sage: TransitiveGroups(14) Transitive Groups of degree 14 sage: TransitiveGroups(14).cardinality() 63 sage: G = TransitiveGroup(14,61) sage: G.cardinality() 50803200 sage: factorial(14)/G.cardinality() 1716 sage: I = InvariantRingPermutationGroup(G, QQ) sage: I.secon I.secondary_invariants I.secondary_invariants_of_degree I.secondary_invariants_series sage: I.secondary_invariants_series() z^48 + z^47 + 2*z^46 + 2*z^45 + 4*z^44 + 5*z^43 + 8*z^42 + 9*z^41 + 14*z^40 + 16*z^39 + 22*z^38 + 25*z^37 + 33*z^36 + 36*z^35 + 45*z^34 + 48*z^33 + 58*z^32 + 61*z^31 + 70*z^30 + 71*z^29 + 80*z^28 + 79*z^27 + 85*z^26 + 82*z^25 + 87*z^24 + 81*z^23 + 83*z^22 + 75*z^21 + 75*z^20 + 66*z^19 + 64*z^18 + 54*z^17 + 52*z^16 + 42*z^15 + 39*z^14 + 30*z^13 + 28*z^12 + 20*z^11 + 18*z^10 + 12*z^9 + 11*z^8 + 7*z^7 + 6*z^6 + 3*z^5 + 3*z^4 + z^3 + z^2 + 1 sage: I.secondary_invariants(verbose=True) Initialiation of secondary of degree 0 ------ Secondary of degree 1 : We must search 0 secondaries invariants ------ Secondary of degree 2 : We must search 1 secondaries invariants Research of product of secondaries of degree smaller Research now to complete with new irreducible secondaries New irreducible [2] ------ Secondary of degree 3 : We must search 1 secondaries invariants Research of product of secondaries of degree smaller Research now to complete with new irreducible secondaries New irreducible [3] ------ Secondary of degree 4 : We must search 3 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 2] Research now to complete with new irreducible secondaries New irreducible [4] (3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [5] ------ Secondary of degree 5 : We must search 3 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 3] Research now to complete with new irreducible secondaries New irreducible [6] (4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [7] ------ Secondary of degree 6 : We must search 6 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 4] Add product [2, 5] Add product [3, 3] Register new relation : [2, 2, 2] Research now to complete with new irreducible secondaries New irreducible [8] (5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [9] (4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (4, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (4, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [10] ------ Secondary of degree 7 : We must search 7 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 6] Add product [2, 7] Register new relation : [3, 4] Add product [3, 5] Add product [2, 2, 3] Research now to complete with new irreducible secondaries New irreducible [11] (6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [12] (5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (5, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (5, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (5, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [13] ------ Secondary of degree 8 : We must search 11 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 8] Add product [2, 9] Add product [2, 10] Add product [3, 6] Add product [3, 7] Add product [2, 2, 4] Register new relation : [2, 2, 5] Register new relation : [4, 4] Register new relation : [4, 5] Add product [5, 5] Add product [2, 3, 3] Research now to complete with new irreducible secondaries New irreducible [14] (7, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [15] (6, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (6, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (6, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [16] ------ Secondary of degree 9 : We must search 12 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 11] Add product [2, 12] Add product [2, 13] Register new relation : [3, 8] Add product [3, 9] Add product [3, 10] Add product [2, 2, 6] Add product [2, 2, 7] Add product [4, 6] Register new relation : [4, 7] Register new relation : [5, 6] Add product [5, 7] Use of the relation [2, 3, 4] Register new relation : [2, 3, 5] Add product [3, 3, 3] Use of the relation [2, 2, 2, 3] Research now to complete with new irreducible secondaries (8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [17] (7, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [18] ------ Secondary of degree 10 : We must search 18 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 14] Add product [2, 15] Add product [2, 16] Add product [3, 11] Add product [3, 12] Add product [3, 13] Add product [2, 2, 8] Add product [2, 2, 9] Add product [2, 2, 10] Add product [4, 8] Register new relation : [4, 9] Add product [4, 10] Register new relation : [5, 8] Add product [5, 9] Add product [5, 10] Add product [2, 3, 6] Add product [2, 3, 7] Register new relation : [6, 6] Register new relation : [6, 7] Register new relation : [7, 7] Use of the relation [2, 4, 4] Use of the relation [2, 4, 5] Register new relation : [2, 5, 5] Use of the relation [3, 3, 4] Register new relation : [3, 3, 5] Add product [2, 2, 3, 3] Use of the relation [2, 2, 2, 4] Research now to complete with new irreducible secondaries (9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [19] (7, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (7, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [20] ------ Secondary of degree 11 : We must search 20 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 17] Add product [2, 18] Add product [3, 14] Add product [3, 15] Add product [3, 16] Add product [2, 2, 11] Add product [2, 2, 12] Add product [2, 2, 13] Add product [4, 11] Add product [4, 12] Add product [4, 13] Add product [5, 11] Add product [5, 12] Add product [5, 13] Use of the relation [2, 3, 8] Add product [2, 3, 9] Register new relation : [2, 3, 10] Register new relation : [6, 8] Register new relation : [6, 9] Register new relation : [6, 10] Register new relation : [7, 8] Register new relation : [7, 9] Add product [7, 10] Add product [2, 4, 6] Use of the relation [2, 4, 7] Use of the relation [2, 5, 6] Add product [2, 5, 7] Register new relation : [3, 3, 6] Register new relation : [3, 3, 7] Use of the relation [3, 4, 5] Register new relation : [3, 5, 5] Use of the relation [2, 2, 3, 4] Use of the relation [2, 2, 3, 5] Add product [2, 3, 3, 3] Use of the relation [2, 2, 2, 6] Use of the relation [2, 2, 2, 7] Research now to complete with new irreducible secondaries (10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (10, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [21] ------ Secondary of degree 12 : We must search 28 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 19] Add product [2, 20] Add product [3, 17] Add product [3, 18] Add product [2, 2, 14] Add product [2, 2, 15] Add product [2, 2, 16] Add product [4, 14] Add product [4, 15] Add product [4, 16] Add product [5, 14] Add product [5, 15] Add product [5, 16] Add product [2, 3, 11] Add product [2, 3, 12] Add product [2, 3, 13] Add product [6, 11] Add product [6, 12] Add product [6, 13] Add product [7, 11] Add product [7, 12] Add product [7, 13] Register new relation : [2, 4, 8] Use of the relation [2, 4, 9] Register new relation : [2, 4, 10] Use of the relation [2, 5, 8] Add product [2, 5, 9] Register new relation : [2, 5, 10] Use of the relation [3, 3, 8] Register new relation : [3, 3, 9] Register new relation : [3, 3, 10] Register new relation : [8, 8] Register new relation : [8, 9] Register new relation : [8, 10] Register new relation : [9, 9] Register new relation : [9, 10] Add product [10, 10] Use of the relation [2, 6, 6] Use of the relation [2, 6, 7] Use of the relation [2, 7, 7] Use of the relation [3, 5, 6] Register new relation : [3, 5, 7] Add product [2, 2, 3, 6] Add product [2, 2, 3, 7] Use of the relation [3, 4, 6] Use of the relation [3, 4, 7] Use of the relation [2, 2, 4, 4] Use of the relation [2, 2, 4, 5] Use of the relation [4, 5, 5] Register new relation : [5, 5, 5] Use of the relation [2, 3, 3, 4] Use of the relation [2, 3, 3, 5] Add product [3, 3, 3, 3] Use of the relation [2, 2, 2, 8] Use of the relation [2, 2, 2, 9] Use of the relation [2, 2, 2, 10] Use of the relation [2, 2, 2, 3, 3] Research now to complete with new irreducible secondaries (11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (11, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (10, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (10, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (10, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (10, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (10, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (9, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (8, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [22] ------ Secondary of degree 13 : We must search 30 secondaries invariants Research of product of secondaries of degree smaller Add product [2, 21] Add product [3, 19] Add product [3, 20] Add product [2, 2, 17] Add product [2, 2, 18] Add product [4, 17] Add product [4, 18] Add product [5, 17] Add product [5, 18] Add product [2, 3, 14] Add product [2, 3, 15] Add product [2, 3, 16] Add product [6, 14] Add product [6, 15] Add product [6, 16] Add product [7, 14] Add product [7, 15] Add product [7, 16] Add product [2, 4, 11] Add product [2, 4, 12] Add product [2, 4, 13] Add product [2, 5, 11] Add product [2, 5, 12] Add product [2, 5, 13] Add product [3, 3, 11] Register new relation : [3, 3, 12] Register new relation : [3, 3, 13] Register new relation : [8, 11] Register new relation : [8, 12] Register new relation : [8, 13] Register new relation : [9, 11] Register new relation : [9, 12] Register new relation : [9, 13] Register new relation : [10, 11] Register new relation : [10, 12] Add product [10, 13] Use of the relation [2, 6, 8] Use of the relation [2, 6, 9] Use of the relation [2, 6, 10] Use of the relation [2, 7, 8] Use of the relation [2, 7, 9] Register new relation : [2, 7, 10] Use of the relation [3, 5, 8] Add product [3, 5, 9] Register new relation : [3, 5, 10] Use of the relation [2, 2, 3, 8] Register new relation : [2, 2, 3, 9] Use of the relation [2, 2, 3, 10] Use of the relation [3, 6, 6] Use of the relation [3, 6, 7] Use of the relation [3, 7, 7] Register new relation : [2, 2, 4, 6] Use of the relation [2, 2, 4, 7] Use of the relation [5, 5, 6] Register new relation : [5, 5, 7] Use of the relation [2, 3, 3, 6] Use of the relation [2, 3, 3, 7] Use of the relation [3, 4, 9] Use of the relation [3, 4, 10] Use of the relation [2, 2, 5, 6] Use of the relation [2, 2, 5, 7] Use of the relation [4, 4, 6] Use of the relation [4, 5, 6] Use of the relation [4, 5, 7] Use of the relation [3, 3, 3, 4] Use of the relation [3, 3, 3, 5] Use of the relation [3, 4, 8] Add product [2, 2, 3, 3, 3] Use of the relation [2, 2, 2, 11] Use of the relation [2, 2, 2, 12] Use of the relation [2, 2, 2, 13] Research now to complete with new irreducible secondaries New irreducible [23] (12, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [24] ------ Secondary of degree 14 : We must search 39 secondaries invariants Correction by adding the space spanned by secondaries of degree 0 Research of product of secondaries of degree smaller Add product [2, 22] Add product [3, 21] Add product [2, 2, 19] Add product [2, 2, 20] Add product [4, 19] Add product [4, 20] Add product [5, 19] Add product [5, 20] Add product [2, 3, 17] Add product [2, 3, 18] Add product [6, 17] Add product [6, 18] Add product [7, 17] Add product [7, 18] Add product [2, 4, 14] Add product [2, 4, 15] Add product [2, 4, 16] Add product [2, 5, 14] Add product [2, 5, 15] Add product [2, 5, 16] Add product [3, 3, 14] Add product [3, 3, 15] Add product [3, 3, 16] Add product [8, 14] Add product [8, 15] Add product [8, 16] Add product [9, 14] Add product [9, 15] Add product [9, 16] Add product [10, 14] Register new relation : [10, 15] Add product [10, 16] Add product [2, 6, 11] Add product [2, 6, 12] Add product [2, 6, 13] Add product [2, 7, 11] Register new relation : [2, 7, 12] Register new relation : [2, 7, 13] Register new relation : [3, 5, 11] Register new relation : [3, 5, 12] Register new relation : [3, 5, 13] Register new relation : [2, 2, 3, 11] Register new relation : [2, 2, 3, 12] Register new relation : [2, 2, 3, 13] Register new relation : [11, 11] Register new relation : [11, 12] Register new relation : [11, 13] Register new relation : [12, 12] Register new relation : [12, 13] Register new relation : [13, 13] Use of the relation [2, 8, 8] Use of the relation [2, 8, 9] Use of the relation [2, 8, 10] Use of the relation [2, 9, 9] Use of the relation [2, 9, 10] Register new relation : [2, 10, 10] Use of the relation [3, 6, 8] Use of the relation [3, 6, 9] Use of the relation [3, 6, 10] Use of the relation [3, 7, 8] Use of the relation [3, 7, 9] Register new relation : [3, 7, 10] Use of the relation [2, 2, 4, 8] Use of the relation [2, 2, 4, 9] Use of the relation [2, 2, 4, 10] Use of the relation [5, 5, 8] Register new relation : [5, 5, 9] Register new relation : [5, 5, 10] Use of the relation [2, 3, 3, 8] Use of the relation [2, 3, 3, 9] Use of the relation [2, 3, 3, 10] Use of the relation [2, 2, 6, 6] Use of the relation [2, 2, 6, 7] Use of the relation [2, 2, 7, 7] Use of the relation [4, 6, 6] Use of the relation [4, 6, 7] Use of the relation [5, 6, 7] Use of the relation [5, 7, 7] Use of the relation [3, 3, 3, 6] Use of the relation [3, 3, 3, 7] Use of the relation [3, 4, 11] Use of the relation [3, 4, 12] Use of the relation [3, 4, 13] Use of the relation [2, 2, 5, 8] Use of the relation [2, 2, 5, 9] Use of the relation [2, 2, 5, 10] Use of the relation [4, 4, 8] Use of the relation [4, 5, 8] Use of the relation [4, 4, 10] Use of the relation [4, 5, 10] Use of the relation [4, 5, 9] Use of the relation [2, 3, 4, 6] Use of the relation [2, 3, 5, 6] Use of the relation [2, 3, 4, 7] Use of the relation [2, 3, 5, 7] Use of the relation [2, 2, 3, 3, 4] Use of the relation [2, 2, 3, 3, 5] Add product [2, 3, 3, 3, 3] Use of the relation [2, 2, 2, 14] Use of the relation [2, 2, 2, 15] Use of the relation [2, 2, 2, 16] Use of the relation [2, 2, 2, 3, 6] Use of the relation [2, 2, 2, 3, 7] Research now to complete with new irreducible secondaries New irreducible [25] (13, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [26] (12, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (12, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (12, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants (12, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) is not a good secondary invariants New irreducible [27] ------ Secondary of degree 15 : We must search 42 secondaries invariants Correction by adding the space spanned by secondaries of degree 1 Research of product of secondaries of degree smaller Add product [2, 23] Add product [2, 24] Add product [3, 22] Add product [2, 2, 21] Add product [4, 21] Add product [5, 21] Add product [2, 3, 19] Add product [2, 3, 20] Add product [6, 19] Add product [6, 20] Add product [7, 19] Add product [7, 20] Add product [2, 4, 17] Add product [2, 4, 18] Add product [2, 5, 17] Add product [2, 5, 18] Add product [3, 3, 17] Add product [3, 3, 18] Add product [8, 17] Add product [8, 18] Add product [9, 17] Add product [9, 18] Add product [10, 17] Add product [10, 18] Add product [2, 6, 14] Add product [2, 6, 15] Add product [2, 6, 16] Add product [2, 7, 14] Add product [2, 7, 15] Add product [2, 7, 16] Add product [3, 5, 14] Add product [3, 5, 15] Add product [3, 5, 16] Add product [2, 2, 3, 14] Add product [2, 2, 3, 15] Add product [2, 2, 3, 16] Register new relation : [11, 14] Register new relation : [11, 15] Register new relation : [11, 16] Register new relation : [12, 14] Register new relation : [12, 15] Register new relation : [12, 16] Register new relation : [13, 14] Register new relation : [13, 15] Register new relation : [13, 16] Use of the relation [2, 8, 11] Use of the relation [2, 8, 12] Use of the relation [2, 8, 13] Use of the relation [2, 9, 11] Use of the relation [2, 9, 12] Use of the relation [2, 9, 13] Use of the relation [2, 10, 11] Use of the relation [2, 10, 12] Add product [2, 10, 13] Add product [3, 6, 11] Add product [3, 6, 12] Add product [3, 6, 13] Register new relation : [3, 7, 11] Register new relation : [3, 7, 12] Register new relation : [3, 7, 13] Register new relation : [2, 2, 4, 11] Register new relation : [2, 2, 4, 12] Register new relation : [2, 2, 4, 13] Register new relation : [5, 5, 11] Register new relation : [5, 5, 12] Register new relation : [5, 5, 13] Register new relation : [2, 3, 3, 11] Use of the relation [2, 3, 3, 12] Use of the relation [2, 3, 3, 13] Use of the relation [3, 8, 9] Use of the relation [3, 9, 9] Use of the relation [3, 9, 10] Use of the relation [3, 8, 10] Register new relation : [3, 10, 10] Use of the relation [2, 2, 6, 8] Use of the relation [2, 2, 6, 9] Use of the relation [2, 2, 6, 10] Use of the relation [2, 2, 7, 8] Use of the relation [2, 2, 7, 9] Use of the relation [2, 2, 7, 10] Use of the relation [4, 6, 8] Use of the relation [4, 6, 9] Use of the relation [4, 6, 10] Use of the relation [5, 7, 8] Use of the relation [5, 7, 9] Register new relation : [5, 7, 10] Use of the relation [3, 3, 3, 8] Use of the relation [3, 3, 3, 9] Use of the relation [3, 3, 3, 10] Use