From 571179cc51d8ee252f018b73b91dff0ca8f1974d Mon Sep 17 00:00:00 2001 From: Benjamin Lorenz Date: Wed, 16 Oct 2024 00:26:33 +0200 Subject: [PATCH] booktests: redo some whitespace / omission / seed fixes --- .../alexander-surface.jlcon | 2 +- .../algebraic-geometry/ex21a.jlcon | 2 +- .../algebraic-geometry/ex23a.jlcon | 5 +- .../algebraic-geometry/ex314.jlcon | 2 + .../algebraic-geometry/param.jlcon | 3 +- test/book/cornerstones/groups/explSL25.jlcon | 46 ++++++------------- .../number-theory/galoismod.jlcon | 2 +- .../cornerstones/number-theory/intro.jlcon | 15 +++++- .../polyhedral-geometry/D222Computation.jlcon | 7 +-- .../g-vector-example.jlcon | 2 - .../g-vectors-upper-bound.jlcon | 1 - .../polyhedral-geometry/not-pointed.jlcon | 3 +- .../polyhedral-geometry/pentagon.jlcon | 1 + .../polyhedral_fan.jlcon | 1 + .../starsubdivision.jlcon | 2 +- .../expl_G23_tbl.jlcon | 4 +- .../decker-schmitt-invariant-theory/sym.jlcon | 2 +- .../eder-mohr-ideal-theoretic/nonproper.jlcon | 2 +- .../eliminate_xz.jlcon | 30 +++++++++++- 19 files changed, 77 insertions(+), 55 deletions(-) diff --git a/test/book/cornerstones/algebraic-geometry/alexander-surface.jlcon b/test/book/cornerstones/algebraic-geometry/alexander-surface.jlcon index 3639a00b22d9..e11ef69384e1 100644 --- a/test/book/cornerstones/algebraic-geometry/alexander-surface.jlcon +++ b/test/book/cornerstones/algebraic-geometry/alexander-surface.jlcon @@ -7,7 +7,7 @@ julia> degree(X) 9 julia> S = ambient_coordinate_ring(X) -Multivariate polynomial ring in 5 variables over GF(31991) graded by +Multivariate polynomial ring in 5 variables over GF(31991) graded by x -> [1] y -> [1] z -> [1] diff --git a/test/book/cornerstones/algebraic-geometry/ex21a.jlcon b/test/book/cornerstones/algebraic-geometry/ex21a.jlcon index 01a275352dd2..4bf42c540163 100644 --- a/test/book/cornerstones/algebraic-geometry/ex21a.jlcon +++ b/test/book/cornerstones/algebraic-geometry/ex21a.jlcon @@ -1,4 +1,4 @@ -julia> J1 = ideal([H(I[1]), H(I[2])]) +julia> J1 = ideal([H(I[1]), H(I[2])]) Ideal generated by x0*x2 - x1^2 x0*x3 - x1*x2 diff --git a/test/book/cornerstones/algebraic-geometry/ex23a.jlcon b/test/book/cornerstones/algebraic-geometry/ex23a.jlcon index eaca161def65..67637c6f9acf 100644 --- a/test/book/cornerstones/algebraic-geometry/ex23a.jlcon +++ b/test/book/cornerstones/algebraic-geometry/ex23a.jlcon @@ -12,10 +12,11 @@ julia> other_pos_abs = pos_abs == 1 ? 