               (37, 1, 52) => 1
                              1
               (37, 2, 52) => -
                              2
                              1
               (37, 4, 52) => -
                              2
               (37, 6, 43) => -1
               (37, 7, 41) => 1
               (37, 9, 39) => -1
               (37, 10, 49) => -1
               (37, 11, 47) => 1
               (37, 13, 45) => -1
               (37, 19, 51) => -1
               (37, 30, 54) => 1
               (37, 32, 53) => -1
               (37, 35, 15) => -1
               (37, 36, 17) => -1
               (37, 37, 1) => -1
               (37, 37, 3) => 1
               (37, 37, 4) => -1
               (37, 38, 34) => -1
               (37, 40, 25) => -1
               (37, 42, 26) => -1
               (37, 44, 28) => 1
               (37, 46, 21) => 1
               (37, 48, 22) => 1
               (37, 50, 24) => -1
                                1
               (38, 0, 51) => - -
                                2
               (38, 1, 51) => -1
                                1
               (38, 2, 51) => - -
                                2
                              1
               (38, 4, 51) => -
                              2
               (38, 6, 42) => 1
               (38, 7, 40) => -1
               (38, 8, 39) => 1
               (38, 10, 48) => 1
               (38, 11, 46) => -1
               (38, 12, 45) => 1
               (38, 31, 54) => 1
               (38, 33, 53) => -1
               (38, 34, 52) => 1
               (38, 35, 16) => -1
               (38, 36, 18) => -1
               (38, 37, 19) => -1
               (38, 38, 1) => -1
               (38, 38, 4) => 1
               (38, 41, 25) => -1
               (38, 43, 26) => -1
               (38, 44, 27) => -1
               (38, 47, 21) => 1
               (38, 49, 22) => 1
               (38, 50, 23) => 1
                              1
               (39, 0, 50) => -
                              2
                              1
               (39, 2, 50) => -
                              2
               (39, 3, 50) => 1
                              1
               (39, 4, 50) => -
                              2
               (39, 5, 44) => -1
               (39, 8, 38) => 1
               (39, 9, 37) => -1
               (39, 15, 47) => -1
               (39, 16, 46) => 1
               (39, 17, 49) => -1
               (39, 18, 48) => 1
               (39, 25, 53) => -1
               (39, 26, 54) => -1
               (39, 35, 11) => 1
               (39, 36, 10) => -1
               (39, 39, 0) => -1
               (39, 39, 1) => 1
               (39, 39, 3) => -1
               (39, 40, 32) => -1
               (39, 41, 33) => -1
               (39, 42, 30) => 1
               (39, 43, 31) => 1
               (39, 45, 20) => -1
               (39, 51, 23) => -1
               (39, 52, 24) => -1
                                1
               (40, 0, 49) => - -
                                2
                                1
               (40, 2, 49) => - -
                                2
                                1
               (40, 4, 49) => - -
                                2
               (40, 5, 43) => 1
               (40, 7, 38) => -1
               (40, 9, 36) => 1
               (40, 14, 47) => 1
               (40, 16, 45) => -1
               (40, 19, 48) => 1
               (40, 25, 52) => 1
               (40, 27, 54) => -1
               (40, 32, 50) => 1
               (40, 35, 12) => 1
               (40, 37, 10) => -1
               (40, 39, 17) => -1
               (40, 40, 0) => -1
               (40, 40, 1) => 1
               (40, 40, 2) => -1
               (40, 40, 3) => 1
               (40, 40, 4) => -1
               (40, 41, 34) => -1
               (40, 42, 29) => -1
               (40, 44, 31) => 1
               (40, 46, 20) => -1
               (40, 51, 22) => 1
               (40, 53, 24) => -1
                              1
               (41, 0, 48) => -
                              2
                              1
               (41, 2, 48) => -
                              2
                                1
               (41, 4, 48) => - -
                                2
               (41, 5, 42) => -1
               (41, 7, 37) => 1
               (41, 8, 36) => -1
               (41, 14, 46) => -1
               (41, 15, 45) => 1
               (41, 25, 51) => -1
               (41, 28, 54) => -1
               (41, 33, 50) => 1
               (41, 34, 49) => -1
               (41, 35, 13) => 1
               (41, 38, 10) => -1