of the relation [4, 7, 8] Use of the relation [4, 7, 10] Use of the relation [5, 6, 9] Use of the relation [5, 6, 10] Use of the relation [2, 3, 6, 6] Use of the relation [2, 3, 6, 7] Use of the relation [2, 3, 7, 7] Use of the relation [2, 2, 3, 3, 6] Use of the relation [2, 2, 3, 3, 7] Use of the relation [3, 4, 14] Use of the relation [3, 4, 15] Use of the relation [3, 4, 16] Use of the relation [2, 2, 5, 11] Use of the relation [2, 2, 5, 12] Use of the relation [2, 2, 5, 13] Use of the relation [4, 4, 11] Use of the relation [4, 5, 11] Use of the relation [4, 4, 12] Use of the relation [4, 5, 12] Use of the relation [4, 4, 13] Use of the relation [4, 5, 13] Use of the relation [2, 3, 4, 9] Use of the relation [2, 3, 5, 9] Use of the relation [2, 4, 4, 6] Use of the relation [2, 4, 5, 6] Use of the relation [2, 4, 5, 7] Use of the relation [2, 5, 5, 7] Use of the relation [2, 3, 3, 3, 4] Use of the relation [2, 3, 3, 3, 5] Add product [3, 3, 3, 3, 3] Use of the relation [2, 2, 2, 17] Use of the relation [2, 2, 2, 18] Use of the relation [2, 2, 2, 3, 3, 3] Research now to complete with new irreducible secondaries New irreducible [28] ------ Secondary of degree 16 : We must search 52 secondaries invariants Correction by adding the space spanned by secondaries of degree 2 Research of product of secondaries of degree smaller Add product [2, 25] Add product [2, 26] Add product [2, 27] Register new relation : [3, 23] Add product [3, 24] Add product [2, 2, 22] Add product [4, 22] Add product [5, 22] Add product [2, 3, 21] Add product [6, 21] Add product [7, 21] Add product [2, 4, 19] Add product [2, 4, 20] Add product [2, 5, 19] Add product [2, 5, 20] Add product [3, 3, 19] Add product [3, 3, 20] Add product [8, 19] Add product [8, 20] Add product [9, 19] Add product [9, 20] Add product [10, 19] Add product [10, 20] Add product [2, 6, 17] Add product [2, 6, 18] Add product [2, 7, 17] Add product [2, 7, 18] Add product [3, 5, 17] Add product [3, 5, 18] Add product [2, 2, 3, 17] Add product [2, 2, 3, 18] Add product [11, 17] Add product [11, 18] Add product [12, 17] Add product [12, 18] Add product [13, 17] Add product [13, 18] Add product [2, 8, 14] Add product [2, 8, 15] Add product [2, 8, 16] Add product [2, 9, 14] Add product [2, 9, 15] Add product [2, 9, 16] Add product [2, 10, 14] Use of the relation [2, 10, 15] Add product [2, 10, 16] Add product [3, 6, 14] Add product [3, 6, 15] Add product [3, 6, 16] Add product [3, 7, 14] Add product [3, 7, 15] Register new relation : [3, 7, 16] Register new relation : [2, 2, 4, 14] Register new relation : [2, 2, 4, 15] Register new relation : [2, 2, 4, 16] Register new relation : [5, 5, 14] Register new relation : [5, 5, 15] Register new relation : [5, 5, 16] Register new relation : [2, 3, 3, 14] Register new relation : [2, 3, 3, 15] Register new relation : [2, 3, 3, 16] Register new relation : [14, 14] Register new relation : [14, 15] Register new relation : [14, 16] Register new relation : [15, 15] Register new relation : [15, 16] Register new relation : [16, 16] Use of the relation [2, 11, 11] Use of the relation [2, 11, 12] Use of the relation [2, 11, 13] Use of the relation [2, 12, 12] Use of the relation [2, 12, 13] Use of the relation [2, 13, 13] Use of the relation [3, 9, 11] Use of the relation [3, 9, 12] Use of the relation [3, 9, 13] Use of the relation [3, 10, 11] Use of the relation [3, 10, 12] Add product [3, 10, 13] Add product [2, 2, 6, 11] Add product [2, 2, 6, 12] ------ Secondary of degree 17 : We must search 54 secondaries invariants Correction by adding the space spanned by secondaries of degree 3 Research of product of secondaries of degree smaller Add product [2, 28] Add product [3, 25] Add product [3, 26] Add product [3, 27] Add product [2, 2, 23] Register new relation : [2, 2, 24] Add product [4, 23] Add product [4, 24] Register new relation : [5, 23] Add product [5, 24] Add product [2, 3, 22] Add product [6, 22] Add product [7, 22] Add product [2, 4, 21] Add product [2, 5, 21] Add product [3, 3, 21] Add product [8, 21] Add product [9, 21] Add product [10, 21] Add product [2, 6, 19] Add product [2, 6, 20] Add product [2, 7, 19] Add product [2, 7, 20] Add product [3, 5, 19] Add product [3, 5, 20] Add product [2, 2, 3, 19] Add product [2, 2, 3, 20] Add product [11, 19] Add product [11, 20] Add product [12, 19] Add product [12, 20] Add product [13, 19] Add product [13, 20] Add product [2, 8, 17] Add product [2, 8, 18] Add product [2, 9, 17] Add product [2, 9, 18] Add product [2, 10, 17] Add product [2, 10, 18] Add product [3, 6, 17] Add product [3, 6, 18] Add product [3, 7, 17] Add product [3, 7, 18] Add product [2, 2, 4, 17] Add product [2, 2, 4, 18] Add product [5, 5, 17] Add product [5, 5, 18] Add product [2, 3, 3, 17] Add product [2, 3, 3, 18] Add product [14, 17] Add product [14, 18] Add product [15, 17] Add product [15, 18] Add product [16, 17] Register new relation : [16, 18] Use of the relation [2, 11, 14] Use of the relation [2, 11, 15] Use of the relation [2, 11, 16] Use of the relation [2, 12, 14] Use of the relation [2, 12, 15] Use of the relation [2, 12, 16] Use of the relation [2, 13, 14] Use of the relation [2, 13, 15] Use of the relation [2, 13, 16] Add product [3, 9, 14] Add product [3, 9, 15] ------ Secondary of degree 18 : We must search 64 secondaries invariants Correction by adding the space spanned by secondaries of degree 4 Research of product of secondaries of degree smaller Add product [3, 28] Add product [2, 2, 25] Add product [2, 2, 26] Add product [2, 2, 27] Add product [4, 25] Add product [4, 26] Add product [4, 27] Add product [5, 25] Add product [5, 26] Add product [5, 27] Use of the relation [2, 3, 23] Register new relation : [2, 3, 24] Add product [6, 23] Add product [6, 24] Register new relation : [7, 23] Add product [7, 24] Add product [2, 4, 22] Add product [2, 5, 22] Add product [3, 3, 22] Add product [8, 22] Add product [9, 22] Add product [10, 22] Add product [2, 6, 21] Add product [2, 7, 21] Add product [3, 5, 21] Add product [2, 2, 3, 21] Add product [11, 21] Add product [12, 21] Add product [13, 21] Add product [2, 8, 19] Add product [2, 8, 20] Add product [2, 9, 19] Add product [2, 9, 20] Add product [2, 10, 19] Add product [2, 10, 20] Add product [3, 6, 19] Add product [3, 6, 20] Add product [3, 7, 19] Add product [3, 7, 20] Add product [2, 2, 4, 19] Add product [2, 2, 4, 20] Add product [5, 5, 19] Add product [5, 5, 20] Add product [2, 3, 3, 19] Add product [2, 3, 3, 20] Add product [14, 19] Add product [14, 20] Add product [15, 19] Add product [15, 20] Add product [16, 19] Add product [16, 20] Add product [2, 11, 17] Add product [2, 11, 18] Add product [2, 12, 17] Add product [2, 12, 18] Add product [2, 13, 17] Add product [2, 13, 18] Add product [3, 9, 17] Add product [3, 9, 18] Add product [3, 10, 17] Add product [3, 10, 18] Add product [2, 2, 6, 17] Add product [2, 2, 6, 18] Add product [2, 2, 7, 17] Add product [2, 2, 7, 18] Add product [4, 6, 17] Add product [4, 6, 18] ------ Secondary of degree 19 : We must search 66 secondaries invariants Correction by adding the space spanned by secondaries of degree 5 Research of product of secondaries of degree smaller Add product [2, 2, 28] Add product [4, 28] Add product [5, 28] Add product [2, 3, 25] Add product [2, 3, 26] Add product [2, 3, 27] Add product [6, 25] Add product [6, 26] Add product [6, 27] Add product [7, 25] Add product [7, 26] Add product [7, 27] Add product [2, 4, 23] Register new relation : [2, 4, 24] Use of the relation [2, 5, 23] Add product [2, 5, 24] Use of the relation [3, 3, 23] Add product [3, 3, 24] Add product [8, 23] Add product [8, 24] Register new relation : [9, 23] Add product [9, 24] Add product [10, 23] Add product [10, 24] Add product [2, 6, 22] Add product [2, 7, 22] Add product [3, 5, 22] Add product [2, 2, 3, 22] Add product [11, 22] Add product [12, 22] Add product [13, 22] Add product [2, 8, 21] Add product [2, 9, 21] Add product [2, 10, 21] Add product [3, 6, 21] Add product [3, 7, 21] Add product [2, 2, 4, 21] Add product [5, 5, 21] Add product [2, 3, 3, 21] Add product [14, 21] Add product [15, 21] Add product [16, 21] Add product [2, 11, 19] Add product [2, 11, 20] Add product [2, 12, 19] Add product [2, 12, 20] Add product [2, 13, 19] Add product [2, 13, 20] Add product [3, 9, 19] Add product [3, 9, 20] Add product [3, 10, 19] Add product [3, 10, 20] Add product [2, 2, 6, 19] Add product [2, 2, 6, 20] Add product [2, 2, 7, 19] Add product [2, 2, 7, 20] Add product [4, 6, 19] Add product [4, 6, 20] Add product [5, 7, 19] Add product [5, 7, 20] Add