Update booktests

test/book/cornerstones/algebraic-geometry/circlepar.jlcon

@@ -4,8 +4,8 @@ julia> I = ideal(R, [x^2 + y^2 - 1, y - t*x - 1]);
 
 julia> Gy = groebner_basis(I, ordering = lex([y, x, t]), complete_reduction=true)
 Gröbner basis with elements
-  1 -> x^2*t^2 + x^2 + 2*x*t
-  2 -> y - x*t - 1
+  1: x^2*t^2 + x^2 + 2*x*t
+  2: y - x*t - 1
 with respect to the ordering
   lex([y, x, t])
 
@@ -14,10 +14,10 @@ julia> factor(Gy[1])
 
 julia> Gx = groebner_basis(I, ordering = lex([x, y, t]), complete_reduction=true)
 Gröbner basis with elements
-  1 -> y^2*t^2 + y^2 - 2*y - t^2 + 1
-  2 -> x*t - y + 1
-  3 -> x*y - x + y^2*t - t
-  4 -> x^2 + y^2 - 1
+  1: y^2*t^2 + y^2 - 2*y - t^2 + 1
+  2: x*t - y + 1
+  3: x*y - x + y^2*t - t
+  4: x^2 + y^2 - 1
 with respect to the ordering
   lex([x, y, t])
 

test/book/cornerstones/algebraic-geometry/ex11.jlcon

@@ -4,8 +4,8 @@ julia> I = ideal(R, [x^2+y^2+2*z^2-8, x^2-y^2-z^2+1, x-y+z]);
 
 julia> groebner_basis(I, ordering = lex(R), complete_reduction = true)
 Gröbner basis with elements
-  1 -> 6*z^4 - 18*z^2 + 1
-  2 -> y + 3*z^3 - 9*z
-  3 -> x + 3*z^3 - 8*z
+  1: 6*z^4 - 18*z^2 + 1
+  2: y + 3*z^3 - 9*z
+  3: x + 3*z^3 - 8*z
 with respect to the ordering
   lex([x, y, z])

test/book/cornerstones/algebraic-geometry/ex314.jlcon

@@ -25,21 +25,21 @@ julia> p1 == ideal(minors(m3x3[1:3, 1:2],2))
 true
 
 julia> mp1 = ideal_as_module(p1)
-Graded submodule of S^1
-1 -> (-x_1*x_3 + x_2^2)*e[1]
-2 -> (-x_0*x_3 + x_1*x_2)*e[1]
-3 -> (-x_0*x_2 + x_1^2)*e[1]
+Graded submodule of S^1 with 3 generators
+  1: (-x_1*x_3 + x_2^2)*e[1]
+  2: (-x_0*x_3 + x_1*x_2)*e[1]
+  3: (-x_0*x_2 + x_1^2)*e[1]
 represented as subquotient with no relations
 
 julia> M1, _ = quo(ambient_free_module(mp1), mp1);
 
 julia> M1
-Graded subquotient of submodule of S^1 generated by
-1 -> e[1]
-by submodule of S^1 generated by
-1 -> (-x_1*x_3 + x_2^2)*e[1]
-2 -> (-x_0*x_3 + x_1*x_2)*e[1]
-3 -> (-x_0*x_2 + x_1^2)*e[1]
+Graded subquotient of graded submodule of S^1 with 1 generator
+  1: e[1]
+by graded submodule of S^1 with 3 generators
+  1: (-x_1*x_3 + x_2^2)*e[1]
+  2: (-x_0*x_3 + x_1*x_2)*e[1]
+  3: (-x_0*x_2 + x_1^2)*e[1]
 
 julia> mJ = ideal_as_module(J);
 
@@ -50,43 +50,45 @@ julia> homM1M, psi = hom(M1, M);
 julia> hom1, tohomM1M = prune_with_map(homM1M);
 
 julia> hom1
-Graded subquotient of submodule of S^2 generated by
-1 -> e[1]
-2 -> e[2]
-by submodule of S^2 generated by
-1 -> -x_2*e[1] + x_3*e[2]
-2 -> x_0*e[1] - x_1*e[2]
-3 -> -x_1*e[1] + x_2*e[2]
+Graded subquotient of graded submodule of S^2 with 2 generators
+  1: e[1]
+  2: e[2]
+by graded submodule of S^2 with 3 generators
+  1: -x_2*e[1] + x_3*e[2]
+  2: x_0*e[1] - x_1*e[2]
+  3: -x_1*e[1] + x_2*e[2]
 
 julia> degrees_of_generators(hom1)
 2-element Vector{FinGenAbGroupElem}:
  [2]
  [2]
 
 julia> phi1 = psi(tohomM1M(hom1[1]))
-M1 -> M
-e[1] -> (-x_0*x_3 + x_1*x_2)*e[1]
 Graded module homomorphism of degree [2]
-
+  from M1
+  to M
+defined by
+  e[1] -> (-x_0*x_3 + x_1*x_2)*e[1]
 