               (41, 39, 18) => -1
               (41, 40, 19) => -1
               (41, 41, 0) => -1
               (41, 41, 1) => 1
               (41, 41, 2) => -1
               (41, 41, 4) => 1
               (41, 43, 29) => -1
               (41, 44, 30) => -1
               (41, 47, 20) => -1
               (41, 52, 22) => 1
               (41, 53, 23) => 1
                              1
               (42, 0, 47) => -
                              2
                                1
               (42, 2, 47) => - -
                                2
                              1
               (42, 4, 47) => -
                              2
               (42, 5, 41) => -1
               (42, 6, 38) => 1
               (42, 9, 35) => -1
               (42, 18, 45) => -1
               (42, 19, 46) => -1
               (42, 26, 52) => 1
               (42, 27, 53) => 1
               (42, 29, 49) => -1
               (42, 30, 50) => -1
               (42, 36, 12) => 1
               (42, 37, 11) => -1
               (42, 39, 15) => 1
               (42, 40, 14) => -1
               (42, 42, 0) => -1
               (42, 42, 2) => 1
               (42, 42, 4) => -1
               (42, 43, 34) => -1
               (42, 44, 33) => 1
               (42, 48, 20) => -1
               (42, 51, 21) => -1
               (42, 54, 24) => -1
                                1
               (43, 0, 46) => - -
                                2
                              1
               (43, 2, 46) => -
                              2
                              1
               (43, 4, 46) => -
                              2
               (43, 5, 40) => 1
               (43, 6, 37) => -1
               (43, 8, 35) => 1
               (43, 17, 45) => 1
               (43, 26, 51) => -1
               (43, 28, 53) => 1
               (43, 29, 48) => 1
               (43, 31, 50) => -1
               (43, 34, 47) => 1
               (43, 36, 13) => 1
               (43, 38, 11) => -1
               (43, 39, 16) => 1
               (43, 41, 14) => -1
               (43, 42, 19) => -1
               (43, 43, 0) => -1
               (43, 43, 2) => 1
               (43, 43, 3) => -1
               (43, 43, 4) => 1
               (43, 44, 32) => -1
               (43, 49, 20) => -1
               (43, 52, 21) => -1
               (43, 54, 23) => 1
                              1
               (44, 0, 45) => -
                              2
                                1
               (44, 2, 45) => - -
                                2
               (44, 3, 45) => -1
                                1
               (44, 4, 45) => - -
                                2
               (44, 5, 39) => -1
               (44, 6, 36) => 1
               (44, 7, 35) => -1
               (44, 27, 51) => -1
               (44, 28, 52) => -1
               (44, 30, 48) => 1
               (44, 31, 49) => 1
               (44, 32, 46) => -1
               (44, 33, 47) => -1
               (44, 37, 13) => 1
               (44, 38, 12) => -1
               (44, 40, 16) => 1
               (44, 41, 15) => -1
               (44, 42, 18) => 1
               (44, 43, 17) => -1
               (44, 44, 0) => -1
               (44, 44, 3) => 1
               (44, 50, 20) => -1
               (44, 53, 21) => -1
               (44, 54, 22) => -1
                              1
               (45, 0, 44) => -
                              2
                                1
               (45, 2, 44) => - -
                                2
               (45, 3, 44) => -1
                                1
               (45, 4, 44) => - -
                                2
               (45, 12, 38) => 1
               (45, 13, 37) => -1
               (45, 15, 41) => 1
               (45, 16, 40) => -1
               (45, 17, 43) => 1
               (45, 18, 42) => -1
               (45, 20, 50) => 1
               (45, 21, 53) => 1
               (45, 22, 54) => 1
               (45, 35, 7) => -1
               (45, 36, 6) => 1
               (45, 39, 5) => -1
               (45, 45, 0) => 1
               (45, 45, 3) => -1
               (45, 46, 32) => -1
               (45, 47, 33) => -1
               (45, 48, 30) => 1
               (45, 49, 31) => 1
               (45, 51, 27) => -1
               (45, 52, 28) => -1
                                1
               (46, 0, 43) => - -
                                2
                              1
               (46, 2, 43) => -
                              2
                              1
               (46, 4, 43) => -