product [3, 3, 3, 19] Add product [3, 3, 3, 20] Add product [17, 19] Add product [17, 20] Add product [18, 19] Add product [18, 20] Add product [2, 14, 17] Add product [2, 14, 18] Add product [2, 15, 17] Add product [2, 15, 18] ------ Secondary of degree 20 : We must search 75 secondaries invariants Correction by adding the space spanned by secondaries of degree 6 Research of product of secondaries of degree smaller Add product [2, 3, 28] Add product [6, 28] Add product [7, 28] Add product [2, 4, 25] Add product [2, 4, 26] Add product [2, 4, 27] Add product [2, 5, 25] Add product [2, 5, 26] Add product [2, 5, 27] Add product [3, 3, 25] Add product [3, 3, 26] Add product [3, 3, 27] Add product [8, 25] Add product [8, 26] Add product [8, 27] Add product [9, 25] Add product [9, 26] Add product [9, 27] Add product [10, 25] Add product [10, 26] Add product [10, 27] Add product [2, 6, 23] Register new relation : [2, 6, 24] Use of the relation [2, 7, 23] Add product [2, 7, 24] Use of the relation [3, 5, 23] Add product [3, 5, 24] Use of the relation [2, 2, 3, 23] Use of the relation [2, 2, 3, 24] Add product [11, 23] Add product [11, 24] Register new relation : [12, 23] Add product [12, 24] Add product [13, 23] Add product [13, 24] Add product [2, 8, 22] Add product [2, 9, 22] Add product [2, 10, 22] Add product [3, 6, 22] Add product [3, 7, 22] Add product [2, 2, 4, 22] Add product [5, 5, 22] Add product [2, 3, 3, 22] Add product [14, 22] Add product [15, 22] Add product [16, 22] Add product [2, 11, 21] Add product [2, 12, 21] Add product [2, 13, 21] Add product [3, 9, 21] Add product [3, 10, 21] Add product [2, 2, 6, 21] Add product [2, 2, 7, 21] Add product [4, 6, 21] Add product [5, 7, 21] Add product [3, 3, 3, 21] Add product [17, 21] Add product [18, 21] Add product [2, 14, 19] Add product [2, 14, 20] Add product [2, 15, 19] Add product [2, 15, 20] Add product [2, 16, 19] Add product [2, 16, 20] Add product [3, 11, 19] Add product [3, 11, 20] Add product [3, 12, 19] Add product [3, 12, 20] Add product [3, 13, 19] Add product [3, 13, 20] Add product [2, 2, 8, 19] Add product [2, 2, 8, 20] Add product [2, 2, 9, 19] Add product [2, 2, 9, 20] Add product [2, 2, 10, 19] Add product [2, 2, 10, 20] Add product [4, 8, 19] Add product [4, 8, 20] Add product [4, 10, 19] Add product [4, 10, 20] Add product [5, 9, 19] ------ Secondary of degree 21 : We must search 75 secondaries invariants Correction by adding the space spanned by secondaries of degree 7 Research of product of secondaries of degree smaller Add product [2, 4, 28] Add product [2, 5, 28] Add product [3, 3, 28] Add product [8, 28] Add product [9, 28] Add product [10, 28] Add product [2, 6, 25] Add product [2, 6, 26] Add product [2, 6, 27] Add product [2, 7, 25] Add product [2, 7, 26] Add product [2, 7, 27] Add product [3, 5, 25] Add product [3, 5, 26] Add product [3, 5, 27] Add product [2, 2, 3, 25] Add product [2, 2, 3, 26] Add product [2, 2, 3, 27] Add product [11, 25] Add product [11, 26] Add product [11, 27] Add product [12, 25] Add product [12, 26] Add product [12, 27] Add product [13, 25] Add product [13, 26] Add product [13, 27] Add product [2, 8, 23] Register new relation : [2, 8, 24] Use of the relation [2, 9, 23] Add product [2, 9, 24] Add product [2, 10, 23] Add product [2, 10, 24] Use of the relation [3, 6, 23] Add product [3, 6, 24] Use of the relation [3, 7, 23] Add product [3, 7, 24] Add product [2, 2, 4, 23] Use of the relation [2, 2, 4, 24] Use of the relation [5, 5, 23] Add product [5, 5, 24] Use of the relation [2, 3, 3, 23] Use of the relation [2, 3, 3, 24] Add product [14, 23] Add product [14, 24] Register new relation : [15, 23] Add product [15, 24] Add product [16, 23] Add product [16, 24] Add product [2, 11, 22] Add product [2, 12, 22] Add product [2, 13, 22] Add product [3, 9, 22] Add product [3, 10, 22] Add product [2, 2, 6, 22] Add product [2, 2, 7, 22] Add product [4, 6, 22] Add product [5, 7, 22] Add product [3, 3, 3, 22] Add product [17, 22] Add product [18, 22] Add product [2, 14, 21] Add product [2, 15, 21] Add product [2, 16, 21] Add product [3, 11, 21] Add product [3, 12, 21] Add product [3, 13, 21] Add product [2, 2, 8, 21] Add product [2, 2, 9, 21] Add product [2, 2, 10, 21] Add product [4, 8, 21] Add product [4, 10, 21] Add product [5, 9, 21] Add product [5, 10, 21] Add product [2, 3, 6, 21] Add product [2, 3, 7, 21] Add product [2, 2, 3, 3, 21] Add product [19, 21] Add product [20, 21] Add product [2, 17, 19] Add product [2, 17, 20] Add product [2, 18, 19] Add product [2, 18, 20] Add product [3, 14, 19] ------ Secondary of degree 22 : We must search 83 secondaries invariants Correction by adding the space spanned by secondaries of degree 8 Research of product of secondaries of degree smaller Add product [2, 6, 28] Add product [2, 7, 28] Add product [3, 5, 28] Add product [2, 2, 3, 28] Add product [11, 28] Add product [12, 28] Add product [13, 28] Add product [2, 8, 25] Add product [2, 8, 26] Add product [2, 8, 27] Add product [2, 9, 25] Add product [2, 9, 26] Add product [2, 9, 27] Add product [2, 10, 25] Add product [2, 10, 26] Add product [2, 10, 27] Add product [3, 6, 25] Add product [3, 6, 26] Add product [3, 6, 27] Add product [3, 7, 25] Add product [3, 7, 26] Add product [3, 7, 27] Add product [2, 2, 4, 25] Add product [2, 2, 4, 26] Add product [2, 2, 4, 27] Add product [5, 5, 25] Add product [5, 5, 26] Add product [5, 5, 27] Add product [2, 3, 3, 25] Add product [2, 3, 3, 26] Add product [2, 3, 3, 27] Add product [14, 25] Add product [14, 26] Add product [14, 27] Add product [15, 25] Add product [15, 26] Add product [15, 27] Add product [16, 25] Add product [16, 26] Add product [16, 27] Add product [2, 11, 23] Register new relation : [2, 11, 24] Use of the relation [2, 12, 23] Add product [2, 12, 24] Add product [2, 13, 23] Add product [2, 13, 24] Use of the relation [3, 9, 23] Add product [3, 9, 24] Use of the relation [3, 10, 23] Add product [3, 10, 24] Add product [2, 2, 6, 23] Use of the relation [2, 2, 6, 24] Use of the relation [2, 2, 7, 23] Use of the relation [2, 2, 7, 24] Register new relation : [4, 6, 23] Register new relation : [4, 6, 24] Use of the relation [5, 7, 23] Add product [5, 7, 24] Use of the relation [3, 3, 3, 23] Register new relation : [3, 3, 3, 24] Register new relation : [17, 23] Add product [17, 24] Add product [18, 23] Add product [18, 24] Add product [2, 14, 22] Add product [2, 15, 22] Add product [2, 16, 22] Add product [3, 11, 22] Add product [3, 12, 22] Add product [3, 13, 22] Add product [2, 2, 8, 22] Add product [2, 2, 9, 22] Add product [2, 2, 10, 22] Add product [4, 8, 22] Add product [4, 10, 22] Add product [5, 9, 22] Add product [5, 10, 22] Add product [2, 3, 6, 22] Add product [2, 3, 7, 22] Add product [2, 2, 3, 3, 22] Add product [19, 22] Add product [20, 22] Add product [2, 17, 21] Add product [2, 18, 21] Add product [3, 14, 21] Add product [3, 15, 21] Add product [3, 16, 21] Add product [2, 2, 11, 21] Add product [2, 2, 12, 21] Add product [2, 2, 13, 21] Add product [4, 11, 21] Add product [4, 12, 21] Add product [4, 13, 21] Add product [5, 11, 21] Add product [5, 12, 21] Add product [5, 13, 21] ------ Secondary of degree 23 : We must search 81 secondaries invariants Correction by adding the space spanned by secondaries of degree 9 Research of product of secondaries of degree smaller Add product [2, 8, 28] Add product [2, 9, 28] Add product [2, 10, 28] Add product [3, 6, 28] Add product [3, 7, 28] Add product [2, 2, 4, 28] Add product [5, 5, 28] Add product [2, 3, 3, 28] Add product [14, 28] Add product [15, 28] Add product [16, 28] Add product [2, 11, 25] Add product [2, 11, 26] Add product [2, 11, 27] Add product [2, 12, 25] Add product [2, 12, 26] Add product [2, 12, 27] Add product [2, 13, 25] Add product [2, 13, 26] Add product [2, 13, 27] Add product [3, 9, 25] Add product [3, 9, 26] Add product [3, 9, 27] Add product [3, 10, 25] Add product [3, 10, 26] Add product [3, 10, 27] Add product [2, 2, 6, 25] Add product [2, 2, 6, 26] Add product [2, 2, 6, 27] Add product [2, 2, 7, 25] Add product [2, 2, 7, 26] Add product [2, 2, 7, 27] Add product [4, 6, 25] Add product [4, 6, 26] Add product [4, 6, 27] Add product [5, 7, 25] Add product [5, 7, 26] Add product [5, 7, 27] Add product [3, 3, 3, 25] Add product [3, 3, 3, 26] Add product [3, 3, 3, 27] Add product [17, 25] Add product [17, 26] Add product [17, 27] Add product [18, 25] Add product [18, 26] Add product [18, 27] Add product [2, 14, 23] Add product [2, 14, 24] Use of the relation [2, 15, 23] Add product [2, 15, 24] Add product [2, 16, 23] Add product [2, 