booktests: redo some whitespace / omission / seed fixes

oscar-system · Oct 18, 2024 · 571179c · 571179c
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diff --git 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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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