################

Для тестирования функции nTorsionPoints(n, a, b, q) 
можно пользоваться встроенной функцией division_points(n)

E = EllipticCurve(F, [a, b])
Origin = E(0)
Origin.division_points(n)

################


nTorsion_extension_deg(3, 3, 17, 23)
	d:  2

nTorsionPoints(3, 3, 17, 23)
[(0 : 1 : 0), (15 : 3*alpha + 17 : 1), (15 : 20*alpha + 6 : 1), (4 : 1 : 1), (4 : 22 : 1), (22*alpha + 4 : 10*alpha + 22 : 1), (22*alpha + 4 : 13*alpha + 1 : 1), (alpha : 13*alpha + 16 : 1), (alpha : 10*alpha + 7 : 1)]

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nTorsion_extension_deg(2, 1, 11, 41)
	d:  1

nTorsionPoints(2, 1, 11, 41)
[(0 : 1 : 0), (27 : 0 : 1), (11 : 0 : 1), (3 : 0 : 1)]

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nTorsion_extension_deg(5, 2, 21, 53)
d:  4

nTorsionPoints(5, 2, 21, 53)
[(0 : 1 : 0), (34 : 37*alpha^3 + 51*alpha^2 + 38*alpha + 12 : 1), (34 : 16*alpha^3 + 2*alpha^2 + 15*alpha + 41 : 1), (52 : 7*alpha^3 + 34*alpha^2 + 43*alpha + 8 : 1), (52 : 46*alpha^3 + 19*alpha^2 + 10*alpha + 45 : 1), (alpha : 10*alpha^2 + 18*alpha + 12 : 1), (alpha : 43*alpha^2 + 35*alpha + 41 : 1), (44*alpha^3 + 52*alpha^2 : 52*alpha^3 + 42*alpha^2 + 6*alpha + 3 : 1), (44*alpha^3 + 52*alpha^2 : alpha^3 + 11*alpha^2 + 47*alpha + 50 : 1), (27*alpha^3 + 10*alpha^2 + 22*alpha + 4 : 28*alpha^3 + 13*alpha^2 + 33*alpha + 10 : 1), (27*alpha^3 + 10*alpha^2 + 22*alpha + 4 : 25*alpha^3 + 40*alpha^2 + 20*alpha + 43 : 1), (2*alpha^3 + 8*alpha^2 + 50*alpha + 5 : 51*alpha^3 + 13*alpha^2 + 24*alpha + 6 : 1), (2*alpha^3 + 8*alpha^2 + 50*alpha + 5 : 2*alpha^3 + 40*alpha^2 + 29*alpha + 47 : 1), (37*alpha^3 + 51*alpha^2 + 37*alpha + 11 : 15*alpha^3 + 25*alpha^2 + 6*alpha + 2 : 1), (37*alpha^3 + 51*alpha^2 + 37*alpha + 11 : 38*alpha^3 + 28*alpha^2 + 47*alpha + 51 : 1), (38*alpha^3 + 51*alpha^2 + 4*alpha + 18 : 7*alpha^3 + 25*alpha^2 + 46*alpha + 16 : 1), (38*alpha^3 + 51*alpha^2 + 4*alpha + 18 : 46*alpha^3 + 28*alpha^2 + 7*alpha + 37 : 1), (26*alpha^3 + 43*alpha^2 + 31*alpha + 18 : 34*alpha^3 + 39*alpha^2 + 25*alpha + 9 : 1), (26*alpha^3 + 43*alpha^2 + 31*alpha + 18 : 19*alpha^3 + 14*alpha^2 + 28*alpha + 44 : 1), (22*alpha^3 + 48*alpha^2 + 52*alpha + 30 : 8*alpha^3 + alpha^2 + 28*alpha + 19 : 1), (22*alpha^3 + 48*alpha^2 + 52*alpha + 30 : 45*alpha^3 + 52*alpha^2 + 25*alpha + 34 : 1), (25*alpha^3 + 51*alpha^2 + 13*alpha + 41 : 25*alpha^3 + 44*alpha^2 + 22*alpha + 5 : 1), (25*alpha^3 + 51*alpha^2 + 13*alpha + 41 : 28*alpha^3 + 9*alpha^2 + 31*alpha + 48 : 1), (44*alpha^3 + 4*alpha^2 + 2*alpha + 52 : 10*alpha^3 + 9*alpha^2 + 51*alpha + 15 : 1), (44*alpha^3 + 4*alpha^2 + 2*alpha + 52 : 43*alpha^3 + 44*alpha^2 + 2*alpha + 38 : 1)]

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nTorsion_extension_deg(7, 1, 7, 11)
d:  21

nTorsionPoints(7, 1, 7, 11)