16, 24] Use of the relation [3, 11, 23] Add product [3, 11, 24] Use of the relation [3, 12, 23] Add product [3, 12, 24] Use of the relation [3, 13, 23] Add product [3, 13, 24] Add product [2, 2, 8, 23] Use of the relation [2, 2, 8, 24] Use of the relation [2, 2, 9, 23] Use of the relation [2, 2, 9, 24] Add product [2, 2, 10, 23] Use of the relation [2, 2, 10, 24] Add product [4, 8, 23] Register new relation : [4, 8, 24] Add product [4, 10, 23] Add product [4, 10, 24] Use of the relation [5, 9, 23] Add product [5, 9, 24] Use of the relation [5, 10, 23] Add product [5, 10, 24] Use of the relation [2, 3, 6, 23] Use of the relation [2, 3, 6, 24] Use of the relation [2, 3, 7, 23] Use of the relation [2, 3, 7, 24] Use of the relation [2, 2, 3, 3, 23] Use of the relation [2, 2, 3, 3, 24] Add product [19, 23] Add product [19, 24] Add product [20, 23] Add product [20, 24] Add product [2, 17, 22] Add product [2, 18, 22] Add product [3, 14, 22] Add product [3, 15, 22] Add product [3, 16, 22] Add product [2, 2, 11, 22] Add product [2, 2, 12, 22] Add product [2, 2, 13, 22] Add product [4, 11, 22] Add product [4, 12, 22] Add product [4, 13, 22] Add product [5, 11, 22] Add product [5, 12, 22] Add product [5, 13, 22] Add product [2, 3, 9, 22] ------ Secondary of degree 24 : We must search 87 secondaries invariants Correction by adding the space spanned by secondaries of degree 10 Research of product of secondaries of degree smaller Add product [2, 11, 28] Add product [2, 12, 28] Add product [2, 13, 28] Add product [3, 9, 28] Add product [3, 10, 28] Add product [2, 2, 6, 28] Add product [2, 2, 7, 28] Add product [4, 6, 28] Add product [5, 7, 28] Add product [3, 3, 3, 28] Add product [17, 28] Add product [18, 28] Add product [2, 14, 25] Add product [2, 14, 26] Add product [2, 14, 27] Add product [2, 15, 25] Add product [2, 15, 26] Add product [2, 15, 27] Add product [2, 16, 25] Add product [2, 16, 26] Add product [2, 16, 27] Add product [3, 11, 25] Add product [3, 11, 26] Add product [3, 11, 27] Add product [3, 12, 25] Add product [3, 12, 26] Add product [3, 12, 27] Add product [3, 13, 25] Add product [3, 13, 26] Add product [3, 13, 27] Add product [2, 2, 8, 25] Add product [2, 2, 8, 26] Add product [2, 2, 8, 27] Add product [2, 2, 9, 25] Add product [2, 2, 9, 26] Add product [2, 2, 9, 27] Add product [2, 2, 10, 25] Add product [2, 2, 10, 26] Add product [2, 2, 10, 27] Add product [4, 8, 25] Add product [4, 8, 26] Add product [4, 8, 27] Add product [4, 10, 25] Add product [4, 10, 26] Add product [4, 10, 27] Add product [5, 9, 25] Add product [5, 9, 26] Add product [5, 9, 27] Add product [5, 10, 25] Add product [5, 10, 26] Add product [5, 10, 27] Add product [2, 3, 6, 25] Add product [2, 3, 6, 26] Add product [2, 3, 6, 27] Add product [2, 3, 7, 25] Add product [2, 3, 7, 26] Add product [2, 3, 7, 27] Add product [2, 2, 3, 3, 25] Add product [2, 2, 3, 3, 26] Add product [2, 2, 3, 3, 27] Add product [19, 25] Add product [19, 26] Add product [19, 27] Add product [20, 25] Add product [20, 26] Add product [20, 27] Use of the relation [2, 17, 23] Add product [2, 17, 24] Add product [2, 18, 23] Add product [2, 18, 24] Use of the relation [3, 14, 23] Add product [3, 14, 24] Use of the relation [3, 15, 23] Add product [3, 15, 24] Use of the relation [3, 16, 23] Add product [3, 16, 24] Add product [2, 2, 11, 23] Use of the relation [2, 2, 11, 24] Use of the relation [2, 2, 12, 23] Use of the relation [2, 2, 12, 24] Add product [2, 2, 13, 23] Use of the relation [2, 2, 13, 24] Add product [4, 11, 23] Add product [4, 11, 24] Use of the relation [4, 12, 23] Register new relation : [4, 12, 24] Add product [4, 13, 23] Add product [4, 13, 24] Use of the relation [5, 11, 23] Register new relation : [5, 11, 24] Use of the relation [5, 12, 23] Add product [5, 12, 24] Use of the relation [5, 13, 23] Add product [5, 13, 24] Use of the relation [2, 3, 9, 23] Use of the relation [2, 3, 9, 24] Use of the relation [7, 10, 23] Add product [7, 10, 24] Use of the relation [2, 4, 6, 23] Use of the relation [2, 4, 6, 24] Use of the relation [2, 5, 7, 23] Register new relation : [2, 5, 7, 24] Use of the relation [2, 3, 3, 3, 23] Use of the relation [2, 3, 3, 3, 24] Add product [21, 23] Add product [21, 24] Add product [2, 19, 22] Add product [2, 20, 22] Add product [3, 17, 22] Add product [3, 18, 22] ------ Secondary of degree 25 : We must search 82 secondaries invariants Correction by adding the space spanned by secondaries of degree 11 Research of product of secondaries of degree smaller Add product [2, 14, 28] Add product [2, 15, 28] Add product [2, 16, 28] Add product [3, 11, 28] Add product [3, 12, 28] Add product [3, 13, 28] Add product [2, 2, 8, 28] Add product [2, 2, 9, 28] Add product [2, 2, 10, 28] Add product [4, 8, 28] Add product [4, 10, 28] Add product [5, 9, 28] Add product [5, 10, 28] Add product [2, 3, 6, 28] Add product [2, 3, 7, 28] Add product [2, 2, 3, 3, 28] Add product [19, 28] Add product [20, 28] Add product [2, 17, 25] Add product [2, 17, 26] Add product [2, 17, 27] Add product [2, 18, 25] Add product [2, 18, 26] Add product [2, 18, 27] Add product [3, 14, 25] Add product [3, 14, 26] Add product [3, 14, 27] Add product [3, 15, 25] Add product [3, 15, 26] Add product [3, 15, 27] Add product [3, 16, 25] Add product [3, 16, 26] Add product [3, 16, 27] Add product [2, 2, 11, 25] Add product [2, 2, 11, 26] Add product [2, 2, 11, 27] Add product [2, 2, 12, 25] Add product [2, 2, 12, 26] Add product [2, 2, 12, 27] Add product [2, 2, 13, 25] Add product [2, 2, 13, 26] Add product [2, 2, 13, 27] Add product [4, 11, 25] Add product [4, 11, 26] Add product [4, 11, 27] Add product [4, 12, 25] Add product [4, 12, 26] Add product [4, 12, 27] Add product [4, 13, 25] Add product [4, 13, 26] Add product [4, 13, 27] Add product [5, 11, 25] Add product [5, 11, 26] Add product [5, 11, 27] Add product [5, 12, 25] Add product [5, 12, 26] Add product [5, 12, 27] Add product [5, 13, 25] Add product [5, 13, 26] Add product [5, 13, 27] Add product [2, 3, 9, 25] Add product [2, 3, 9, 26] Add product [2, 3, 9, 27] Add product [7, 10, 25] Add product [7, 10, 26] Add product [7, 10, 27] Add product [2, 4, 6, 25] Add product [2, 4, 6, 26] Add product [2, 4, 6, 27] Add product [2, 5, 7, 25] Add product [2, 5, 7, 26] Add product [2, 5, 7, 27] Add product [2, 3, 3, 3, 25] Add product [2, 3, 3, 3, 26] Add product [2, 3, 3, 3, 27] Add product [21, 25] Add product [21, 26] Add product [21, 27] Add product [2, 19, 23] Add product [2, 19, 24] Add product [2, 20, 23] Add product [2, 20, 24] ------ Secondary of degree 26 : We must search 85 secondaries invariants Correction by adding the space spanned by secondaries of degree 12 Research of product of secondaries of degree smaller Add product [2, 17, 28] Add product [2, 18, 28] Add product [3, 14, 28] Add product [3, 15, 28] Add product [3, 16, 28] Add product [2, 2, 11, 28] Add product [2, 2, 12, 28] Add product [2, 2, 13, 28] Add product [4, 11, 28] Add product [4, 12, 28] Add product [4, 13, 28] Add product [5, 11, 28] Add product [5, 12, 28] Add product [5, 13, 28] Add product [2, 3, 9, 28] Add product [7, 10, 28] Add product [2, 4, 6, 28] Add product [2, 5, 7, 28] Add product [2, 3, 3, 3, 28] Add product [21, 28] Add product [2, 19, 25] Add product [2, 19, 26] Add product [2, 19, 27] Add product [2, 20, 25] Add product [2, 20, 26] Add product [2, 20, 27] Add product [3, 17, 25] Add product [3, 17, 26] Add product [3, 17, 27] Add product [3, 18, 25] Add product [3, 18, 26] Add product [3, 18, 27] Add product [2, 2, 14, 25] Add product [2, 2, 14, 26] Add product [2, 2, 14, 27] Add product [2, 2, 15, 25] Add product [2, 2, 15, 26] Add product [2, 2, 15, 27] Add product [2, 2, 16, 25] Add product [2, 2, 16, 26] Add product [2, 2, 16, 27] Add product [4, 14, 25] Add product [4, 14, 26] Add product [4, 14, 27] Add product [4, 15, 25] Add product [4, 15, 26] Add product [4, 15, 27] Add product [4, 16, 25] Add product [4, 16, 26] Add product [4, 16, 27] Add product [5, 14, 25] Add product [5, 14, 26] Add product [5, 14, 27] Add product [5, 15, 25] Add product [5, 15, 26] Add product [5, 15, 27] Add product [5, 16, 25] Add product [5, 16, 26] Add product [5, 16, 27] Add product [2, 3, 11, 25] Add product [2, 3, 11, 26] Add product [2, 3, 11, 27] Add product [2, 3, 12, 25] Add product [2, 3, 12, 26] Add product [2, 3, 12, 27] Add product [2, 3, 13, 25] Add product [2, 3, 13, 26] Add product [2, 3, 13, 27] Add product [6, 11, 25] Add product [6, 11, 26] Add product [6, 11, 27] Add product [6, 12, 25] Add product [6, 12, 26] Add product [6, 12, 27] Add product [6, 13, 