                              2
               (46, 11, 38) => -1
               (46, 13, 36) => 1
               (46, 14, 41) => -1
               (46, 16, 39) => 1
               (46, 19, 42) => -1
               (46, 20, 49) => -1
               (46, 21, 52) => -1
               (46, 23, 54) => 1
               (46, 32, 44) => -1
               (46, 35, 8) => -1
               (46, 37, 6) => 1
               (46, 40, 5) => -1
               (46, 45, 17) => -1
               (46, 46, 0) => 1
               (46, 46, 2) => -1
               (46, 46, 3) => 1
               (46, 46, 4) => -1
               (46, 47, 34) => -1
               (46, 48, 29) => -1
               (46, 50, 31) => 1
               (46, 51, 26) => 1
               (46, 53, 28) => -1
                              1
               (47, 0, 42) => -
                              2
                                1
               (47, 2, 42) => - -
                                2
                              1
               (47, 4, 42) => -
                              2
               (47, 11, 37) => 1
               (47, 12, 36) => -1
               (47, 14, 40) => 1
               (47, 15, 39) => -1
               (47, 20, 48) => 1
               (47, 21, 51) => 1
               (47, 24, 54) => 1
               (47, 33, 44) => -1
               (47, 34, 43) => 1
               (47, 35, 9) => -1
               (47, 38, 6) => 1
               (47, 41, 5) => -1
               (47, 45, 18) => -1
               (47, 46, 19) => -1
               (47, 47, 0) => 1
               (47, 47, 2) => -1
               (47, 47, 4) => 1
               (47, 49, 29) => -1
               (47, 50, 30) => -1
               (47, 52, 26) => 1
               (47, 53, 27) => 1
                              1
               (48, 0, 41) => -
                              2
                              1
               (48, 2, 41) => -
                              2
                                1
               (48, 4, 41) => - -
                                2
               (48, 10, 38) => 1
               (48, 13, 35) => -1
               (48, 18, 39) => 1
               (48, 19, 40) => 1
               (48, 20, 47) => 1
               (48, 22, 52) => -1
               (48, 23, 53) => -1
               (48, 29, 43) => 1
               (48, 30, 44) => 1
               (48, 36, 8) => -1
               (48, 37, 7) => 1
               (48, 42, 5) => -1
               (48, 45, 15) => 1
               (48, 46, 14) => -1
               (48, 48, 0) => 1
               (48, 48, 1) => -1
               (48, 48, 2) => 1
               (48, 48, 4) => -1
               (48, 49, 34) => -1
               (48, 50, 33) => 1
               (48, 51, 25) => -1
               (48, 54, 28) => -1
                                1
               (49, 0, 40) => - -
                                2
                                1
               (49, 2, 40) => - -
                                2
                                1
               (49, 4, 40) => - -
                                2
               (49, 10, 37) => -1
               (49, 12, 35) => 1
               (49, 17, 39) => -1
               (49, 20, 46) => -1
               (49, 22, 51) => 1
               (49, 24, 53) => -1
               (49, 29, 42) => -1
               (49, 31, 44) => 1
               (49, 34, 41) => -1
               (49, 36, 9) => -1
               (49, 38, 7) => 1
               (49, 43, 5) => -1
               (49, 45, 16) => 1
               (49, 47, 14) => -1
               (49, 48, 19) => -1
               (49, 49, 0) => 1
               (49, 49, 1) => -1
               (49, 49, 2) => 1
               (49, 49, 3) => -1
               (49, 49, 4) => 1
               (49, 50, 32) => -1
               (49, 52, 25) => -1
               (49, 54, 27) => 1
                              1
               (50, 0, 39) => -
                              2
                              1
               (50, 2, 39) => -
                              2
               (50, 3, 39) => 1
                              1
               (50, 4, 39) => -
                              2
               (50, 10, 36) => 1
               (50, 11, 35) => -1
               (50, 20, 45) => 1
               (50, 23, 51) => 1
               (50, 24, 52) => 1
               (50, 30, 42) => -1
               (50, 31, 43) => -1
               (50, 32, 40) => 1
               (50, 33, 41) => 1
               (50, 37, 9) => -1
               (50, 38, 8) => 1
               (50, 44, 5) => -1
               (50, 46, 16) => 1
               (50, 47, 15) => -1
               (50, 48, 18) => 1
