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Fix vinberg booktests #3939

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merged 5 commits into from
Jul 24, 2024
Merged

Fix vinberg booktests #3939

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942bb3b
fix booktests for vinberg_3.jlcon and move it to vinberg_2.jlcon
simonbrandhorst Jul 15, 2024
0870a49
remove vinberg from ordered_examples.json
simonbrandhorst Jul 16, 2024
a913f80
fix tests
simonbrandhorst Jul 17, 2024
8d48266
suppress printing of unstable outputs
simonbrandhorst Jul 23, 2024
5f00b70
booktest: explicitly destroy mongodb db and client (#3963)
benlorenz Jul 23, 2024
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1 change: 1 addition & 0 deletions experimental/Schemes/src/elliptic_surface.jl
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Expand Up @@ -1350,6 +1350,7 @@ function horizontal_decomposition(X::EllipticSurface, F::Vector{QQFieldElem})
E = generic_fiber(X)
basisNS, tors, NS = algebraic_lattice(X)
V = ambient_space(NS)
@req F in algebraic_lattice(X)[3] "not in the algebraic lattice"
@req inner_product(V, F, F)==0 "not an isotropic divisor"
@req euler_characteristic(X) == 2 "not a K3 surface"
# how to give an ample divisor automagically in general?
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3 changes: 1 addition & 2 deletions test/book/ordered_examples.json
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Expand Up @@ -230,8 +230,7 @@
],
"specialized/brandhorst-zach-fibration-hopping": [
"vinberg_1.jlcon",
"vinberg_2.jlcon",
"vinberg_3.jlcon"
"vinberg_2.jlcon"
],
"specialized/breuer-nebe-parker-orthogonal-discriminants": [
"expl_order.jlcon",
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127 changes: 74 additions & 53 deletions test/book/specialized/brandhorst-zach-fibration-hopping/vinberg_2.jlcon
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Expand Up @@ -50,7 +50,26 @@ with default covering
6: [(z//y), (x//y), s]

julia> piS = weierstrass_contraction(Y1)
Composite morphism of[...]
Composite morphism of
Hom: elliptic surface with generic fiber -x^3 + y^2 - t^7 + 2*t^6 - t^5 -> scheme over QQ covered with 44 patches
Hom: scheme over QQ covered with 44 patches -> scheme over QQ covered with 40 patches
Hom: scheme over QQ covered with 40 patches -> scheme over QQ covered with 38 patches
Hom: scheme over QQ covered with 38 patches -> scheme over QQ covered with 36 patches
Hom: scheme over QQ covered with 36 patches -> scheme over QQ covered with 32 patches
Hom: scheme over QQ covered with 32 patches -> scheme over QQ covered with 30 patches
Hom: scheme over QQ covered with 30 patches -> scheme over QQ covered with 28 patches
Hom: scheme over QQ covered with 28 patches -> scheme over QQ covered with 26 patches
Hom: scheme over QQ covered with 26 patches -> scheme over QQ covered with 24 patches
Hom: scheme over QQ covered with 24 patches -> scheme over QQ covered with 22 patches
Hom: scheme over QQ covered with 22 patches -> scheme over QQ covered with 20 patches
Hom: scheme over QQ covered with 20 patches -> scheme over QQ covered with 18 patches
Hom: scheme over QQ covered with 18 patches -> scheme over QQ covered with 16 patches
Hom: scheme over QQ covered with 16 patches -> scheme over QQ covered with 14 patches
Hom: scheme over QQ covered with 14 patches -> scheme over QQ covered with 12 patches
Hom: scheme over QQ covered with 12 patches -> scheme over QQ covered with 10 patches
Hom: scheme over QQ covered with 10 patches -> scheme over QQ covered with 6 patches



julia> basisNSY1, gramTriv = trivial_lattice(Y1);