[(0 : 1 : 0), (alpha : 6*alpha^20 + alpha^17 + alpha^15 + 4*alpha^14 + 2*alpha^13 + 3*alpha^12 + 8*alpha^11 + 9*alpha^10 + 4*alpha^8 + 10*alpha^6 + 2*alpha^5 + 2*alpha^4 + 9*alpha^3 + 2*alpha^2 + 4*alpha : 1), (alpha : 5*alpha^20 + 10*alpha^17 + 10*alpha^15 + 7*alpha^14 + 9*alpha^13 + 8*alpha^12 + 3*alpha^11 + 2*alpha^10 + 7*alpha^8 + alpha^6 + 9*alpha^5 + 9*alpha^4 + 2*alpha^3 + 9*alpha^2 + 7*alpha : 1), (alpha^11 : 2*alpha^20 + 10*alpha^19 + 2*alpha^18 + 6*alpha^17 + 10*alpha^16 + 5*alpha^15 + 10*alpha^14 + 6*alpha^13 + alpha^12 + 2*alpha^11 + 10*alpha^10 + 10*alpha^9 + alpha^8 + 4*alpha^7 + 2*alpha^6 + 2*alpha^5 + alpha^4 + 5*alpha^3 + 4*alpha^2 + 3*alpha + 5 : 1), (alpha^11 : 9*alpha^20 + alpha^19 + 9*alpha^18 + 5*alpha^17 + alpha^16 + 6*alpha^15 + alpha^14 + 5*alpha^13 + 10*alpha^12 + 9*alpha^11 + alpha^10 + alpha^9 + 10*alpha^8 + 7*alpha^7 + 9*alpha^6 + 9*alpha^5 + 10*alpha^4 + 6*alpha^3 + 7*alpha^2 + 8*alpha + 6 : 1), (5*alpha^19 + 10*alpha^18 + 10*alpha^17 + 5*alpha^16 + 9*alpha^14 + 6*alpha^13 + 9*alpha^12 + 3*alpha^11 + 9*alpha^10 + 9*alpha^9 + 7*alpha^7 + 8*alpha^5 + 8*alpha^4 + 4*alpha^3 + 4*alpha : 10*alpha^20 + 5*alpha^19 + 9*alpha^18 + alpha^17 + 4*alpha^16 + 7*alpha^15 + 7*alpha^14 + 6*alpha^13 + 9*alpha^12 + 3*alpha^11 + 10*alpha^9 + 3*alpha^8 + 9*alpha^7 + 7*alpha^6 + 3*alpha^5 + 7*alpha^4 + 4*alpha^3 + 7 : 1), (5*alpha^19 + 10*alpha^18 + 10*alpha^17 + 5*alpha^16 + 9*alpha^14 + 6*alpha^13 + 9*alpha^12 + 3*alpha^11 + 9*alpha^10 + 9*alpha^9 + 7*alpha^7 + 8*alpha^5 + 8*alpha^4 + 4*alpha^3 + 4*alpha : alpha^20 + 6*alpha^19 + 2*alpha^18 + 10*alpha^17 + 7*alpha^16 + 4*alpha^15 + 4*alpha^14 + 5*alpha^13 + 2*alpha^12 + 8*alpha^11 + alpha^9 + 8*alpha^8 + 2*alpha^7 + 4*alpha^6 + 8*alpha^5 + 4*alpha^4 + 7*alpha^3 + 4 : 1), (9*alpha^19 + 4*alpha^18 + 6*alpha^17 + 7*alpha^16 + 5*alpha^15 + 9*alpha^14 + 9*alpha^12 + 4*alpha^11 + 7*alpha^10 + 7*alpha^9 + 10*alpha^8 + 9*alpha^7 + 5*alpha^6 + 5*alpha^5 + alpha^4 + 6*alpha^3 + 9*alpha^2 + 8*alpha + 3 : 5*alpha^20 + alpha^19 + alpha^18 + 10*alpha^17 + 6*alpha^16 + 5*alpha^15 + 8*alpha^14 + 10*alpha^12 + alpha^10 + 6*alpha^8 + 6*alpha^7 + 8*alpha^6 + 10*alpha^5 + 2*alpha^4 + 2*alpha^3 + 3*alpha^2 + 7*alpha + 3 : 1), (9*alpha^19 + 4*alpha^18 + 6*alpha^17 + 7*alpha^16 + 5*alpha^15 + 9*alpha^14 + 9*alpha^12 + 4*alpha^11 + 7*alpha^10 + 7*alpha^9 + 10*alpha^8 + 9*alpha^7 + 5*alpha^6 + 5*alpha^5 + alpha^4 + 6*alpha^3 + 9*alpha^2 + 8*alpha + 3 : 6*alpha^20 + 10*alpha^19 + 10*alpha^18 + alpha^17 + 5*alpha^16 + 6*alpha^15 + 3*alpha^14 + alpha^12 + 10*alpha^10 + 5*alpha^8 + 5*alpha^7 + 3*alpha^6 + alpha^5 + 9*alpha^4 + 9*alpha^3 + 8*alpha^2 + 4*alpha + 8 : 1), (3*alpha^19 + 6*alpha^18 + 10*alpha^17 + 5*alpha^16 + 3*alpha^15 + 4*alpha^14 + 5*alpha^13 + alpha^12 + 5*alpha^10 + 4*alpha^9 + 8*alpha^8 + alpha^7 + 9*alpha^6 + 8*alpha^5 + 3*alpha^4 + 4*alpha^3 + 10*alpha^2 + 8*alpha + 2 : 9*alpha^19 + 7*alpha^18 + 8*alpha^17 + 4*alpha^16 + 9*alpha^15 + alpha^14 + 4*alpha^13 + 3*alpha^12 + 4*alpha^10 + alpha^9 + 2*alpha^8 + 3*alpha^7 + 5*alpha^6 + 2*alpha^5 + 9*alpha^4 + alpha^3 + 8*alpha^2 + 2*alpha + 3 : 1), (3*alpha^19 + 6*alpha^18 + 10*alpha^17 + 5*alpha^16 + 3*alpha^15 + 4*alpha^14 + 5*alpha^13 + alpha^12 + 5*alpha^10 + 4*alpha^9 + 8*alpha^8 + alpha^7 + 9*alpha^6 + 8*alpha^5 + 3*alpha^4 + 4*alpha^3 + 10*alpha^2 + 8*alpha + 2 : 2*alpha^19 + 4*alpha^18 + 3*alpha^17 + 7*alpha^16 + 2*alpha^15 + 10*alpha^14 + 7*alpha^13 + 8*alpha^12 + 7*alpha^10 + 10*alpha^9 + 9*alpha^8 + 8*alpha^7 + 6*alpha^6 + 9*alpha^5 + 2*alpha^4 + 10*alpha^3 + 3*alpha^2 + 9*alpha + 8 : 1), (5*alpha^20 + 3*alpha^19 + 9*alpha^18 + alpha^15 + 9*alpha^14 + 5*alpha^13 + 2*alpha^12 + 2*alpha^10 + alpha^9 + 8*alpha^8 + 4*alpha^7 + 8*alpha^6 + 8*alpha^5 + 10*alpha^4 + 9*alpha^3 + 2*alpha^2 + 6*alpha : 8*alpha^20 + 2*alpha^19 + 3*alpha^17 + 3*alpha^16 + 6*alpha^15 + 6*alpha^14 + 8*alpha^13 + 3*alpha^11 + 8*alpha^10 + alpha^9 + 5*alpha^8 + 2*alpha^7 + 5*alpha^6 + 2*alpha^5 + 10*alpha^4 + 4*alpha^3 + 3*alpha^2 + 2*alpha + 5 : 1), (5*alpha^20 + 3*alpha^19 + 9*alpha^18 + alpha^15 + 9*alpha^14 + 5*alpha^13 + 2*alpha^12 + 2*alpha^10 + alpha^9 + 8*alpha^8 + 4*alpha^7 + 8*alpha^6 + 8*alpha^5 + 10*alpha^4 + 9*alpha^3 + 2*alpha^2 + 6*alpha : 3*alpha^20 + 9*alpha^19 + 8*alpha^17 + 8*alpha^16 + 5*alpha^15 + 5*alpha^14 + 3*alpha^13 + 8*alpha^11 + 3*alpha^10 + 10*alpha^9 + 6*alpha^8 + 9*alpha^7 + 6*alpha^6 + 9*alpha^5 + alpha^4 + 7*alpha^3 + 8*alpha^2 + 9*alpha + 6 : 1), (8*alpha^20 + 7*alpha^19 + 6*alpha^18 + 8*alpha^17 + 6*alpha^14 + alpha^13 + 3*alpha^12 + 7*alpha^11 + 7*alpha^10 + 9*alpha^9 + 10*alpha^8 + 5*alpha^7 + 7*alpha^6 + 3*alpha^5 + alpha^3 + 4*alpha^2 + 3*alpha : 2*alpha^20 + 6*alpha^19 + 3*alpha^18 + 2*alpha^17 + 5*alpha^16 + alpha^15 + 8*alpha^14 + 2*alpha^13 + 8*alpha^12 + 3*alpha^10 + 8*alpha^8 + 9*alpha^7 + alpha^6 + 3*alpha^5 + 6*alpha^4 + 8*alpha^3 + alpha^2 + 9*alpha + 2 : 1), (8*alpha^20 + 7*alpha^19 + 6*alpha^18 + 8*alpha^17 + 6*alpha^14 + alpha^13 + 3*alpha^12 + 7*alpha^11 + 7*alpha^10 + 9*alpha^9 + 10*alpha^8 + 5*alpha^7 + 7*alpha^6 + 3*alpha^5 + alpha^3 + 4*alpha^2 + 3*alpha : 9*alpha^20 + 5*alpha^19 + 8*alpha^18 + 9*alpha^17 + 6*alpha^16 + 10*alpha^15 + 3*alpha^14 + 9*alpha^13 + 3*alpha^12 + 8*alpha^10 + 3*alpha^8 + 2*alpha^7 + 10*alpha^6 + 8*alpha^5 + 5*alpha^4 + 3*alpha^3 + 10*alpha^2 + 2*alpha + 9 : 1), (9*alpha^20 + 4*alpha^18 + 10*alpha^17 + 3*alpha^16 + 9*alpha^13 + 5*alpha^12 + 6*alpha^11 + 3*alpha^10 + 2*alpha^9 + 8*alpha^8 + 7*alpha^7 + 9*alpha^6 + 10*alpha^5 + alpha^4 + 9*alpha^3 + 8*alpha^2 + 10*alpha + 10 : 5*alpha^20 + alpha^18 + 8*alpha^17 + 9*alpha^16 + 5*alpha^13 + 4*alpha^12 + 7*alpha^11 + 9*alpha^10 + 6*alpha^9 + 2*alpha^8 + 10*alpha^7 + 5*alpha^6 + 8*alpha^5 + 3*alpha^4 + 5*alpha^3 + 2*alpha^2 + 8*alpha + 5 : 1), (9*alpha^20 + 4*alpha^18 + 10*alpha^17 + 3*alpha^16 + 9*alpha^13 + 5*alpha^12 + 6*alpha^11 + 3*alpha^10 + 2*alpha^9 + 8*alpha^8 + 7*alpha^7 + 9*alpha^6 + 10*alpha^5 + alpha^4 + 9*alpha^3 + 8*alpha^2 + 10*alpha + 10 : 6*alpha^20 + 10*alpha^18 + 3*alpha^17 + 2*alpha^16 + 6*alpha^13 + 7*alpha^12 + 4*alpha^11 + 2*alpha^10 + 5*alpha^9 + 9*alpha^8 + alpha^7 + 6*alpha^6 + 3*alpha^5 + 8*alpha^4 + 6*alpha^3 + 9*alpha^2 + 3*alpha + 6 : 1), (3*alpha^20 + 9*alpha^19 + 7*alpha^18 + alpha^17 + 5*alpha^16 + 5*alpha^15 + 8*alpha^14 + 5*alpha^13 + 8*alpha^12 + 10*alpha^11 + 7*alpha^9 + 6*alpha^8 + 10*alpha^7 + 6*alpha^6 + 3*alpha^5 + 3*alpha^4 + 7*alpha^3 + 8*alpha + 9 : 10*alpha^20 + 3*alpha^19 + alpha^18 + 10*alpha^17 + 9*alpha^16 + 9*alpha^15 + 9*alpha^14 + 10*alpha^13 + 5*alpha^12 + 4*alpha^11 + 8*alpha^10 + 9*alpha^9 + 7*alpha^8 + 3*alpha^7 + 3*alpha^6 + 8*alpha^5 + 6*alpha^4 + 10*alpha^3 + 7*alpha^2 + 4*alpha + 7 : 1), (3*alpha^20 + 9*alpha^19 + 7*alpha^18 + alpha^17 + 5*alpha^16 + 5*alpha^15 + 8*alpha^14 + 5*alpha^13 + 8*alpha^12 + 10*alpha^11 + 7*alpha^9 + 6*alpha^8 + 10*alpha^7 + 6*alpha^6 + 3*alpha^5 + 3*alpha^4 + 7*alpha^3 + 8*alpha + 9 : alpha^20 + 8*alpha^19 + 10*alpha^18 + alpha^17 + 2*alpha^16 + 2*alpha^15 + 2*alpha^14 + alpha^13 + 6*alpha^12 + 7*alpha^11 + 3*alpha^10 + 2*alpha^9 + 4*alpha^8 + 8*alpha^7 + 8*alpha^6 + 3*alpha^5 + 5*alpha^4 + alpha^3 + 4*alpha^2 + 7*alpha + 4 : 1), (4*alpha^20 + 5*alpha^19 + alpha^17 + 10*alpha^16 + 9*alpha^15 + 6*alpha^14 + 5*alpha^13 + 7*alpha^12 + 4*alpha^11 + 7*alpha^10 + 4*alpha^9 + 5*alpha^8 + 10*alpha^7 + 2*alpha^6 + 10*alpha^4 + 3*alpha^3 + alpha^2 + 7*alpha + 8 : 7*alpha^20 + 8*alpha^19 + 10*alpha^18 + 6*alpha^17 + 4*alpha^16 + 7*alpha^15 + 8*alpha^14 + 10*alpha^13 + 8*alpha^12 + alpha^11 + 9*alpha^10 + 10*alpha^8 + 7*alpha^7 + 2*alpha^6 + 9*alpha^5 + 2*alpha^4 + 10*alpha^3 + 9*alpha^2 + 9*alpha : 1), (4*alpha^20 + 5*alpha^19 + alpha^17 + 10*alpha^16 + 9*alpha^15 + 6*alpha^14 + 5*alpha^13 + 7*alpha^12 + 4*alpha^11 + 7*alpha^10 + 4*alpha^9 + 5*alpha^8 + 10*alpha^7 + 2*alpha^6 + 10*alpha^4 + 3*alpha^3 + alpha^2 + 7*alpha + 8 : 4*alpha^20 + 3*alpha^19 + alpha^18 + 5*alpha^17 + 7*alpha^16 + 4*alpha^15 + 3*alpha^14 + alpha^13 + 3*alpha^12 + 10*alpha^11 + 2*alpha^10 + alpha^8 + 4*alpha^7 + 9*alpha^6 + 2*alpha^5 + 9*alpha^4 + alpha^3 + 2*alpha^2 + 2*alpha : 1), (9*alpha^20 + 7*alpha^19 + 7*alpha^18 + 8*alpha^17 + 7*alpha^16 + 3*alpha^15 + 6*alpha^14 + 10*alpha^13 + 4*alpha^12 + 4*alpha^11 + 4*alpha^10 + 8*alpha^9 + 10*alpha^8 + 10*alpha^7 + 8*alpha^6 + 5*alpha^5 + 7*alpha^4 + 2*alpha^2 + 6*alpha + 8 : 6*alpha^20 + 5*alpha^19 + 3*alpha^18 + 2*alpha^17 + alpha^16 + 9*alpha^15 + 3*alpha^14 + 8*alpha^12 + 4*alpha^11 + 2*alpha^10 + 4*alpha^9 + 9*alpha^8 + 7*alpha^7 + 6*alpha^6 + 5*alpha^5 + alpha^4 + alpha^3 + 5*alpha + 7 : 1), (9*alpha^20 + 7*alpha^19 + 7*alpha^18 + 8*alpha^17 + 7*alpha^16 + 3*alpha^15 + 6*alpha^14 + 10*alpha^13 + 4*alpha^12 + 4*alpha^11 + 4*alpha^10 + 8*alpha^9 + 10*alpha^8 + 10*alpha^7 + 8*alpha^6 + 5*alpha^5 + 7*alpha^4 + 2*alpha^2 + 6*alpha + 8 : 5*alpha^20 + 6*alpha^19 + 8*alpha^18 + 9*alpha^17 + 10*alpha^16 + 2*alpha^15 + 8*alpha^14 + 3*alpha^12 + 7*alpha^11 + 9*alpha^10 + 7*alpha^9 + 2*alpha^8 + 4*alpha^7 + 5*alpha^6 + 6*alpha^5 + 10*alpha^4 + 10*alpha^3 + 6*alpha + 4 : 1), (2*alpha^20 + 8*alpha^19 + alpha^18 + 2*alpha^17 + 3*alpha^16 + 8*alpha^15 + 7*alpha^14 + 8*alpha^13 + 5*alpha^12 + 5*alpha^11 + 3*alpha^10 + 5*alpha^9 + 6*alpha^8 + 3*alpha^7 + 4*alpha^6 + 4*alpha^5 + 