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Revert "Fix vinberg booktests (#3939)"
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84 changes: 84 additions & 0 deletions
84
test/book/specialized/brandhorst-zach-fibration-hopping/vinberg_3.jlcon
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,84 @@ | ||
| julia> K = QQ | ||
| Rational field | ||
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| julia> Kt, t = polynomial_ring(K, :t) | ||
| (Univariate polynomial ring in t over QQ, t) | ||
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| julia> Ktf = fraction_field(Kt) | ||
| Fraction field | ||
| of univariate polynomial ring in t over QQ | ||
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| julia> E = elliptic_curve(Ktf, [0, -t^3, 0, t^3, 0]) | ||
| Elliptic curve with equation | ||
| y^2 = x^3 - t^3*x^2 + t^3*x | ||
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| julia> P = E([t^3, t^3]); | ||
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| julia> Y2 = elliptic_surface(E, 2, [P]); | ||
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| julia> S = weierstrass_model(Y2)[1]; | ||
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| julia> basisNSY2, _, NSY2 = algebraic_lattice(Y2); | ||
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| julia> fibers_in_Y2 = [QQ.(vec(collect(i))) for i in [ | ||
| [4 2 0 0 0 0 0 0 0 -4 -4 -8 -7 -6 -5 -4 -3 -2 -1 0], | ||
| [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0], | ||
| [5 2 -2 -3 -4 -3 -2 -1 -2 -5 -4 -8 -7 -6 -5 -4 -3 -2 -1 0], | ||
| [4 2 -2 -4 -6 -9//2 -3 -3//2 -7//2 -3 -5//2 -5 -9//2 -4 -7//2 -3 -5//2 -2 -3//2 0], | ||
| [2 1 -1 -2 -3 -2 -1 0 -2 -1 -1 -2 -2 -2 -2 -2 -2 -1 0 1], | ||
| [2 1 0 0 0 0 0 0 0 -2 -2 -4 -4 -4 -4 -3 -2 -1 0 1] | ||
| ]] | ||
| 6-element Vector{Vector{QQFieldElem}}: | ||
| [4, 2, 0, 0, 0, 0, 0, 0, 0, -4, -4, -8, -7, -6, -5, -4, -3, -2, -1, 0] | ||
| [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] | ||
| [5, 2, -2, -3, -4, -3, -2, -1, -2, -5, -4, -8, -7, -6, -5, -4, -3, -2, -1, 0] | ||
| [4, 2, -2, -4, -6, -9//2, -3, -3//2, -7//2, -3, -5//2, -5, -9//2, -4, -7//2, -3, -5//2, -2, -3//2, 0] | ||
| [2, 1, -1, -2, -3, -2, -1, 0, -2, -1, -1, -2, -2, -2, -2, -2, -2, -1, 0, 1] | ||
| [2, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -4, -4, -4, -4, -3, -2, -1, 0, 1] | ||
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| julia> @assert all(inner_product(ambient_space(NSY2), i,i) == 0 for i in fibers_in_Y2) | ||
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| julia> [representative(elliptic_parameter(Y2, f)) for f in fibers_in_Y2[4:6]] | ||
| 3-element Vector{AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}}: | ||
| (y//z)//((x//z)*t) | ||
| ((y//z) + t^3)//((x//z)*t - t^4) | ||
| ((y//z) + t^3)//((x//z) - t^3) | ||
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| julia> g,_ = two_neighbor_step(Y2, fibers_in_Y2[4]);g | ||
| -1//4*x^4 - 1//2*t^2*x^3 - 1//4*t^4*x^2 + x + y^2 | ||
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| julia> R = parent(g); K_t = base_ring(R); | ||
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| julia> (x,y) = gens(R); P = K_t.([0,0]); # rational point | ||
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| julia> g, _ = transform_to_weierstrass(g, x, y, P); | ||
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| julia> E4 = elliptic_curve(g, x, y) | ||
| Elliptic curve with equation | ||
| y^2 = x^3 + 1//4*t^4*x^2 - 1//2*t^2*x + 1//4 | ||
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| julia> g,_ = two_neighbor_step(Y2, fibers_in_Y2[5]);g | ||
| t^2*x^3 + (-1//4*t^4 + 2*t)*x^2 + x + y^2 | ||
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| julia> R = parent(g); K_t = base_ring(R); | ||
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| julia> (x,y) = gens(R); P = K_t.([0,0]); # rational point | ||
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| julia> g, _ = transform_to_weierstrass(g, x, y, P); | ||
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| julia> E5 = elliptic_curve(g, x, y) | ||
| Elliptic curve with equation | ||
| y^2 = x^3 + (1//4*t^4 - 2*t)*x^2 + t^2*x | ||
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| julia> g,_ = two_neighbor_step(Y2, fibers_in_Y2[6]);g | ||
| (t^2 + 2*t + 1)*x^3 + y^2 - 1//4*t^4 | ||
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| julia> R = parent(g); K_t = base_ring(R); t = gen(K_t); | ||
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| julia> (x,y) = gens(R); P = K_t.([0,1//2*t^2]); # rational point | ||
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| julia> g, _ = transform_to_weierstrass(g, x, y, P); | ||
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| julia> E6 = elliptic_curve(g, x, y) | ||
| Elliptic curve with equation | ||
| y^2 + (-t^2 - 2*t - 1)//t^4*y = x^3 |
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