2 : 1 julia> cI2 = cIabs[other_pos_abs][3] Ideal generated by 648*y + (-160*_a^3 - 1269*_a^2 + 22446*_a + 972)*z - 184147758075888*x + (2850969000960*_a^3 + 22611747888864*_a^2 - 399955313722176*_a - 17319636680832)*y + (2884707374400*_a^3 + 22782606070410*_a^2 - 405172045313820*_a - 57843867366864)*z + 184147758075888*x + (2850969000960*_a^3 + 22611747888864*_a^2 - 399955313722176*_a - 17319636680832)*y + (2884707374400*_a^3 + 2 + 2782606070410*_a^2 - 405172045313820*_a - 57843867366864)*z julia> R2 = base_ring(cI2) -Multivariate polynomial ring in 3 variables over number field graded by +Multivariate polynomial ring in 3 variables over number field graded by x -> [1] y -> [1] z -> [1] diff --git a/test/book/cornerstones/algebraic-geometry/ex314.jlcon b/test/book/cornerstones/algebraic-geometry/ex314.jlcon index d387821bc9bc..3a15caec9592 100644 --- a/test/book/cornerstones/algebraic-geometry/ex314.jlcon +++ b/test/book/cornerstones/algebraic-geometry/ex314.jlcon @@ -68,11 +68,13 @@ M1 -> M e[1] -> (-x_0*x_3 + x_1*x_2)*e[1] Graded module homomorphism of degree [2] + julia> phi2 = psi(tohomM1M(hom1[2])) M1 -> M e[1] -> (-x_0*x_2 + x_1^2)*e[1] Graded module homomorphism of degree [2] + julia> kerphi2, _ = kernel(phi2); julia> iszero(kerphi2) diff --git a/test/book/cornerstones/algebraic-geometry/param.jlcon b/test/book/cornerstones/algebraic-geometry/param.jlcon index 1e975acf1854..b8e9dbe6e490 100644 --- a/test/book/cornerstones/algebraic-geometry/param.jlcon +++ b/test/book/cornerstones/algebraic-geometry/param.jlcon @@ -4,7 +4,8 @@ julia> f = x^5 + 10*x^4*y + 20*x^3*y^2 + 130*x^2*y^3 - 20*x*y^4 + 20*y^5 - 2*x^4 julia> C = plane_curve(f) Projective plane curve - defined by 0 = x^5 + 10*x^4*y - 2*x^4*z + 20*x^3*y^2 - 40*x^3*y*z + x^3*z^2 + 130*x^2*y^3 - 150*x^2*y^2*z + 30*x^2*y*z^2 - 20*x*y^4 - 90*x*y^3*z + 110*x*y^2*z^2 + 20*y^5 - 40*y^4*z + 20*y^3*z^2 + defined by 0 = x^5 + 10*x^4*y - 2*x^4*z + 20*x^3*y^2 - 40*x^3*y*z + x^3*z^2 + 130*x^2*y^3 - 150*x^2*y^2*z + 30*x^2*y*z^2 - 20*x* + y^4 - 90*x*y^3*z + 110*x*y^2*z^2 + 20*y^5 - 40*y^4*z + 20*y^3*z^2 julia> conics = [x^2-x*z, y^2-y*z]; diff --git a/test/book/cornerstones/groups/explSL25.jlcon b/test/book/cornerstones/groups/explSL25.jlcon index 62ecf567ff0b..bfe5f0582ff9 100644 --- a/test/book/cornerstones/groups/explSL25.jlcon +++ b/test/book/cornerstones/groups/explSL25.jlcon @@ -4,37 +4,21 @@ SL(2,5) julia> T = character_table(G) Character table of SL(2,5) - 2 3 1 1 3 1 - 3 1 . . 1 . - 5 1 1 1 1 1 - - 1a 10a 10b 2a 5a - -X_1 1 1 1 1 1 -X_2 2 z_5^3 + z_5^2 + 1 -z_5^3 - z_5^2 -2 -z_5^3 - z_5^2 - 1 -X_3 2 -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 -2 z_5^3 + z_5^2 -X_4 3 -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 3 -z_5^3 - z_5^2 -X_5 3 z_5^3 + z_5^2 + 1 -z_5^3 - z_5^2 3 z_5^3 + z_5^2 + 1 -X_6 4 -1 -1 4 -1 -X_7 4 1 1 -4 -1 -X_8 5 . . 5 . -X_9 6 -1 -1 -6 1 - - 2 1 1 1 2 - 3 . 1 1 . - 5 1 . . . - - 5b 3a 6a 4a - -X_1 1 1 1 1 -X_2 z_5^3 + z_5^2 -1 1 . -X_3 -z_5^3 - z_5^2 - 1 -1 1 . -X_4 z_5^3 + z_5^2 + 1 . . -1 -X_5 -z_5^3 - z_5^2 . . -1 -X_6 -1 1 1 . -X_7 -1 1 -1 . -X_8 . -1 -1 1 -X_9 1 . . . + 2 3 1 1 3 1 1 1 1 2 + 3 1 . . 