7*alpha^4 + 9*alpha^3 + 4*alpha^2 + 4*alpha + 8 : 6*alpha^20 + 2*alpha^19 + 3*alpha^18 + 6*alpha^17 + 9*alpha^16 + 2*alpha^15 + 10*alpha^14 + 2*alpha^13 + 4*alpha^12 + 4*alpha^11 + 9*alpha^10 + 4*alpha^9 + 7*alpha^8 + 9*alpha^7 + alpha^6 + alpha^5 + 10*alpha^4 + 5*alpha^3 + alpha^2 + alpha + 10 : 1), (2*alpha^20 + 8*alpha^19 + alpha^18 + 2*alpha^17 + 3*alpha^16 + 8*alpha^15 + 7*alpha^14 + 8*alpha^13 + 5*alpha^12 + 5*alpha^11 + 3*alpha^10 + 5*alpha^9 + 6*alpha^8 + 3*alpha^7 + 4*alpha^6 + 4*alpha^5 + 7*alpha^4 + 9*alpha^3 + 4*alpha^2 + 4*alpha + 8 : 5*alpha^20 + 9*alpha^19 + 8*alpha^18 + 5*alpha^17 + 2*alpha^16 + 9*alpha^15 + alpha^14 + 9*alpha^13 + 7*alpha^12 + 7*alpha^11 + 2*alpha^10 + 7*alpha^9 + 4*alpha^8 + 2*alpha^7 + 10*alpha^6 + 10*alpha^5 + alpha^4 + 6*alpha^3 + 10*alpha^2 + 10*alpha + 1 : 1), (2*alpha^20 + 3*alpha^19 + 4*alpha^18 + 2*alpha^17 + 4*alpha^16 + 10*alpha^15 + 3*alpha^14 + 10*alpha^13 + 2*alpha^12 + 5*alpha^11 + 4*alpha^10 + 8*alpha^9 + alpha^8 + 6*alpha^7 + 5*alpha^6 + 2*alpha^5 + alpha^4 + 7*alpha^3 + 6*alpha^2 + 6*alpha + 7 : 5*alpha^20 + alpha^19 + 5*alpha^18 + 9*alpha^17 + 3*alpha^16 + alpha^15 + alpha^14 + 2*alpha^13 + 6*alpha^12 + 4*alpha^10 + 8*alpha^9 + 3*alpha^8 + 6*alpha^7 + 8*alpha^6 + 3*alpha^5 + 8*alpha^4 + 2*alpha^3 + 10*alpha^2 + 5*alpha : 1), (2*alpha^20 + 3*alpha^19 + 4*alpha^18 + 2*alpha^17 + 4*alpha^16 + 10*alpha^15 + 3*alpha^14 + 10*alpha^13 + 2*alpha^12 + 5*alpha^11 + 4*alpha^10 + 8*alpha^9 + alpha^8 + 6*alpha^7 + 5*alpha^6 + 2*alpha^5 + alpha^4 + 7*alpha^3 + 6*alpha^2 + 6*alpha + 7 : 6*alpha^20 + 10*alpha^19 + 6*alpha^18 + 2*alpha^17 + 8*alpha^16 + 10*alpha^15 + 10*alpha^14 + 9*alpha^13 + 5*alpha^12 + 7*alpha^10 + 3*alpha^9 + 8*alpha^8 + 5*alpha^7 + 3*alpha^6 + 8*alpha^5 + 3*alpha^4 + 9*alpha^3 + alpha^2 + 6*alpha : 1), (3*alpha^20 + 10*alpha^19 + 3*alpha^18 + 5*alpha^17 + 3*alpha^16 + 5*alpha^15 + 5*alpha^13 + 2*alpha^11 + 3*alpha^10 + 9*alpha^8 + 8*alpha^7 + 6*alpha^6 + 4*alpha^5 + 8*alpha^4 + 5*alpha^3 + 7*alpha^2 + 5*alpha + 7 : 7*alpha^20 + 7*alpha^19 + 6*alpha^18 + 9*alpha^17 + 4*alpha^16 + alpha^14 + 5*alpha^13 + alpha^12 + 8*alpha^11 + 5*alpha^10 + 3*alpha^9 + 4*alpha^8 + 8*alpha^7 + 5*alpha^6 + 5*alpha^5 + 7*alpha^4 + 8*alpha^3 + 9*alpha^2 + 10*alpha + 8 : 1), (3*alpha^20 + 10*alpha^19 + 3*alpha^18 + 5*alpha^17 + 3*alpha^16 + 5*alpha^15 + 5*alpha^13 + 2*alpha^11 + 3*alpha^10 + 9*alpha^8 + 8*alpha^7 + 6*alpha^6 + 4*alpha^5 + 8*alpha^4 + 5*alpha^3 + 7*alpha^2 + 5*alpha + 7 : 4*alpha^20 + 4*alpha^19 + 5*alpha^18 + 2*alpha^17 + 7*alpha^16 + 10*alpha^14 + 6*alpha^13 + 10*alpha^12 + 3*alpha^11 + 6*alpha^10 + 8*alpha^9 + 7*alpha^8 + 3*alpha^7 + 6*alpha^6 + 6*alpha^5 + 4*alpha^4 + 3*alpha^3 + 2*alpha^2 + alpha + 3 : 1), (2*alpha^20 + 3*alpha^19 + 6*alpha^18 + alpha^17 + 7*alpha^16 + 5*alpha^15 + 6*alpha^14 + 4*alpha^13 + 7*alpha^12 + 7*alpha^11 + alpha^10 + 7*alpha^9 + 10*alpha^8 + alpha^7 + 8*alpha^6 + 2*alpha^5 + 3*alpha^4 + 8*alpha^3 + 5*alpha^2 + 10*alpha + 6 : 2*alpha^20 + 5*alpha^19 + 3*alpha^18 + 