Fix vinberg booktests (oscar-system#3939)

* fix booktests for vinberg_3.jlcon and move it to vinberg_2.jlcon

* remove vinberg from ordered_examples.json

* fix tests

* suppress printing of unstable outputs

* booktest: explicitly destroy mongodb db and client (oscar-system#3963)

* booktest: explicitly destroy mongodb db and client

* booktest-polydb-cleanup: try nicer cleanup

---------

Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com>

experimental/Schemes/src/elliptic_surface.jl

@@ -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?

test/book/ordered_examples.json

@@ -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",

test/book/specialized/brandhorst-zach-fibration-hopping/vinberg_2.jlcon

@@ -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);
 
@@ -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
 
@@ -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)
@@ -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
 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)
@@ -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

test/book/specialized/kuehne-schroeter-matroids/realization_space.jlcon

@@ -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

test/book/test.jl

@@ -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)