               (50, 49, 17) => -1
               (50, 50, 0) => 1
               (50, 50, 1) => -1
               (50, 50, 3) => 1
               (50, 53, 25) => -1
               (50, 54, 26) => -1
                                1
               (51, 0, 38) => - -
                                2
               (51, 1, 38) => -1
                                1
               (51, 2, 38) => - -
                                2
                              1
               (51, 4, 38) => -
                              2
               (51, 16, 35) => -1
               (51, 18, 36) => -1
               (51, 19, 37) => -1
               (51, 21, 47) => 1
               (51, 22, 49) => 1
               (51, 23, 50) => 1
               (51, 25, 41) => -1
               (51, 26, 43) => -1
               (51, 27, 44) => -1
               (51, 39, 8) => -1
               (51, 40, 7) => 1
               (51, 42, 6) => -1
               (51, 45, 12) => -1
               (51, 46, 11) => 1
               (51, 48, 10) => -1
               (51, 51, 1) => 1
               (51, 51, 4) => -1
               (51, 52, 34) => -1
               (51, 53, 33) => 1
               (51, 54, 31) => -1
                              1
               (52, 0, 37) => -
                              2
               (52, 1, 37) => 1
                              1
               (52, 2, 37) => -
                              2
                              1
               (52, 4, 37) => -
                              2
               (52, 15, 35) => 1
               (52, 17, 36) => 1
               (52, 21, 46) => -1
               (52, 22, 48) => -1
               (52, 24, 50) => 1
               (52, 25, 40) => 1
               (52, 26, 42) => 1
               (52, 28, 44) => -1
               (52, 34, 38) => 1
               (52, 39, 9) => -1
               (52, 41, 7) => 1
               (52, 43, 6) => -1
               (52, 45, 13) => -1
               (52, 47, 11) => 1
               (52, 49, 10) => -1
               (52, 51, 19) => -1
               (52, 52, 1) => 1
               (52, 52, 3) => -1
               (52, 52, 4) => 1
               (52, 53, 32) => -1
               (52, 54, 30) => 1
                                1
               (53, 0, 36) => - -
                                2
               (53, 1, 36) => -1
                                1
               (53, 2, 36) => - -
                                2
               (53, 3, 36) => -1
                                1
               (53, 4, 36) => - -
                                2
               (53, 14, 35) => -1
               (53, 21, 45) => 1
               (53, 23, 48) => -1
               (53, 24, 49) => -1
               (53, 25, 39) => -1
               (53, 27, 42) => 1
               (53, 28, 43) => 1
               (53, 32, 37) => -1
               (53, 33, 38) => -1
               (53, 40, 9) => -1
               (53, 41, 8) => 1
               (53, 44, 6) => -1
               (53, 46, 13) => -1
               (53, 47, 12) => 1
               (53, 50, 10) => -1
               (53, 51, 18) => 1
               (53, 52, 17) => -1
               (53, 53, 1) => 1
               (53, 53, 2) => -1
               (53, 53, 3) => 1
               (53, 54, 29) => -1
                              1
               (54, 0, 35) => -
                              2
               (54, 1, 35) => 1
                              3
               (54, 2, 35) => -
                              2
               (54, 3, 35) => 1
                              1
               (54, 4, 35) => -
                              2
               (54, 22, 45) => 1
               (54, 23, 46) => 1
               (54, 24, 47) => 1
               (54, 26, 39) => -1
               (54, 27, 40) => -1
               (54, 28, 41) => -1
               (54, 29, 36) => 1
               (54, 30, 37) => 1
               (54, 31, 38) => 1
               (54, 42, 9) => -1
               (54, 43, 8) => 1
               (54, 44, 7) => -1
               (54, 48, 13) => -1
               (54, 49, 12) => 1
               (54, 50, 11) => -1
               (54, 51, 16) => -1
               (54, 52, 15) => 1
               (54, 53, 14) => -1
               (54, 54, 2) => 1

o3 : HashTable

This tensor B can be used to compute any product of basis elements -- the number in \(B(i,j,k)\) is the coefficient on \(e_k\) of the product of \(e_i\) and \(e_j\).

Ways to use structureTensor:

structureTensor(ExteriorExtension) (missing documentation)

For the programmer

The object structureTensor is a method function.

The source of this document is in ExteriorExtensions.m2:640:0.