3*alpha^16 + 8*alpha^15 + 6*alpha^14 + alpha^13 + 5*alpha^12 + 6*alpha^11 + 10*alpha^10 + 2*alpha^9 + 10*alpha^8 + 9*alpha^7 + 4*alpha^6 + 5*alpha^5 + 7*alpha^4 + 9*alpha^3 + 2*alpha^2 + 2*alpha + 5 : 1), (2*alpha^20 + 3*alpha^19 + 6*alpha^18 + alpha^17 + 7*alpha^16 + 5*alpha^15 + 6*alpha^14 + 4*alpha^13 + 7*alpha^12 + 7*alpha^11 + alpha^10 + 7*alpha^9 + 10*alpha^8 + alpha^7 + 8*alpha^6 + 2*alpha^5 + 3*alpha^4 + 8*alpha^3 + 5*alpha^2 + 10*alpha + 6 : 9*alpha^20 + 6*alpha^19 + 8*alpha^18 + 8*alpha^16 + 3*alpha^15 + 5*alpha^14 + 10*alpha^13 + 6*alpha^12 + 5*alpha^11 + alpha^10 + 9*alpha^9 + alpha^8 + 2*alpha^7 + 7*alpha^6 + 6*alpha^5 + 4*alpha^4 + 2*alpha^3 + 9*alpha^2 + 9*alpha + 6 : 1), (3*alpha^20 + 8*alpha^19 + 8*alpha^18 + 4*alpha^17 + 6*alpha^16 + 10*alpha^15 + 4*alpha^14 + 2*alpha^13 + 9*alpha^12 + 4*alpha^11 + alpha^10 + 2*alpha^9 + 2*alpha^7 + 9*alpha^6 + 8*alpha^3 + 10*alpha^2 + 10*alpha + 5 : alpha^20 + 5*alpha^18 + 6*alpha^17 + 7*alpha^16 + 3*alpha^15 + 6*alpha^14 + 6*alpha^13 + 3*alpha^12 + 10*alpha^11 + 4*alpha^10 + 9*alpha^9 + alpha^8 + 2*alpha^7 + 2*alpha^6 + 6*alpha^5 + 6*alpha^4 + 7*alpha^3 + 7*alpha^2 + 10*alpha + 6 : 1), (3*alpha^20 + 8*alpha^19 + 8*alpha^18 + 4*alpha^17 + 6*alpha^16 + 10*alpha^15 + 4*alpha^14 + 2*alpha^13 + 9*alpha^12 + 4*alpha^11 + alpha^10 + 2*alpha^9 + 2*alpha^7 + 9*alpha^6 + 8*alpha^3 + 10*alpha^2 + 10*alpha + 5 : 10*alpha^20 + 6*alpha^18 + 5*alpha^17 + 4*alpha^16 + 8*alpha^15 + 5*alpha^14 + 5*alpha^13 + 8*alpha^12 + alpha^11 + 7*alpha^10 + 2*alpha^9 + 10*alpha^8 + 9*alpha^7 + 9*alpha^6 + 5*alpha^5 + 5*alpha^4 + 4*alpha^3 + 4*alpha^2 + alpha + 5 : 1), (2*alpha^20 + 4*alpha^19 + 9*alpha^18 + 4*alpha^17 + 10*alpha^15 + 2*alpha^14 + 6*alpha^13 + 9*alpha^12 + 3*alpha^10 + 3*alpha^9 + 5*alpha^7 + 3*alpha^6 + alpha^5 + 4*alpha^4 + 4*alpha^3 + 5*alpha + 5 : alpha^20 + 10*alpha^19 + 7*alpha^18 + 6*alpha^17 + 6*alpha^16 + 7*alpha^15 + 3*alpha^14 + 4*alpha^13 + 4*alpha^12 + alpha^10 + 6*alpha^9 + 6*alpha^8 + 7*alpha^7 + 5*alpha^6 + 7*alpha^5 + 9*alpha^4 + alpha^3 + 2*alpha^2 + alpha + 5 : 1), (2*alpha^20 + 4*alpha^19 + 9*alpha^18 + 4*alpha^17 + 10*alpha^15 + 2*alpha^14 + 6*alpha^13 + 9*alpha^12 + 3*alpha^10 + 3*alpha^9 + 5*alpha^7 + 3*alpha^6 + alpha^5 + 4*alpha^4 + 4*alpha^3 + 5*alpha + 5 : 10*alpha^20 + alpha^19 + 4*alpha^18 + 5*alpha^17 + 5*alpha^16 + 4*alpha^15 + 8*alpha^14 + 7*alpha^13 + 7*alpha^12 + 10*alpha^10 + 5*alpha^9 + 5*alpha^8 + 4*alpha^7 + 6*alpha^6 + 4*alpha^5 + 2*alpha^4 + 10*alpha^3 + 9*alpha^2 + 10*alpha + 6 : 1), (4*alpha^20 + 3*alpha^19 + 4*alpha^17 + 6*alpha^16 + alpha^15 + 4*alpha^14 + 7*alpha^13 + 5*alpha^12 + 7*alpha^10 + 8*alpha^9 + 8*alpha^8 + 9*alpha^7 + 9*alpha^6 + 9*alpha^5 + 5*alpha^4 + 7*alpha^3 + 7*alpha^2 + 6*alpha + 4 : alpha^20 + 7*alpha^18 + 4*alpha^17 + 6*alpha^16 + alpha^15 + alpha^14 + 10*alpha^13 + 7*alpha^12 + 5*alpha^11 + 9*alpha^9 + alpha^8 + 4*alpha^7 + 7*alpha^6 + 4*alpha^5 + 7*alpha^4 + 4*alpha^3 + 10*alpha^2 + 10 : 1), (4*alpha^20 + 3*alpha^19 + 4*alpha^17 + 6*alpha^16 + alpha^15 + 4*alpha^14 + 7*alpha^13 + 5*alpha^12 + 7*alpha^10 + 8*alpha^9 + 8*alpha^8 + 9*alpha^7 + 9*alpha^6 + 9*alpha^5 + 5*alpha^4 + 7*alpha^3 + 7*alpha^2 + 6*alpha + 4 : 10*alpha^20 + 4*alpha^18 + 7*alpha^17 + 5*alpha^16 + 10*alpha^15 + 10*alpha^14 + alpha^13 + 4*alpha^12 + 6*alpha^11 + 2*alpha^9 + 10*alpha^8 + 7*alpha^7 + 4*alpha^6 + 7*alpha^5 + 4*alpha^4 + 7*alpha^3 + alpha^2 + 1 : 1), (4*alpha^20 + 7*alpha^19 + 4*alpha^18 + 8*alpha^17 + 6*alpha^16 + 9*alpha^15 + 3*alpha^14 + alpha^13 + 9*alpha^12 + 3*alpha^11 + 8*alpha^10 + 4*alpha^9 + 2*alpha^8 + 6*alpha^7 + 10*alpha^6 + 8*alpha^5 + 6*alpha^4 + alpha^3 + 7*alpha^2 + 3 : 9*alpha^20 + 8*alpha^19 + alpha^18 + 2*alpha^17 + 6*alpha^16 + 6*alpha^15 + 7*alpha^14 + 10*alpha^13 + 9*alpha^12 + alpha^11 + 4*alpha^10 + 9*alpha^9 + 5*alpha^8 + 8*alpha^7 + 3*alpha^6 + 5*alpha^5 + 8*alpha^4 + 8*alpha^3 + 9*alpha^2 + 7 : 1), (4*alpha^20 + 7*alpha^19 + 4*alpha^18 + 8*alpha^17 + 6*alpha^16 + 9*alpha^15 + 3*alpha^14 + alpha^13 + 9*alpha^12 + 3*alpha^11 + 8*alpha^10 + 4*alpha^9 + 2*alpha^8 + 6*alpha^7 + 10*alpha^6 + 8*alpha^5 + 6*alpha^4 + alpha^3 + 7*alpha^2 + 3 : 2*alpha^20 + 3*alpha^19 + 10*alpha^18 + 9*alpha^17 + 5*alpha^16 + 5*alpha^15 + 4*alpha^14 + alpha^13 + 2*alpha^12 + 10*alpha^11 + 7*alpha^10 + 2*alpha^9 + 6*alpha^8 + 3*alpha^7 + 8*alpha^6 + 6*alpha^5 + 3*alpha^4 + 3*alpha^3 + 2*alpha^2 + 4 : 1), (7*alpha^20 + 4*alpha^19 + 5*alpha^18 + 8*alpha^17 + 6*alpha^16 + 10*alpha^15 + 5*alpha^14 + 10*alpha^13 + 8*alpha^12 + 3*alpha^11 + 3*alpha^10 + alpha^9 + alpha^7 + 10*alpha^6 + 3*alpha^5 + 10*alpha^4 + 10*alpha^3 + 2*alpha^2 + 3 : 9*alpha^20 + alpha^19 + 7*alpha^18 + 3*alpha^17 + alpha^16 + 2*alpha^14 + 8*alpha^13 + 3*alpha^12 + 9*alpha^11 + 3*alpha^10 + 7*alpha^9 + 5*alpha^8 + 4*alpha^7 + alpha^6 + 3*alpha^5 + 10*alpha^4 + 8*alpha + 7 : 1), (7*alpha^20 + 4*alpha^19 + 5*alpha^18 + 8*alpha^17 + 6*alpha^16 + 10*alpha^15 + 5*alpha^14 + 10*alpha^13 + 8*alpha^12 + 3*alpha^11 + 3*alpha^10 + alpha^9 + alpha^7 + 10*alpha^6 + 3*alpha^5 + 10*alpha^4 + 10*alpha^3 + 2*alpha^2 + 3 : 2*alpha^20 + 10*alpha^19 + 4*alpha^18 + 8*alpha^17 + 10*alpha^16 + 9*alpha^14 + 3*alpha^13 + 8*alpha^12 + 2*alpha^11 + 8*alpha^10 + 4*alpha^9 + 6*alpha^8 + 7*alpha^7 + 10*alpha^6 + 8*alpha^5 + alpha^4 + 3*alpha + 4 : 1), (2*alpha^20 + alpha^19 + 7*alpha^18 + 6*alpha^17 + 2*alpha^16 + 9*alpha^15 + 7*alpha^14 + 4*alpha^13 + alpha^12 + 6*alpha^11 + 3*alpha^10 + 8*alpha^9 + 2*alpha^8 + 4*alpha^7 + 2*alpha^5 + 8*alpha^4 + 4*alpha^3 + 3*alpha^2 + 9*alpha + 3 : 9*alpha^20 + alpha^18 + 5*alpha^17 + 4*alpha^16 + 7*alpha^15 + 5*alpha^14 + 3*alpha^13 + 3*alpha^12 + 3*alpha^11 + 5*alpha^10 + 9*alpha^9 + 7*alpha^8 + 10*alpha^7 + 2*alpha^6 + 10*alpha^5 + 4*alpha^4 + 4*alpha^3 + 3*alpha^2 + 7*alpha + 4 : 1), (2*alpha^20 + alpha^19 + 7*alpha^18 + 6*alpha^17 + 2*alpha^16 + 9*alpha^15 + 7*alpha^14 + 4*alpha^13 + alpha^12 + 6*alpha^11 + 3*alpha^10 + 8*alpha^9 + 2*alpha^8 + 4*alpha^7 + 2*alpha^5 + 8*alpha^4 + 4*alpha^3 + 3*alpha^2 + 9*alpha + 3 : 2*alpha^20 + 10*alpha^18 + 6*alpha^17 + 7*alpha^16 + 4*alpha^15 + 6*alpha^14 + 8*alpha^13 + 8*alpha^12 + 8*alpha^11 + 6*alpha^10 + 2*alpha^9 + 4*alpha^8 + alpha^7 + 9*alpha^6 + alpha^5 + 7*alpha^4 + 7*alpha^3 + 8*alpha^2 + 4*alpha + 7 : 1), (9*alpha^20 + alpha^19 + 3*alpha^18 + 5*alpha^17 + 4*alpha^15 + 5*alpha^13 + 3*alpha^12 + 9*alpha^11 + 6*alpha^10 + 9*alpha^9 + 3*alpha^8 + 7*alpha^7 + 3*alpha^6 + 5*alpha^5 + 6*alpha^4 + 7*alpha^3 + 9*alpha^2 + 2*alpha + 3 : 10*alpha^19 + 5*alpha^18 + 6*alpha^17 + 8*alpha^16 + 6*alpha^15 + alpha^14 + 4*alpha^13 + 6*alpha^12 + 4*alpha^11 + 9*alpha^10 + 7*alpha^9 + 3*alpha^8 + 4*alpha^7 + 3*alpha^6 + 4*alpha^5 + 4*alpha^4 + 2*alpha^3 + 8*alpha^2 + 10*alpha + 8 : 1), (9*alpha^20 + alpha^19 + 3*alpha^18 + 5*alpha^17 + 4*alpha^15 + 5*alpha^13 + 3*alpha^12 + 9*alpha^11 + 6*alpha^10 + 9*alpha^9 + 3*alpha^8 + 7*alpha^7 + 3*alpha^6 + 5*alpha^5 + 6*alpha^4 + 7*alpha^3 + 9*alpha^2 + 2*alpha + 3 : alpha^19 + 6*alpha^18 + 5*alpha^17 + 3*alpha^16 + 5*alpha^15 + 10*alpha^14 + 7*alpha^13 + 5*alpha^12 + 7*alpha^11 + 2*alpha^10 + 4*alpha^9 + 8*alpha^8 + 7*alpha^7 + 8*alpha^6 + 7*alpha^5 + 7*alpha^4 + 9*alpha^3 + 3*alpha^2 + alpha + 3 : 1), (alpha^20 + 6*alpha^19 + 3*alpha^18 + 10*alpha^16 + 2*alpha^15 + 5*alpha^14 + 10*alpha^13 + 4*alpha^12 + 6*alpha^11 + 2*alpha^10 + 6*alpha^9 + 10*alpha^8 + 5*alpha^7 + 5*alpha^6 + 6*alpha^5 + 8*alpha^4 + 8*alpha^3 + 7*alpha^2 + 2*alpha + 3 : 7*alpha^20 + 5*alpha^17 + 2*alpha^16 + 6*alpha^15 + 2*alpha^14 + 6*alpha^13 + 5*alpha^12 + 10*alpha^11 + 2*alpha^10 + 7*alpha^9 + 9*alpha^8 + 8*alpha^7 + 9*alpha^6 + 2*alpha^5 + alpha^4 + 3*alpha^3 + 7*alpha^2 + 10*alpha + 3 : 1), (alpha^20 + 6*alpha^19 + 3*alpha^18 + 10*alpha^16 + 2*alpha^15 + 5*alpha^14 + 10*alpha^13 + 4*alpha^12 + 6*alpha^11 + 2*alpha^10 + 6*alpha^9 + 10*alpha^8 + 5*alpha^7 + 5*alpha^6 + 6*alpha^5 + 8*alpha^4 + 8*alpha^3 + 7*alpha^2 + 2*alpha + 3 : 4*alpha^20 + 6*alpha^17 + 9*alpha^16 + 5*alpha^15 + 9*alpha^14 + 5*alpha^13 + 6*alpha^12 + alpha^11 + 9*alpha^10 + 4*alpha^9 + 2*alpha^8 + 3*alpha^7 + 2*alpha^6 + 9*alpha^5 + 10*alpha^4 + 8*alpha^3 + 4*alpha^2 + alpha + 8 : 1), (9*alpha^20 + 4*alpha^19 + 4*alpha^18 + 7*alpha^17 + 4*alpha^16 + alpha^15 + 7*alpha^14 + 3*alpha^13 + 10*alpha^11 + 9*alpha^9 + 5*alpha^8 + alpha^7 + 6*alpha^6 + 3*alpha^5 + alpha^4 + 7*alpha^2 + alpha + 2 : 3*alpha^20 + 6*alpha^19 + alpha^18 + 3*alpha^17 + 7*alpha^16 + 4*alpha^15 + alpha^14 + 7*alpha^13 + 6*alpha^12 + 7*alpha^11 + 2*alpha^10 + 3*alpha^8 + 4*alpha^7 + 6*alpha^6 + alpha^5 + 2*alpha^4 + 9*alpha^3 + 3*alpha^2 + 4*alpha + 1 : 1), (9*alpha^20 + 4*alpha^19 + 4*alpha^18 + 7*alpha^17 + 4*alpha^16 + alpha^15 + 7*alpha^14 + 3*alpha^13 + 10*alpha^11 + 9*alpha^9 + 5*alpha^8 + alpha^7 + 6*alpha^6 + 3*alpha^5 + alpha^4 + 7*alpha^2 + alpha + 2 : 8*alpha^20 + 5*alpha^19 + 10*alpha^18 + 8*alpha^17 + 4*alpha^16 + 7*alpha^15 + 10*alpha^14 + 4*alpha^13 + 5*alpha^12 + 4*alpha^11 + 9*alpha^10 + 8*alpha^8 + 7*alpha^7 + 5*alpha^6 + 10*alpha^5 + 9*alpha^4 + 2*alpha^3 + 8*alpha^2 + 7*alpha + 10 : 1)] 49