25] Add product [6, 13, 26] Add product [6, 13, 27] Add product [7, 11, 25] Add product [7, 11, 26] Add product [7, 11, 27] Add product [7, 12, 25] Add product [7, 12, 26] Add product [7, 12, 27] Add product [7, 13, 25] Add product [7, 13, 26] ------ Secondary of degree 27 : We must search 79 secondaries invariants Correction by adding the space spanned by secondaries of degree 13 Research of product of secondaries of degree smaller Add product [2, 19, 28] Add product [2, 20, 28] Add product [3, 17, 28] Add product [3, 18, 28] Add product [2, 2, 14, 28] Add product [2, 2, 15, 28] Add product [2, 2, 16, 28] Add product [4, 14, 28] Add product [4, 15, 28] Add product [4, 16, 28] Add product [5, 14, 28] Add product [5, 15, 28] Add product [5, 16, 28] Add product [2, 3, 11, 28] Add product [2, 3, 12, 28] Add product [2, 3, 13, 28] Add product [6, 11, 28] Add product [6, 12, 28] Add product [6, 13, 28] Add product [7, 11, 28] Add product [7, 12, 28] Add product [7, 13, 28] Add product [2, 5, 9, 28] Add product [10, 10, 28] Add product [2, 2, 3, 6, 28] Add product [2, 2, 3, 7, 28] Add product [3, 3, 3, 3, 28] Add product [22, 28] Add product [2, 21, 25] Add product [2, 21, 26] Add product [2, 21, 27] Add product [3, 19, 25] Add product [3, 19, 26] Add product [3, 19, 27] Add product [3, 20, 25] Add product [3, 20, 26] Add product [3, 20, 27] Add product [2, 2, 17, 25] Add product [2, 2, 17, 26] Add product [2, 2, 17, 27] Add product [2, 2, 18, 25] Add product [2, 2, 18, 26] Add product [2, 2, 18, 27] Add product [4, 17, 25] Add product [4, 17, 26] Add product [4, 17, 27] Add product [4, 18, 25] Add product [4, 18, 26] Add product [4, 18, 27] Add product [5, 17, 25] Add product [5, 17, 26] Add product [5, 17, 27] Add product [5, 18, 25] Add product [5, 18, 26] Add product [5, 18, 27] Add product [2, 3, 14, 25] Add product [2, 3, 14, 26] Add product [2, 3, 14, 27] Add product [2, 3, 15, 25] Add product [2, 3, 15, 26] Add product [2, 3, 15, 27] Add product [2, 3, 16, 25] Add product [2, 3, 16, 26] Add product [2, 3, 16, 27] Add product [6, 14, 25] Add product [6, 14, 26] Add product [6, 14, 27] Add product [6, 15, 25] Add product [6, 15, 26] Add product [6, 15, 27] Add product [6, 16, 25] Add product [6, 16, 26] Add product [6, 16, 27] Add product [7, 14, 25] Add product [7, 14, 26] Add product [7, 14, 27] Add product [7, 15, 25] Add product [7, 15, 26] Add product [7, 15, 27] ------ Secondary of degree 28 : We must search 80 secondaries invariants Correction by adding the space spanned by secondaries of degree 14 Correction by adding the space spanned by secondaries of degree 0 Research of product of secondaries of degree smaller Add product [2, 21, 28] Add product [3, 19, 28] Add product [3, 20, 28] Add product [2, 2, 17, 28] Add product [2, 2, 18, 28] Add product [4, 17, 28] Add product [4, 18, 28] Add product [5, 17, 28] Add product [5, 18, 28] Add product [2, 3, 14, 28] Add product [2, 3, 15, 28] Add product [2, 3, 16, 28] Add product [6, 14, 28] Add product [6, 15, 28] Add product [6, 16, 28] Add product [7, 14, 28] Add product [7, 15, 28] Add product [7, 16, 28] Add product [2, 4, 11, 28] Add product [2, 4, 12, 28] Add product [2, 4, 13, 28] Add product [2, 5, 11, 28] Add product [2, 5, 12, 28] Add product [2, 5, 13, 28] Add product [3, 3, 11, 28] Add product [10, 13, 28] Add product [3, 5, 9, 28] Add product [2, 2, 3, 3, 3, 28] Add product [23, 28] Add product [24, 28] Add product [2, 22, 25] Add product [2, 22, 26] Add product [2, 22, 27] Add product [3, 21, 25] Add product [3, 21, 26] Add product [3, 21, 27] Add product [2, 2, 19, 25] Add product [2, 2, 19, 26] Add product [2, 2, 19, 27] Add product [2, 2, 20, 25] Add product [2, 2, 20, 26] Add product [2, 2, 20, 27] Add product [4, 19, 25] Add product [4, 19, 26] Add product [4, 19, 27] Add product [4, 20, 25] Add product [4, 20, 26] Add product [4, 20, 27] Add product [5, 19, 25] Add product [5, 19, 26] Add product [5, 19, 27] Add product [5, 20, 25] Add product [5, 20, 26] Add product [5, 20, 27] Add product [2, 3, 17, 25] Add product [2, 3, 17, 26] Add product [2, 3, 17, 27] Add product [2, 3, 18, 25] Add product [2, 3, 18, 26] Add product [2, 3, 18, 27] Add product [6, 17, 25] Add product [6, 17, 26] Add product [6, 17, 27] Add product [6, 18, 25] Add product [6, 18, 26] Add product [6, 18, 27] Add product [7, 17, 25] Add product [7, 17, 26] Add product [7, 17, 27] Add product [7, 18, 25] Add product [7, 18, 26] Add product [7, 18, 27] Add product [2, 4, 14, 25] Add product [2, 4, 14, 26] Add product [2, 4, 14, 27] Add product [2, 4, 15, 25] Add product [2, 4, 15, 26] Add product [2, 4, 15, 27] Add product [2, 4, 16, 25] Add product [2, 4, 16, 26] ------ Secondary of degree 29 : We must search 71 secondaries invariants Correction by adding the space spanned by secondaries of degree 15 Correction by adding the space spanned by secondaries of degree 1 Research of product of secondaries of degree smaller Add product [2, 22, 28] Add product [3, 21, 28] Add product [2, 2, 19, 28] Add product [2, 2, 20, 28] Add product [4, 19, 28] Add product [4, 20, 28] Add product [5, 19, 28] Add product [5, 20, 28] Add product [2, 3, 17, 28] Add product [2, 3, 18, 28] Add product [6, 17, 28] Add product [6, 18, 28] Add product [7, 17, 28] Add product [7, 18, 28] Add product [2, 4, 14, 28] Add product [2, 4, 15, 28] Add product [2, 4, 16, 28] Add product [2, 5, 14, 28] Add product [2, 5, 15, 28] Add product [2, 5, 16, 28] Add product [3, 3, 14, 28] Add product [3, 3, 15, 28] Add product [3, 3, 16, 28] Add product [8, 14, 28] Add product [8, 15, 28] Add product [8, 16, 28] Add product [9, 14, 28] Add product [9, 15, 28] Add product [9, 16, 28] Add product [10, 14, 28] Add product [10, 16, 28] Add product [2, 6, 11, 28] Add product [2, 6, 12, 28] Add product [2, 6, 13, 28] Add product [2, 7, 11, 28] Add product [2, 3, 3, 3, 3, 28] Add product [25, 28] Add product [26, 28] Add product [27, 28] Add product [2, 23, 25] Add product [2, 23, 26] Add product [2, 23, 27] Add product [2, 24, 25] Add product [2, 24, 26] Add product [2, 24, 27] Add product [3, 22, 25] Add product [3, 22, 26] Add product [3, 22, 27] Add product [2, 2, 21, 25] Add product [2, 2, 21, 26] Add product [2, 2, 21, 27] Add product [4, 21, 25] Add product [4, 21, 26] Add product [4, 21, 27] Add product [5, 21, 25] Add product [5, 21, 26] Add product [5, 21, 27] Add product [2, 3, 19, 25] Add product [2, 3, 19, 26] Add product [2, 3, 19, 27] Add product [2, 3, 20, 25] Add product [2, 3, 20, 26] Add product [2, 3, 20, 27] Add product [6, 19, 25] Add product [6, 19, 26] Add product [6, 19, 27] Add product [6, 20, 25] Add product [6, 20, 26] Add product [6, 20, 27] Add product [7, 19, 25] Add product [7, 19, 26] ------ Secondary of degree 30 : We must search 70 secondaries invariants Correction by adding the space spanned by secondaries of degree 16 Correction by adding the space spanned by secondaries of degree 2 Research of product of secondaries of degree smaller Add product [2, 23, 28] Add product [2, 24, 28] Add product [3, 22, 28] Add product [2, 2, 21, 28] Add product [4, 21, 28] Add product [5, 21, 28] Add product [2, 3, 19, 28] Add product [2, 3, 20, 28] Add product [6, 19, 28] Add product [6, 20, 28] Add product [7, 19, 28] Add product [7, 20, 28] Add product [2, 4, 17, 28] Add product [2, 4, 18, 28] Add product [2, 5, 17, 28] Add product [2, 5, 18, 28] Add product [3, 3, 17, 28] Add product [3, 3, 18, 28] Add product [8, 17, 28] Add product [8, 18, 28] Add product [9, 17, 28] Add product [9, 18, 28] Add product [10, 17, 28] Add product [10, 18, 28] Add product [2, 6, 14, 28] Add product [2, 6, 15, 28] Add product [2, 6, 16, 28] Add product [2, 7, 14, 28] Add product [2, 7, 15, 28] Add product [2, 7, 16, 28] Add product [3, 5, 14, 28] Add product [3, 5, 15, 28] Add product [3, 5, 16, 28] Add product [2, 2, 3, 14, 28] Add product [2, 2, 3, 15, 28] Add product [2, 2, 3, 16, 28] Add product [2, 10, 13, 28] Add product [3, 6, 11, 28] Add product [3, 6, 12, 28] Add product [3, 6, 13, 28] Add product [3, 3, 3, 3, 3, 28] Add product [28, 28] Add product [2, 25, 25] Add product [2, 25, 26] Add product [2, 25, 27] Add product [2, 26, 26] Add product [2, 26, 27] Add product [2, 27, 27] Add product [3, 24, 25] Add product [3, 24, 26] Add product [3, 24, 27] Add product [2, 2, 22, 25] Add product [2, 2, 22, 26] Add product [2, 2, 22, 27] Add product [4, 22, 25] Add product [4, 22, 26] Add product [4, 22, 27] Add product [5, 22, 25] Add product [5, 22, 26] Add product [5, 22, 27] Add product [2, 3, 21, 25] Add product [2, 3, 21, 26] Add product [2, 3, 21, 