1 . . 1 1 . + 5 1 1 1 1 1 1 . . . + + 1a 10a 10b 2a 5a 5b 3a 6a 4a + +X_1 1 1 1 1 1 1 1 1 1 +X_2 2 z_5^3 + z_5^2 + 1 -z_5^3 - z_5^2 -2 -z_5^3 - z_5^2 - 1 z_5^3 + z_5^2 -1 1 . +X_3 2 -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 -2 z_5^3 + z_5^2 -z_5^3 - z_5^2 - 1 -1 1 . +X_4 3 -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 3 -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 . . -1 +X_5 3 z_5^3 + z_5^2 + 1 -z_5^3 - z_5^2 3 z_5^3 + z_5^2 + 1 -z_5^3 - z_5^2 . . -1 +X_6 4 -1 -1 4 -1 -1 1 1 . +X_7 4 1 1 -4 -1 -1 1 -1 . +X_8 5 . . 5 . . -1 -1 1 +X_9 6 -1 -1 -6 1 1 . . . julia> R = gmodule(T[end]) G-module for G acting on vector space of dimension 6 over abelian closure of Q diff --git a/test/book/cornerstones/number-theory/galoismod.jlcon b/test/book/cornerstones/number-theory/galoismod.jlcon index 2bab69bb351c..f6fa0f89fa4c 100644 --- a/test/book/cornerstones/number-theory/galoismod.jlcon +++ b/test/book/cornerstones/number-theory/galoismod.jlcon @@ -1,4 +1,4 @@ -julia> Oscar.randseed!(3371100); +julia> Oscar.randseed!(7360734); julia> Qx, x = QQ["x"]; diff --git a/test/book/cornerstones/number-theory/intro.jlcon b/test/book/cornerstones/number-theory/intro.jlcon index 8a7bda27db33..b1a77a32dd84 100644 --- a/test/book/cornerstones/number-theory/intro.jlcon +++ b/test/book/cornerstones/number-theory/intro.jlcon @@ -39,7 +39,13 @@ julia> discriminant(OK) julia> prime_ideals_over(OK, 7) 2-element Vector{AbsSimpleNumFieldOrderIdeal}: <7, a + 5> +Norm: 7 +Minimum: 7 +two normal wrt: 7 <7, a + 2> +Norm: 7 +Minimum: 7 +two normal wrt: 7 julia> factor(change_coefficient_ring(GF(7), x^2 - 235)) 1 * (x + 5) * (x + 2) @@ -56,11 +62,16 @@ Z/6 julia> m(zero(A)) # apply m to the neutral element of A <1, 1> -[...] +Norm: 1 +Minimum: 1 +principal generator 1 +two normal wrt: 1 julia> P = prime_ideals_over(OK, 2)[1] <2, a + 1> -[...] +Norm: 2 +Minimum: 2 +two normal wrt: 2 julia> preimage(m, P) Abelian group element [3] diff --git a/test/book/cornerstones/polyhedral-geometry/D222Computation.jlcon b/test/book/cornerstones/polyhedral-geometry/D222Computation.jlcon index 8d187fd581c5..76949e796f79 100644 --- a/test/book/cornerstones/polyhedral-geometry/D222Computation.jlcon +++ b/test/book/cornerstones/polyhedral-geometry/D222Computation.jlcon @@ -4,12 +4,9 @@ julia> R, x, c = polynomial_ring(QQ, :x=>1:3, :c=>(0:1,0:1,0:1)); julia> f = sum(prod(x[i]^Int(p[i]) for i=1:3) * c[(Vector{Int}(p)+[1,1,1])...] for p=lattice_points(C)) -x[1]*x[2]*x[3]*c[1, 1, 1] + x[1]*x[2]*c[1, 1, 0] + -x[1]*x[3]*c[1, 0, 1] + x[1]*c[1, 0, 0] + -x[2]*x[3]*c[0, 1, 1] + x[2]*c[0, 1, 0] + -x[3]*c[0, 0, 1] + c[0, 0, 0] +x[1]*x[2]*x[3]*c[1, 1, 1] + x[1]*x[2]*c[1, 1, 0] + x[1]*x[3]*c[1, 0, 1] + x[1]*c[1, 0, 0] + x[2]*x[3]*c[0, 1, 