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 : []