Expand Down Expand Up @@ -88,7 +107,7 @@ julia> basisNSY1
julia> basisNSY1[1]
Effective weil divisor Fiber over (2, 1)
on elliptic surface with generic fiber -x^3 + y^2 - t^7 + 2*t^6 - t^5
with coefficients in integer Ring
with coefficients in integer ring
given as the formal sum of
1 * sheaf of ideals

Expand All @@ -97,22 +116,7 @@ julia> b, I = Oscar._is_equal_up_to_permutation_with_permutation(gram_matrix(NS)

julia> @assert gram_matrix(NSY1) == gram_matrix(NS)[I,I]

julia> Oscar.horizontal_decomposition(Y1, fibers[2][I])[2]
Effective weil divisor
on elliptic surface with generic fiber -x^3 + y^2 - t^7 + 2*t^6 - t^5
with coefficients in integer Ring
given as the formal sum of
2 * component E8_7 of fiber over (0, 1)
2 * section: (0 : 1 : 0)
1 * component A2_0 of fiber over (1, 1)
1 * component E8_0 of fiber over (1, 0)
2 * component E8_4 of fiber over (0, 1)
2 * component E8_3 of fiber over (0, 1)
1 * component E8_2 of fiber over (0, 1)
2 * component E8_0 of fiber over (0, 1)
2 * component E8_6 of fiber over (0, 1)
2 * component E8_5 of fiber over (0, 1)
1 * component E8_8 of fiber over (0, 1)
julia> Oscar.horizontal_decomposition(Y1, fibers[2][I])[2];

julia> representative(elliptic_parameter(Y1, fibers[2][I]))
(x//z)//(t^3 - t^2)
Expand All @@ -122,22 +126,20 @@ julia> g, phi1 = two_neighbor_step(Y1, fibers[2][I]); g

julia> kt2 = base_ring(parent(g)); P = kt2.([0,0]);

julia> Y2, phi2 = elliptic_surface(g, P); Y2
julia> Y2, phi2 = elliptic_surface(g, P; minimize=false); Y2
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not sure in which Oscar versions this works. It is a recent addition. in 5dcfffb

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I think it should work in 1.1.1, but not in 1.1.0.

Elliptic surface
over rational field
with generic fiber
-x^3 + t^3*x^2 - t^3*x + y^2
and relatively minimal model
scheme over QQ covered with 47 patches

julia> E2 = generic_fiber(Y2); t2 = gen(kt2);
julia> E2 = generic_fiber(Y2); tt = gen(kt2);

julia> P2 = E2([t2^3, t2^3]); set_mordell_weil_basis!(Y2, [P2]);
julia> P2 = E2([tt^3, tt^3]); set_mordell_weil_basis!(Y2, [P2]);

julia> U2 = weierstrass_chart_on_minimal_model(Y2); U1 = weierstrass_chart_on_minimal_model(Y1);

julia> imgs = phi2.(phi1.(ambient_coordinates(U1))) # k(Y1) -> k(Y2)
3-element Vector{AbstractAlgebra.Generic.Frac{QQMPolyRingElem}}:
3-element Vector{AbstractAlgebra.Generic.FracFieldElem{QQMPolyRingElem}}:
(-(x//z)*t + t)//(x//z)^3
((x//z)*(y//z) - (y//z))//(x//z)^5
1//(x//z)
Expand All @@ -149,45 +151,64 @@ julia> set_attribute!(phi_rat, :is_isomorphism=>true);
julia> pullbackDivY1 = [pullback(phi_rat, D) for D in basisNSY1];

julia> B = [basis_representation(Y2, D) for D in pullbackDivY1];
20-element Vector{Vector{QQFieldElem}}:
[4, 2, 0, 0, 0, 0, 0, 0, 0, -4, -4, -8, -7, -6, -5, -4, -3, -2, -1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[4, 2, -1, -2, -3, -5//2, -2, -3//2, -3//2, -3, -5//2, -5, -9//2, -4, -7//2, -3, -5//2, -2, -3//2, -1]
[0, 0, 1, 2, 3, 5//2, 2, 3//2, 3//2, -2, -3//2, -3, -5//2, -2, -3//2, -1, -1//2, 0, 1//2, 1]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -2, -2, -2, -2, -2, -2, -2, -1, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[2, 1, -1, -2, -3, -5//2, -2, -3//2, -3//2, -2, -5//2, -4, -7//2, -3, -5//2, -2, -3//2, -1, -1//2, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