1] + x[2]*c[0, 1, 0] + x[3]*c[0, 0, 1] + c[0, 0, 0] julia> I = ideal(R, vcat([derivative(f,t) for t = x], [f])); julia> D222 = eliminate(I,x)[1] -c[0, 0, 0]^2*c[1, 1, 1]^2 - 2*c[0, 0, 0]*c[1, 0, 0]*c[0, 1, 1]*c[1, 1, 1] - [...] + c[1, 1, 0]^2*c[0, 0, 1]^2 +c[0, 0, 0]^2*c[1, 1, 1]^2 - 2*c[0, 0, 0]*c[1, 0, 0]*c[0, 1, 1]*c[1, 1, 1] - 2*c[0, 0, 0]*c[0, 1, 0]*c[1, 0, 1]*c[1, 1, 1] - 2*c[0, 0, 0]*c[1, 1, 0]*c[0, 0, 1]*c[1, 1, 1] + 4*c[0, 0, 0]*c[1, 1, 0]*c[1, 0, 1]*c[0, 1, 1] + c[1, 0, 0]^2*c[0, 1, 1]^2 + 4*c[1, 0, 0]*c[0, 1, 0]*c[0, 0, 1]*c[1, 1, 1] - 2*c[1, 0, 0]*c[0, 1, 0]*c[1, 0, 1]*c[0, 1, 1] - 2*c[1, 0, 0]*c[1, 1, 0]*c[0, 0, 1]*c[0, 1, 1] + c[0, 1, 0]^2*c[1, 0, 1]^2 - 2*c[0, 1, 0]*c[1, 1, 0]*c[0, 0, 1]*c[1, 0, 1] + c[1, 1, 0]^2*c[0, 0, 1]^2 diff --git a/test/book/cornerstones/polyhedral-geometry/g-vector-example.jlcon b/test/book/cornerstones/polyhedral-geometry/g-vector-example.jlcon index 1ac2ceeb3ad1..192fe9c80752 100644 --- a/test/book/cornerstones/polyhedral-geometry/g-vector-example.jlcon +++ b/test/book/cornerstones/polyhedral-geometry/g-vector-example.jlcon @@ -3,9 +3,7 @@ Polytope in ambient dimension 6 julia> show(f_vector(P)) ZZRingElem[30, 336, 1468, 2874, 2568, 856] - julia> show(h_vector(P)) ZZRingElem[1, 24, 201, 404, 201, 24, 1] - julia> show(g_vector(P)) ZZRingElem[1, 23, 177, 203] diff --git a/test/book/cornerstones/polyhedral-geometry/g-vectors-upper-bound.jlcon b/test/book/cornerstones/polyhedral-geometry/g-vectors-upper-bound.jlcon index 95f007329a82..38deeb26b927 100644 --- a/test/book/cornerstones/polyhedral-geometry/g-vectors-upper-bound.jlcon +++ b/test/book/cornerstones/polyhedral-geometry/g-vectors-upper-bound.jlcon @@ -6,7 +6,6 @@ julia> max_g2 = maximum(g_vectors[:,1]) julia> show(upper_bound_g_vector(6,30)) [1, 23, 276, 2300] - julia> ub = [ Int(Polymake.polytope.pseudopower(g2,2)) for g2 in min_g2:max_g2 ] 34-element Vector{Int64}: 990 diff --git a/test/book/cornerstones/polyhedral-geometry/not-pointed.jlcon b/test/book/cornerstones/polyhedral-geometry/not-pointed.jlcon index 5c0317e19c89..58bf9c305357 100644 --- a/test/book/cornerstones/polyhedral-geometry/not-pointed.jlcon +++ b/test/book/cornerstones/polyhedral-geometry/not-pointed.jlcon @@ -5,5 +5,4 @@ julia> vertices(Q) 0-element SubObjectIterator{PointVector{QQFieldElem}} julia> minimal_faces(Q) -(base_points = PointVector{QQFieldElem}[[0, 0, 0]], - lineality_basis = RayVector{QQFieldElem}[[1, 0, 0]]) +(base_points = PointVector{QQFieldElem}[[0, 0, 0]], lineality_basis = RayVector{QQFieldElem}[[1, 0, 0]]) diff --git a/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon b/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon index 7d2aefecf1e5..cf96a5f18ba5 100644 --- a/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon +++ b/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon @@ -11,6 +11,7 @@ x_1 - 2*x_2 <= 1 x_1 <= 1 x_2 <= 1 + julia> f_vector(P) 2-element Vector{ZZRingElem}: 5 diff --git a/test/book/specialized/bies-kastner-toric-geometry/polyhedral_fan.jlcon b/test/book/specialized/bies-kastner-toric-geometry/polyhedral_fan.jlcon index d8a4134ddece..b9ebde553b16 100644 --- a/test/book/specialized/bies-kastner-toric-geometry/polyhedral_fan.jlcon +++ b/test/book/specialized/bies-kastner-toric-geometry/polyhedral_fan.jlcon @@ -18,5 +18,6 @@ julia> maximal_cones(IncidenceMatrix, tv) [2, 3] [2, 4] + julia> Sigma = polyhedral_fan(tv) Polyhedral fan in ambient dimension 2 diff --git a/test/book/specialized/bies-kastner-toric-geometry/starsubdivision.jlcon b/test/book/specialized/bies-kastner-toric-geometry/starsubdivision.jlcon index b7aa7131a187..3279c6193f74 100644 --- a/test/book/specialized/bies-kastner-toric-geometry/starsubdivision.jlcon +++ b/test/book/specialized/bies-kastner-toric-geometry/starsubdivision.jlcon @@ -31,7 +31,7 @@ julia> is_affine(v2) false julia> cox_ring(v2) -Multivariate polynomial ring in 3 variables over QQ graded by +Multivariate polynomial ring in 3 variables over QQ graded by u1 -> [1] u2 -> [1] e -> [-2] diff --git a/test/book/specialized/breuer-nebe-parker-orthogonal-discriminants/expl_G23_tbl.jlcon b/test/book/specialized/breuer-nebe-parker-orthogonal-discriminants/expl_G23_tbl.jlcon index 3a9caef550a6..8245714a6134 100644 --- a/test/book/specialized/breuer-nebe-parker-orthogonal-discriminants/expl_G23_tbl.jlcon +++ b/test/book/specialized/breuer-nebe-parker-orthogonal-discriminants/expl_G23_tbl.jlcon @@ -6,13 +6,13 @@ G2(3)mod2 3 6 6 6 6 4 4 . 3 3 3 . . 7 1 . . . . . 1 . . . . . 13 1 . . . . . . . . . 1 1 - + 1a 3a 3b 3c 3d 3e 7a 9a 9b 9c 13a 13b 2P 1a 3a 3b 3c 3d 3e 7a 9a 9c 9b 13b 13a 3P 1a 1a 1a 1a 1a 1a 7a 3c 3c 3c 13a 13b 7P 1a 3a 3b 3c 3d 3e 1a 9a 9b 9c 13b 13a 13P 1a 3a 3b 3c 3d 3e 7a 9a 9b 9c 1a 1a - d OD 2 + d OD 2 X_1 1 + 1 1 1 1 1 1 1 1 1 1 1 1 X_2 1 O- + 14 5 5 -4 2 -1 . 2 -1 -1 1 1 X_3 2 o 64 -8 -8 1 4 -2 1 1 A /A -1 -1 diff --git a/test/book/specialized/decker-schmitt-invariant-theory/sym.jlcon b/test/book/specialized/decker-schmitt-invariant-theory/sym.jlcon index cf1e7f8df41d..7377a2268415 100644 --- a/test/book/specialized/decker-schmitt-invariant-theory/sym.jlcon +++ b/test/book/specialized/decker-schmitt-invariant-theory/sym.jlcon @@ -15,7 +15,7 @@ true julia> RS3 = invariant_ring(QQ, symmetric_group(3)); julia> R = polynomial_ring(RS3) -Multivariate polynomial ring in 3 variables over QQ graded by +Multivariate polynomial ring in 3 variables over QQ graded by x[1] -> [1] x[2] -> [1] x[3] -> [1] diff --git a/test/book/specialized/eder-mohr-ideal-theoretic/nonproper.jlcon