27] Add product [6, 21, 25] Add product [6, 21, 26] Add product [6, 21, 27] Add product [7, 21, 25] Add product [7, 21, 26] Add product [7, 21, 27] Add product [2, 4, 19, 25] ------ Secondary of degree 31 : We must search 61 secondaries invariants Correction by adding the space spanned by secondaries of degree 17 Correction by adding the space spanned by secondaries of degree 3 Research of product of secondaries of degree smaller Add product [2, 25, 28] Add product [2, 26, 28] Add product [2, 27, 28] Add product [3, 24, 28] Add product [2, 2, 22, 28] Add product [4, 22, 28] Add product [5, 22, 28] Add product [2, 3, 21, 28] Add product [6, 21, 28] Add product [7, 21, 28] Add product [2, 4, 19, 28] Add product [2, 4, 20, 28] Add product [2, 5, 19, 28] Add product [2, 5, 20, 28] Add product [3, 3, 19, 28] Add product [3, 3, 20, 28] Add product [8, 19, 28] Add product [8, 20, 28] Add product [9, 19, 28] Add product [9, 20, 28] Add product [10, 19, 28] Add product [10, 20, 28] Add product [2, 6, 17, 28] Add product [2, 6, 18, 28] Add product [2, 7, 17, 28] Add product [2, 7, 18, 28] Add product [3, 5, 17, 28] Add product [3, 5, 18, 28] Add product [2, 2, 3, 17, 28] Add product [2, 2, 3, 18, 28] Add product [11, 17, 28] Add product [11, 18, 28] Add product [12, 17, 28] Add product [12, 18, 28] Add product [13, 17, 28] Add product [13, 18, 28] Add product [2, 8, 14, 28] Add product [2, 8, 15, 28] Add product [2, 8, 16, 28] Add product [2, 9, 14, 28] Add product [2, 9, 15, 28] Add product [2, 9, 16, 28] Add product [2, 10, 14, 28] Add product [2, 10, 16, 28] Add product [3, 6, 14, 28] Add product [3, 6, 15, 28] Add product [3, 6, 16, 28] Add product [3, 7, 14, 28] Add product [3, 7, 15, 28] Add product [3, 10, 13, 28] Add product [2, 2, 6, 11, 28] Add product [2, 2, 6, 12, 28] Add product [3, 25, 25] Add product [3, 25, 26] Add product [3, 25, 27] Add product [3, 26, 26] Add product [3, 26, 27] Add product [3, 27, 27] Add product [2, 2, 23, 25] Add product [2, 2, 23, 26] Add product [2, 2, 23, 27] ------ Secondary of degree 32 : We must search 58 secondaries invariants Correction by adding the space spanned by secondaries of degree 18 Correction by adding the space spanned by secondaries of degree 4 Research of product of secondaries of degree smaller Add product [2, 28, 28] Add product [3, 25, 28] Add product [3, 26, 28] Add product [3, 27, 28] Add product [2, 2, 23, 28] Add product [4, 23, 28] Add product [4, 24, 28] Add product [5, 24, 28] Add product [2, 3, 22, 28] Add product [6, 22, 28] Add product [7, 22, 28] Add product [2, 4, 21, 28] Add product [2, 5, 21, 28] Add product [3, 3, 21, 28] Add product [8, 21, 28] Add product [9, 21, 28] Add product [10, 21, 28] Add product [2, 6, 19, 28] Add product [2, 6, 20, 28] Add product [2, 7, 19, 28] Add product [2, 7, 20, 28] Add product [3, 5, 19, 28] Add product [3, 5, 20, 28] Add product [2, 2, 3, 19, 28] Add product [2, 2, 3, 20, 28] Add product [11, 19, 28] Add product [11, 20, 28] Add product [12, 19, 28] Add product [12, 20, 28] Add product [13, 19, 28] Add product [13, 20, 28] Add product [2, 8, 17, 28] Add product [2, 8, 18, 28] Add product [2, 9, 17, 28] Add product [2, 9, 18, 28] Add product [2, 10, 17, 28] Add product [2, 10, 18, 28] Add product [3, 6, 17, 28] Add product [3, 6, 18, 28] Add product [3, 7, 17, 28] Add product [3, 7, 18, 28] Add product [2, 2, 4, 17, 28] Add product [2, 2, 4, 18, 28] Add product [5, 5, 17, 28] Add product [5, 5, 18, 28] Add product [2, 3, 3, 17, 28] Add product [2, 3, 3, 18, 28] Add product [14, 17, 28] Add product [14, 18, 28] Add product [15, 17, 28] Add product [15, 18, 28] Add product [16, 17, 28] Add product [3, 9, 14, 28] Add product [3, 9, 15, 28] Add product [2, 2, 25, 25] Add product [2, 2, 25, 26] Add product [2, 2, 25, 27] Add product [2, 2, 26, 26] ------ Secondary of degree 33 : We must search 48 secondaries invariants Correction by adding the space spanned by secondaries of degree 19 Correction by adding the space spanned by secondaries of degree 5 Research of product of secondaries of degree smaller Add product [3, 28, 28] Add product [2, 2, 25, 28] Add product [2, 2, 26, 28] Add product [2, 2, 27, 28] Add product [4, 25, 28] Add product [4, 26, 28] Add product [4, 27, 28] Add product [5, 25, 28] Add product [5, 26, 28] Add product [5, 27, 28] Add product [6, 23, 28] Add product [6, 24, 28] Add product [7, 24, 28] Add product [2, 4, 22, 28] Add product [2, 5, 22, 28] Add product [3, 3, 22, 28] Add product [8, 22, 28] Add product [9, 22, 28] Add product [10, 22, 28] Add product [2, 6, 21, 28] Add product [2, 7, 21, 28] Add product [3, 5, 21, 28] Add product [2, 2, 3, 21, 28] Add product [11, 21, 28] Add product [12, 21, 28] Add product [13, 21, 28] Add product [2, 8, 19, 28] Add product [2, 8, 20, 28] Add product [2, 9, 19, 28] Add product [2, 9, 20, 28] Add product [2, 10, 19, 28] Add product [2, 10, 20, 28] Add product [3, 6, 19, 28] Add product [3, 6, 20, 28] Add product [3, 7, 19, 28] Add product [3, 7, 20, 28] Add product [2, 2, 4, 19, 28] Add product [2, 2, 4, 20, 28] Add product [5, 5, 19, 28] Add product [5, 5, 20, 28] Add product [2, 3, 3, 19, 28] Add product [2, 3, 3, 20, 28] Add product [14, 19, 28] Add product [14, 20, 28] Add product [15, 19, 28] Add product [15, 20, 28] Add product [16, 19, 28] Add product [16, 20, 28] ------ Secondary of degree 34 : We must search 45 secondaries invariants Correction by adding the space spanned by secondaries of degree 20 Correction by adding the space spanned by secondaries of degree 6 Research of product of secondaries of degree smaller Add product [2, 2, 28, 28] Add product [4, 28, 28] Add product [5, 28, 28] Add product [2, 3, 25, 28] Add product [2, 3, 26, 28] Add product [2, 3, 27, 28] Add product [6, 25, 28] Add product [6, 26, 28] Add product [6, 27, 28] Add product [7, 25, 28] Add product [7, 26, 28] Add product [7, 27, 28] Add product [2, 4, 23, 28] Add product [2, 5, 24, 28] Add product [3, 3, 24, 28] Add product [8, 23, 28] Add product [8, 24, 28] Add product [9, 24, 28] Add product [10, 23, 28] Add product [10, 24, 28] Add product [2, 6, 22, 28] Add product [2, 7, 22, 28] Add product [3, 5, 22, 28] Add product [2, 2, 3, 22, 28] Add product [11, 22, 28] Add product [12, 22, 28] Add product [13, 22, 28] Add product [2, 8, 21, 28] Add product [2, 9, 21, 28] Add product [2, 10, 21, 28] Add product [3, 6, 21, 28] Add product [3, 7, 21, 28] Add product [2, 2, 4, 21, 28] Add product [5, 5, 21, 28] Add product [2, 3, 3, 21, 28] Add product [14, 21, 28] Add product [15, 21, 28] Add product [16, 21, 28] Add product [2, 11, 19, 28] Add product [2, 11, 20, 28] Add product [2, 12, 19, 28] Add product [2, 12, 20, 28] Add product [2, 13, 19, 28] Add product [2, 13, 20, 28] Add product [3, 9, 19, 28] ------ Secondary of degree 35 : We must search 36 secondaries invariants Correction by adding the space spanned by secondaries of degree 21 Correction by adding the space spanned by secondaries of degree 7 Research of product of secondaries of degree smaller Add product [2, 3, 28, 28] Add product [6, 28, 28] Add product [7, 28, 28] Add product [2, 4, 25, 28] Add product [2, 4, 26, 28] Add product [2, 4, 27, 28] Add product [2, 5, 25, 28] Add product [2, 5, 26, 28] Add product [2, 5, 27, 28] Add product [3, 3, 25, 28] Add product [3, 3, 26, 28] Add product [3, 3, 27, 28] Add product [8, 25, 28] Add product [8, 26, 28] Add product [8, 27, 28] Add product [9, 25, 28] Add product [9, 26, 28] Add product [9, 27, 28] Add product [10, 25, 28] Add product [10, 26, 28] Add product [10, 27, 28] Add product [2, 6, 23, 28] Add product [2, 7, 24, 28] Add product [3, 5, 24, 28] Add product [11, 23, 28] Add product [11, 24, 28] Add product [12, 24, 28] Add product [13, 23, 28] Add product [13, 24, 28] Add product [2, 8, 22, 28] Add product [2, 9, 22, 28] Add product [2, 10, 22, 28] Add product [3, 6, 22, 28] Add product [3, 7, 22, 28] Add product [2, 2, 4, 22, 28] Add product [5, 5, 22, 28] ------ Secondary of degree 36 : We must search 33 secondaries invariants Correction by adding the space spanned by secondaries of degree 22 Correction by adding the space spanned by secondaries of degree 8 Research of product of secondaries of degree smaller Add product [2, 4, 28, 28] Add product [2, 5, 28, 28] Add product [3, 3, 28, 28] Add product [8, 28, 28] Add product [9, 28, 28] Add product [10, 28, 28] Add product [2, 6, 25, 28] Add product [2, 6, 26, 28] Add product [2, 6, 27, 28] Add product [2, 7, 25, 28] Add product [2, 7, 26, 28] Add product [2, 7, 27, 28] Add product [3, 5, 25, 28] Add product [3, 5, 26, 28] Add product [3, 