julia> B = matrix(QQ, 20, 20, reduce(vcat, B)); NSY2 = algebraic_lattice(Y2)[3];

julia> NSY1inY2 = lattice(ambient_space(NSY2),B);

julia> @assert NSY1inY2 == NSY2 && gram_matrix(NSY1inY2) == gram_matrix(NSY1)

julia> fibers_in_Y2 = [f[I]*B for f in fibers]
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]
julia> fibers_in_Y2 = [f[I]*B for f in fibers];

julia> f3 = fibers[3][I]; representative(elliptic_parameter(Y1, f3))
(x//z)//t^2

julia> g3a, phi3a = two_neighbor_step(Y1, f3); g3a
-x^3 + (-t^3 + 2)*x^2 - x + y^2

julia> @assert all(inner_product(ambient_space(NSY2), i,i) == 0 for i in fibers_in_Y2)

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)

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

julia> R = parent(g); K_t = base_ring(R);

julia> (x,y) = gens(R); P = K_t.([0,0]); # rational point

julia> g, _ = transform_to_weierstrass(g, x, y, P);

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

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

julia> R = parent(g); K_t = base_ring(R);

julia> (x,y) = gens(R); P = K_t.([0,0]); # rational point

julia> g, _ = transform_to_weierstrass(g, x, y, P);

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

julia> g,_ = two_neighbor_step(Y2, fibers_in_Y2[6]);g
(t^2 + 2*t + 1)*x^3 + y^2 - 1//4*t^4

julia> R = parent(g); K_t = base_ring(R); t = gen(K_t);

julia> (x,y) = gens(R); P = K_t.([0,1//2*t^2]); # rational point

julia> g, _ = transform_to_weierstrass(g, x, y, P);

julia> E6 = elliptic_curve(g, x, y)
Elliptic curve with equation
y^2 + (-t^2 - 2*t - 1)//t^4*y = x^3
84 changes: 0 additions & 84 deletions test/book/specialized/brandhorst-zach-fibration-hopping/vinberg_3.jlcon
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2 changes: 2 additions & 0 deletions test/book/specialized/kuehne-schroeter-matroids/realization_space.jlcon
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Expand Up @@ -124,3 +124,5 @@ One realization is given by
[0 1 1 0 1 1 1 1 1]
[0 0 0 1 2 3 6 3 2]
in the rational field

julia> results = collection = db = 0; # allow connection cleanup
4 changes: 2 additions & 2 deletions test/book/test.jl
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Expand Up @@ -24,15 +24,15 @@ isdefined(Main, :FakeTerminals) || include(joinpath(pkgdir(REPL),"test","FakeTer
# these are skipped because they slow down the tests too much:

# sometimes very slow: 4000-30000s
"specialized/brandhorst-zach-fibration-hopping/vinberg_2.jlcon",
#"specialized/brandhorst-zach-fibration-hopping/vinberg_2.jlcon",
# very slow: 24000s
"cornerstones/number-theory/cohenlenstra.jlcon",
# ultra slow: time unknown
"specialized/markwig-ristau-schleis-faithful-tropicalization/eliminate_yz.jlcon",

# somewhat slow (~300s)
"cornerstones/polyhedral-geometry/ch-benchmark.jlcon",
"specialized/brandhorst-zach-fibration-hopping/vinberg_3.jlcon",
#"specialized/brandhorst-zach-fibration-hopping/vinberg_3.jlcon",
]

dispsize = (40, 130)
Expand Down
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