b/test/book/specialized/eder-mohr-ideal-theoretic/nonproper.jlcon index b1911fd8d4c6..ca08d4aa827c 100644 --- a/test/book/specialized/eder-mohr-ideal-theoretic/nonproper.jlcon +++ b/test/book/specialized/eder-mohr-ideal-theoretic/nonproper.jlcon @@ -19,7 +19,7 @@ Ideal generated by x^2 - x*w julia> S = base_ring(clo) -Multivariate polynomial ring in 5 variables over QQ graded by +Multivariate polynomial ring in 5 variables over QQ graded by x -> [1] y -> [1] z -> [1] diff --git a/test/book/specialized/markwig-ristau-schleis-faithful-tropicalization/eliminate_xz.jlcon b/test/book/specialized/markwig-ristau-schleis-faithful-tropicalization/eliminate_xz.jlcon index 536e974116ef..b5abf8cf3424 100644 --- a/test/book/specialized/markwig-ristau-schleis-faithful-tropicalization/eliminate_xz.jlcon +++ b/test/book/specialized/markwig-ristau-schleis-faithful-tropicalization/eliminate_xz.jlcon @@ -12,4 +12,32 @@ julia> Igf = ideal(R,[g,f]); julia> eliminate(Igf,[y]) Ideal generated by - -x^7 + (b2^2 + b34^2 + 2*b34*b4 + 2*b4^2 + b56^2 + 2*b56*b6 + 2*b6^2)*x^6 + (-b2^2*b34^2 - 2*b2^2*b34*b4 - 2*b2^2*b4^2 - b2^2*b56^2 - 2*b2^2*b56*b6 - 2*b2^2*b6^2 + b2^2*b7^2 - b34^2*b4^2 - b34^2*b56^2 - 2*b34^2*b56*b6 - 2*b34^2*b6^2 + b34^2*b7^2 - 2*b34*b4^3 - 2*b34*b4*b56^2 - 4*b34*b4*b56*b6 - 4*b34*b4*b6^2 + 2*b34*b4*b7^2 - b4^4 - 2*b4^2*b56^2 - 4*b4^2*b56*b6 - 4*b4^2*b6^2 + 2*b4^2*b7^2 - b56^2*b6^2 + b56^2*b7^2 - 2*b56*b6^3 - b6^4)*x^5 + (b2^2*b34^2*b4^2 + b2^2*b34^2*b56^2 + 2*b2^2*b34^2*b56*b6 + 2*b2^2*b34^2*b6^2 - b2^2*b34^2*b7^2 + 2*b2^2*b34*b4^3 + 2*b2^2*b34*b4*b56^2 + 4*b2^2*b34*b4*b56*b6 + 4*b2^2*b34*b4*b6^2 - 2*b2^2*b34*b4*b7^2 + b2^2*b4^4 + 2*b2^2*b4^2*b56^2 + 4*b2^2*b4^2*b56*b6 + 4*b2^2*b4^2*b6^2 - 2*b2^2*b4^2*b7^2 + b2^2*b56^2*b6^2 - b2^2*b56^2*b7^2 + 2*b2^2*b56*b6^3 - 2*b2^2*b56*b6*b7^2 + b2^2*b6^4 - 2*b2^2*b6^2*b7^2 + b34^2*b4^2*b56^2 + 2*b34^2*b4^2*b56*b6 + 2*b34^2*b4^2*b6^2 - b34^2*b4^2*b7^2 + b34^2*b56^2*b6^2 - b34^2*b56^2*b7^2 + 2*b34^2*b56*b6^3 - 2*b34^2*b56*b6*b7^2 + b34^2*b6^4 - 2*b34^2*b6^2*b7^2 + 2*b34*b4^3*b56^2 + 4*b34*b4^3*b56*b6 + 4*b34*b4^3*b6^2 - 2*b34*b4^3*b7^2 + 2*b34*b4*b56^2*b6^2 - 2*b34*b4*b56^2*b7^2 + 4*b34*b4*b56*b6^3 - 2*b34*b4*b56*b6*b7^2 + 2*b34*b4*b6^4 - 2*b34*b4*b6^2*b7^2 + b4^4*b56^2 + 2*b4^4*b56*b6 + 2*b4^4*b6^2 - b4^4*b7^2 + 2*b4^2*b56^2*b6^2 - 2*b4^2*b56^2*b7^2 + 4*b4^2*b56*b6^3 - 2*b4^2*b56*b6*b7^2 + 2*b4^2*b6^4 - 2*b4^2*b6^2*b7^2)*x^4 + (-b2^2*b34^2*b4^2*b56^2 - 2*b2^2*b34^2*b4^2*b56*b6 - 2*b2^2*b34^2*b4^2*b6^2 + b2^2*b34^2*b4^2*b7^2 - b2^2*b34^2*b56^2*b6^2 + b2^2*b34^2*b56^2*b7^2 - 2*b2^2*b34^2*b56*b6^3 + 2*b2^2*b34^2*b56*b6*b7^2 - b2^2*b34^2*b6^4 + 2*b2^2*b34^2*b6^2*b7^2 - 2*b2^2*b34*b4^3*b56^2 - 4*b2^2*b34*b4^3*b56*b6 - 4*b2^2*b34*b4^3*b6^2 + 2*b2^2*b34*b4^3*b7^2 - 2*b2^2*b34*b4*b56^2*b6^2 + 2*b2^2*b34*b4*b56^2*b7^2 - 