5, 27, 28] Add product [2, 2, 3, 25, 28] Add product [2, 2, 3, 26, 28] Add product [2, 2, 3, 27, 28] Add product [11, 25, 28] Add product [11, 26, 28] Add product [11, 27, 28] Add product [12, 25, 28] Add product [12, 26, 28] Add product [12, 27, 28] Add product [13, 25, 28] Add product [13, 26, 28] Add product [13, 27, 28] Add product [2, 8, 23, 28] Add product [2, 9, 24, 28] Add product [2, 10, 23, 28] Add product [2, 10, 24, 28] Add product [3, 6, 24, 28] Add product [3, 7, 24, 28] ------ Secondary of degree 37 : We must search 25 secondaries invariants Correction by adding the space spanned by secondaries of degree 23 Correction by adding the space spanned by secondaries of degree 9 Research of product of secondaries of degree smaller Add product [2, 6, 28, 28] Add product [2, 7, 28, 28] Add product [3, 5, 28, 28] Add product [2, 2, 3, 28, 28] Add product [11, 28, 28] Add product [12, 28, 28] Add product [13, 28, 28] Add product [2, 8, 25, 28] Add product [2, 8, 26, 28] Add product [2, 8, 27, 28] Add product [2, 9, 25, 28] Add product [2, 9, 26, 28] Add product [2, 9, 27, 28] Add product [2, 10, 25, 28] Add product [2, 10, 26, 28] Add product [2, 10, 27, 28] Add product [3, 6, 25, 28] Add product [3, 6, 26, 28] Add product [3, 6, 27, 28] Add product [3, 7, 25, 28] Add product [3, 7, 26, 28] Add product [3, 7, 27, 28] Add product [2, 2, 4, 25, 28] Add product [2, 2, 4, 26, 28] Add product [2, 2, 4, 27, 28] ------ Secondary of degree 38 : We must search 22 secondaries invariants Correction by adding the space spanned by secondaries of degree 24 Correction by adding the space spanned by secondaries of degree 10 Research of product of secondaries of degree smaller Add product [2, 8, 28, 28] Add product [2, 9, 28, 28] Add product [2, 10, 28, 28] Add product [3, 6, 28, 28] Add product [3, 7, 28, 28] Add product [2, 2, 4, 28, 28] Add product [5, 5, 28, 28] Add product [2, 3, 3, 28, 28] Add product [14, 28, 28] Add product [15, 28, 28] Add product [16, 28, 28] Add product [2, 11, 25, 28] Add product [2, 11, 26, 28] Add product [2, 11, 27, 28] Add product [2, 12, 25, 28] Add product [2, 12, 26, 28] Add product [2, 12, 27, 28] Add product [2, 13, 25, 28] Add product [2, 13, 26, 28] Add product [2, 13, 27, 28] Add product [3, 9, 25, 28] Add product [3, 9, 26, 28] ------ Secondary of degree 39 : We must search 16 secondaries invariants Correction by adding the space spanned by secondaries of degree 25 Correction by adding the space spanned by secondaries of degree 11 Research of product of secondaries of degree smaller Add product [2, 11, 28, 28] Add product [2, 12, 28, 28] Add product [2, 13, 28, 28] Add product [3, 9, 28, 28] Add product [3, 10, 28, 28] Add product [2, 2, 6, 28, 28] Add product [2, 2, 7, 28, 28] Add product [4, 6, 28, 28] Add product [5, 7, 28, 28] Add product [3, 3, 3, 28, 28] Add product [17, 28, 28] Add product [18, 28, 28] Add product [2, 14, 25, 28] Add product [2, 14, 26, 28] Add product [2, 14, 27, 28] Add product [2, 15, 25, 28] ------ Secondary of degree 40 : We must search 14 secondaries invariants Correction by adding the space spanned by secondaries of degree 26 Correction by adding the space spanned by secondaries of degree 12 Research of product of secondaries of degree smaller Add product [2, 14, 28, 28] Add product [2, 15, 28, 28] Add product [2, 16, 28, 28] Add product [3, 11, 28, 28] Add product [3, 12, 28, 28] Add product [3, 13, 28, 28] Add product [2, 2, 8, 28, 28] Add product [2, 2, 9, 28, 28] Add product [2, 2, 10, 28, 28] Add product [4, 8, 28, 28] Add product [4, 10, 28, 28] Add product [5, 9, 28, 28] Add product [5, 10, 28, 28] Add product [2, 3, 6, 28, 28] ------ Secondary of degree 41 : We must search 9 secondaries invariants Correction by adding the space spanned by secondaries of degree 27 Correction by adding the space spanned by secondaries of degree 13 Research of product of secondaries of degree smaller Add product [2, 17, 28, 28] Add product [2, 18, 28, 28] Add product [3, 14, 28, 28] Add product [3, 15, 28, 28] Add product [3, 16, 28, 28] Add product [2, 2, 11, 28, 28] Add product [2, 2, 12, 28, 28] Add product [2, 2, 13, 28, 28] Add product [4, 11, 28, 28] ------ Secondary of degree 42 : We must search 8 secondaries invariants Correction by adding the space spanned by secondaries of degree 28 Correction by adding the space spanned by secondaries of degree 14 Correction by adding the space spanned by secondaries of degree 0 Research of product of secondaries of degree smaller Add product [2, 19, 28, 28] Add product [2, 20, 28, 28] Add product [3, 17, 28, 28] Add product [3, 18, 28, 28] Add product [2, 2, 14, 28, 28] Add product [2, 2, 15, 28, 28] Add product [2, 2, 16, 28, 28] Add product [4, 14, 28, 28] ------ Secondary of degree 43 : We must search 5 secondaries invariants Correction by adding the space spanned by secondaries of degree 29 Correction by adding the space spanned by secondaries of degree 15 Correction by adding the space spanned by secondaries of degree 1 Research of product of secondaries of degree smaller Add product [2, 21, 28, 28] Add product [3, 19, 28, 28] Add product [3, 20, 28, 28] Add product [2, 2, 17, 28, 28] Add product [2, 2, 18, 28, 28] ------ Secondary of degree 44 : We must search 4 secondaries invariants Correction by adding the space spanned by secondaries of degree 30 Correction by adding the space spanned by secondaries of degree 16 Correction by adding the space spanned by secondaries of degree 2 Research of product of secondaries of degree smaller Add product [2, 22, 28, 28] Add product [3, 21, 28, 28] Add product [2, 2, 19, 28, 28] Add product [2, 2, 20, 28, 28] ------ Secondary of degree 45 : We must search 2 secondaries invariants Correction by adding the space spanned by secondaries of degree 31 Correction by adding the space spanned by secondaries of degree 17 Correction by adding the space spanned by secondaries of degree 3 Research of product of secondaries of degree smaller Add product [2, 23, 28, 28] Add product [2, 24, 28, 28] ------ Secondary of degree 46 : We must search 2 secondaries invariants Correction by adding the space spanned by secondaries of degree 32 Correction by adding the space spanned by secondaries of degree 18 Correction by adding the space spanned by secondaries of degree 4 Research of product of secondaries of degree smaller Add product [2, 25, 28, 28] Add product [2, 26, 28, 28] ------ Secondary of degree 47 : We must search 1 secondaries invariants Correction by adding the space spanned by secondaries of degree 33 Correction by adding the space spanned by secondaries of degree 19 Correction by adding the space spanned by secondaries of degree 5 Research of product of secondaries of degree smaller Add product [2, 28, 28, 28] ------ Secondary of degree 48 : We must search 1 secondaries invariants Correction by adding the space spanned by secondaries of degree 34 Correction by adding the space spanned by secondaries of degree 20 Correction by adding the space spanned by secondaries of degree 6 Research of product of secondaries of degree smaller Add product [3, 28, 28, 28] ... sage: for i in range(49): print i," : ", I.irreducible_secondary_invariants_of_degree(i) ....: 0 : [[(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 1 : [] 2 : [[(1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 3 : [[(2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 4 : [[(3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 5 : [[(4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 6 : [[(5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 7 : [[(6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 8 : [[(7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 9 : [[(7, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 10 : [[(7, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 11 : [[(7, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 12 : [[(7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 13 : [[(12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(11, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 14 : [[(13, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(12, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)], [(11, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 15 : [[(13, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)]] 16 : [] 17 : [] 18 : [] 19 : [] 20 : [] 21 : [] 22 : [] 23 : [] 24 : [] 25 : [] 26 : [] 27 : [] 28 : [] 29 : [] 30 : [] 31 : [] 32 : [] 33 : [] 34 : [] 35 : [] 36 : [] 37 : [] 38 : [] 39 : [] 40 : [] 41 : [] 42 : [] 43 : [] 44 : [] 45 : [] 46 : [] 47 : [] 48 : []