4*b2^2*b34*b4*b56*b6^3 + 4*b2^2*b34*b4*b56*b6*b7^2 - 2*b2^2*b34*b4*b6^4 + 4*b2^2*b34*b4*b6^2*b7^2 - b2^2*b4^4*b56^2 - 2*b2^2*b4^4*b56*b6 - 2*b2^2*b4^4*b6^2 + b2^2*b4^4*b7^2 - 2*b2^2*b4^2*b56^2*b6^2 + 2*b2^2*b4^2*b56^2*b7^2 - 4*b2^2*b4^2*b56*b6^3 + 4*b2^2*b4^2*b56*b6*b7^2 - 2*b2^2*b4^2*b6^4 + 4*b2^2*b4^2*b6^2*b7^2 + b2^2*b56^2*b6^2*b7^2 + 2*b2^2*b56*b6^3*b7^2 + b2^2*b6^4*b7^2 - b34^2*b4^2*b56^2*b6^2 + b34^2*b4^2*b56^2*b7^2 - 2*b34^2*b4^2*b56*b6^3 + 2*b34^2*b4^2*b56*b6*b7^2 - b34^2*b4^2*b6^4 + 2*b34^2*b4^2*b6^2*b7^2 + b34^2*b56^2*b6^2*b7^2 + 2*b34^2*b56*b6^3*b7^2 + b34^2*b6^4*b7^2 - 2*b34*b4^3*b56^2*b6^2 + 2*b34*b4^3*b56^2*b7^2 - 4*b34*b4^3*b56*b6^3 + 4*b34*b4^3*b56*b6*b7^2 - 2*b34*b4^3*b6^4 + 4*b34*b4^3*b6^2*b7^2 - b4^4*b56^2*b6^2 + b4^4*b56^2*b7^2 - 2*b4^4*b56*b6^3 + 2*b4^4*b56*b6*b7^2 - b4^4*b6^4 + 2*b4^4*b6^2*b7^2)*x^3 + (b2^2*b34^2*b4^2*b56^2*b6^2 - b2^2*b34^2*b4^2*b56^2*b7^2 + 2*b2^2*b34^2*b4^2*b56*b6^3 - 2*b2^2*b34^2*b4^2*b56*b6*b7^2 + b2^2*b34^2*b4^2*b6^4 - 2*b2^2*b34^2*b4^2*b6^2*b7^2 - b2^2*b34^2*b56^2*b6^2*b7^2 - 2*b2^2*b34^2*b56*b6^3*b7^2 - b2^2*b34^2*b6^4*b7^2 + 2*b2^2*b34*b4^3*b56^2*b6^2 - 2*b2^2*b34*b4^3*b56^2*b7^2 + 4*b2^2*b34*b4^3*b56*b6^3 - 4*b2^2*b34*b4^3*b56*b6*b7^2 + 2*b2^2*b34*b4^3*b6^4 - 4*b2^2*b34*b4^3*b6^2*b7^2 - 2*b2^2*b34*b4*b56^2*b6^2*b7^2 - 4*b2^2*b34*b4*b56*b6^3*b7^2 - 2*b2^2*b34*b4*b6^4*b7^2 + b2^2*b4^4*b56^2*b6^2 - b2^2*b4^4*b56^2*b7^2 + 2*b2^2*b4^4*b56*b6^3 - 2*b2^2*b4^4*b56*b6*b7^2 + b2^2*b4^4*b6^4 - 2*b2^2*b4^4*b6^2*b7^2 - 2*b2^2*b4^2*b56^2*b6^2*b7^2 - 4*b2^2*b4^2*b56*b6^3*b7^2 - 2*b2^2*b4^2*b6^4*b7^2)*x^2 + (b2^2*b34^2*b4^2*b56^2*b6^2*b7^2 + 2*b2^2*b34^2*b4^2*b56*b6^3*b7^2 + b2^2*b34^2*b4^2*b6^4*b7^2 + 2*b2^2*b34*b4^3*b56^2*b6^2*b7^2 + 4*b2^2*b34*b4^3*b56*b6^3*b7^2 + 2*b2^2*b34*b4^3*b6^4*b7^2 + b2^2*b4^4*b56^2*b6^2*b7^2 + 2*b2^2*b4^4*b56*b6^3*b7^2 + b2^2*b4^4*b6^4*b7^2)*x + -x^7 + (b2^2 + b34^2 + 2*b34*b4 + 2*b4^2 + b56^2 + 2*b56*b6 + 2*b6^2)*x^6 + (-b2^2*b34^2 - 2*b2^2*b34*b4 - 2*b2^2*b4^2 - b2^2*b5 + 6^2 - 2*b2^2*b56*b6 - 2*b2^2*b6^2 + b2^2*b7^2 - b34^2*b4^2 - b34^2*b56^2 - 2*b34^2*b56*b6 - 2*b34^2*b6^2 + b34^2*b7^2 - 2*b34*b4 + ^3 - 2*b34*b4*b56^2 - 4*b34*b4*b56*b6 - 4*b34*b4*b6^2 + 2*b34*b4*b7^2 - b4^4 - 2*b4^2*b56^2 - 4*b4^2*b56*b6 - 4*b4^2*b6^2 + 2*b4 + ^2*b7^2 - b56^2*b6^2 + b56^2*b7^2 - 2*b56*b6^3 - b6^4)*x^5 + (b2^2*b34^2*b4^2 + b2^2*b34^2*b56^2 + 2*b2^2*b34^2*b56*b6 + 2*b2^2* + b34^2*b6^2 - b2^2*b34^2*b7^2 + 2*b2^2*b34*b4^3 + 2*b2^2*b34*b4*b56^2 + 4*b2^2*b34*b4*b56*b6 + 4*b2^2*b34*b4*b6^2 - 2*b2^2*b34*b4 + *b7^2 + b2^2*b4^4 + 2*b2^2*b4^2*b56^2 + 4*b2^2*b4^2*b56*b6 + 4*b2^2*b4^2*b6^2 - 2*b2^2*b4^2*b7^2 + b2^2*b56^2*b6^2 - b2^2*b56^2* + b7^2 + 2*b2^2*b56*b6^3 - 2*b2^2*b56*b6*b7^2 + b2^2*b6^4 - 2*b2^2*b6^2*b7^2 + b34^2*b4^2*b56^2 + 2*b34^2*b4^2*b56*b6 + 2*b34^2*b4 + ^2*b6^2 - b34^2*b4^2*b7^2 + b34^2*b56^2*b6^2 - b34^2*b56^2*b7^2 + 2*b34^2*b56*b6^3 - 2*b34^2*b56*b6*b7^2 + b34^2*b6^4 - 2*b34^2* + b6^2*b7^2 + 2*b34*b4^3*b56^2 + 4*b34*b4^3*b56*b6 + 4*b34*b4^3*b6^2 - 2*b34*b4^3*b7^2 + 2*b34*b4*b56^2*b6^2 - 2*b34*b4*b56^2*b7^2 + + 4*b34*b4*b56*b6^3 - 2*b34*b4*b56*b6*b7^2 + 2*b34*b4*b6^4 - 2*b34*b4*b6^2*b7^2 + b4^4*b56^2 + 2*b4^4*b56*b6 + 2*b4^4*b6^2 - b4 + ^4*b7^2 + 2*b4^2*b56^2*b6^2 - 2*b4^2*b56^2*b7^2 + 4*b4^2*b56*b6^3 - 2*b4^2*b56*b6*b7^2 + 2*b4^2*b6^4 - 2*b4^2*b6^2*b7^2)*x^4 + ( + -b2^2*b34^2*b4^2*b56^2 - 2*b2^2*b34^2*b4^2*b56*b6 - 2*b2^2*b34^2*b4^2*b6^2 + b2^2*b34^2*b4^2*b7^2 - b2^2*b34^2*b56^2*b6^2 + b2^2 + *b34^2*b56^2*b7^2 - 2*b2^2*b34^2*b56*b6^3 + 2*b2^2*b34^2*b56*b6*b7^2 - b2^2*b34^2*b6^4 + 2*b2^2*b34^2*b6^2*b7^2 - 2*b2^2*b34*b4^ + 3*b56^2 - 4*b2^2*b34*b4^3*b56*b6 - 4*b2^2*b34*b4^3*b6^2 + 2*b2^2*b34*b4^3*b7^2 - 2*b2^2*b34*b4*b56^2*b6^2 + 2*b2^2*b34*b4*b56^2* + b7^2 - 4*b2^2*b34*b4*b56*b6^3 + 4*b2^2*b34*b4*b56*b6*b7^2 - 2*b2^2*b34*b4*b6^4 + 4*b2^2*b34*b4*b6^2*b7^2 - b2^2*b4^4*b56^2 - 2*b + 2^2*b4^4*b56*b6 - 2*b2^2*b4^4*b6^2 + b2^2*b4^4*b7^2 - 2*b2^2*b4^2*b56^2*b6^2 + 2*b2^2*b4^2*b56^2*b7^2 - 4*b2^2*b4^2*b56*b6^3 + 4 + *b2^2*b4^2*b56*b6*b7^2 - 2*b2^2*b4^2*b6^4 + 4*b2^2*b4^2*b6^2*b7^2 + b2^2*b56^2*b6^2*b7^2 + 2*b2^2*b56*b6^3*b7^2 + b2^2*b6^4*b7^2 + - b34^2*b4^2*b56^2*b6^2 + b34^2*b4^2*b56^2*b7^2 - 2*b34^2*b4^2*b56*b6^3 + 2*b34^2*b4^2*b56*b6*b7^2 - b34^2*b4^2*b6^4 + 2*b34^2* + b4^2*b6^2*b7^2 + b34^2*b56^2*b6^2*b7^2 + 2*b34^2*b56*b6^3*b7^2 + b34^2*b6^4*b7^2 - 2*b34*b4^3*b56^2*b6^2 + 2*b34*b4^3*b56^2*b7^2 + - 4*b34*b4^3*b56*b6^3 + 4*b34*b4^3*b56*b6*b7^2 - 2*b34*b4^3*b6^4 + 4*b34*b4^3*b6^2*b7^2 - b4^4*b56^2*b6^2 + b4^4*b56^2*b7^2 - 2 + *b4^4*b56*b6^3 + 2*b4^4*b56*b6*b7^2 - b4^4*b6^4 + 2*b4^4*b6^2*b7^2)*x^3 + (b2^2*b34^2*b4^2*b56^2*b6^2 - b2^2*b34^2*b4^2*b56^2*b7 + ^2 + 2*b2^2*b34^2*b4^2*b56*b6^3 - 2*b2^2*b34^2*b4^2*b56*b6*b7^2 + b2^2*b34^2*b4^2*b6^4 - 2*b2^2*b34^2*b4^2*b6^2*b7^2 - b2^2*b34^ + 2*b56^2*b6^2*b7^2 - 2*b2^2*b34^2*b56*b6^3*b7^2 - b2^2*b34^2*b6^4*b7^2 + 2*b2^2*b34*b4^3*b56^2*b6^2 - 2*b2^2*b34*b4^3*b56^2*b7^2 + + 4*b2^2*b34*b4^3*b56*b6^3 - 4*b2^2*b34*b4^3*b56*b6*b7^2 + 2*b2^2*b34*b4^3*b6^4 - 4*b2^2*b34*b4^3*b6^2*b7^2 - 2*b2^2*b34*b4*b56^ + 2*b6^2*b7^2 - 4*b2^2*b34*b4*b56*b6^3*b7^2 - 2*b2^2*b34*b4*b6^4*b7^2 + b2^2*b4^4*b56^2*b6^2 - b2^2*b4^4*b56^2*b7^2 + 2*b2^2*b4^4* + b56*b6^3 - 2*b2^2*b4^4*b56*b6*b7^2 + b2^2*b4^4*b6^4 - 2*b2^2*b4^4*b6^2*b7^2 - 2*b2^2*b4^2*b56^2*b6^2*b7^2 - 4*b2^2*b4^2*b56*b6^3 + *b7^2 - 2*b2^2*b4^2*b6^4*b7^2)*x^2 + (b2^2*b34^2*b4^2*b56^2*b6^2*b7^2 + 2*b2^2*b34^2*b4^2*b56*b6^3*b7^2 + b2^2*b34^2*b4^2*b6^4*b + 7^2 + 2*b2^2*b34*b4^3*b56^2*b6^2*b7^2 + 4*b2^2*b34*b4^3*b56*b6^3*b7^2 + 2*b2^2*b34*b4^3*b6^4*b7^2 + b2^2*b4^4*b56^2*b6^2*b7^2 + + 2*b2^2*b4^4*b56*b6^3*b7^2 + b2^2*b4^4*b6^4*b7^2)*x