 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]
-
+  from M1
+  to M
+defined by
+  e[1] -> (-x_0*x_2 + x_1^2)*e[1]
 
 julia> kerphi2, _ = kernel(phi2);
 
 julia> iszero(kerphi2)
 true
 
 julia> MmodM1 = cokernel(phi2)
-Graded subquotient of submodule of S^1 generated by
-1 -> e[1]
-by submodule of S^1 generated by
-1 -> (x_1*x_3 - x_2^2)*e[1]
-2 -> (-x_0^2*x_3 + 2*x_0*x_1*x_2 - x_1^3)*e[1]
-3 -> (-x_0*x_2 + x_1^2)*e[1]
+Graded subquotient of graded submodule of S^1 with 1 generator
+  1: e[1]
+by graded submodule of S^1 with 3 generators
+  1: (x_1*x_3 - x_2^2)*e[1]
+  2: (-x_0^2*x_3 + 2*x_0*x_1*x_2 - x_1^3)*e[1]
+  3: (-x_0*x_2 + x_1^2)*e[1]
 
 julia> p2 = ideal([x[1],x[2],x[3]])
 Ideal generated by

test/book/specialized/decker-schmitt-invariant-theory/bertin.jlcon

@@ -20,11 +20,11 @@ julia> secondary_invariants(RG)
 julia> M, MtoR, StoR = module_syzygies(RG);
 
 julia> M
-Subquotient of Submodule with 5 generators
-1 -> e[1]
-2 -> e[2]
-3 -> e[3]
-4 -> e[4]
-5 -> e[5]
-by Submodule with 1 generator
-1 -> t2*e[2] + (t2 + t3)*e[3] + t1*e[4]
+Subquotient of submodule with 5 generators
+  1: e[1]
+  2: e[2]
+  3: e[3]
+  4: e[4]
+  5: e[5]
+by submodule with 1 generator
+  1: t2*e[2] + (t2 + t3)*e[3] + t1*e[4]

test/book/specialized/eder-mohr-ideal-theoretic/gbeliminate.jlcon

@@ -6,10 +6,10 @@ julia> I = ideal(R, [x^2 + y + z - 1, x + y^2 + z - 1, x + y + z^2 - 1]);
 
 julia> groebner_basis(I, ordering = o)
 Gröbner basis with elements
-  1 -> z^6 - 4*z^4 + 4*z^3 - z^2
-  2 -> 2*y*z^2 + z^4 - z^2
-  3 -> x + y + z^2 - 1
-  4 -> y^2 + x + z - 1
+  1: z^6 - 4*z^4 + 4*z^3 - z^2
+  2: 2*y*z^2 + z^4 - z^2
+  3: x + y + z^2 - 1
+  4: y^2 + x + z - 1
 with respect to the ordering
   degrevlex([x, y])*degrevlex([z])
 
@@ -19,8 +19,8 @@ Ideal generated by
 
 julia> groebner_basis(I)
 Gröbner basis with elements
-  1 -> z^2 + x + y - 1
-  2 -> y^2 + x + z - 1
-  3 -> x^2 + y + z - 1
+  1: z^2 + x + y - 1
+  2: y^2 + x + z - 1
+  3: x^2 + y + z - 1
 with respect to the ordering
   degrevlex([x, y, z])

test/book/specialized/eder-mohr-ideal-theoretic/lcis.jlcon

@@ -3,17 +3,17 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
 julia> I = ideal(R, [x*y, x*z, y*z]);
 
 julia> conorm = subquotient(matrix(gens(I)), matrix(gens(I^2)))
-Subquotient of Submodule with 3 generators
-1 -> x*y*e[1]
-2 -> x*z*e[1]
-3 -> y*z*e[1]
-by Submodule with 6 generators
-1 -> x^2*y^2*e[1]
-2 -> x^2*y*z*e[1]
-3 -> x*y^2*z*e[1]
-4 -> x^2*z^2*e[1]
-5 -> x*y*z^2*e[1]
-6 -> y^2*z^2*e[1]
+Subquotient of submodule with 3 generators
+  1: x*y*e[1]
+  2: x*z*e[1]
+  3: y*z*e[1]
+by submodule with 6 generators
+  1: x^2*y^2*e[1]
+  2: x^2*y*z*e[1]
+  3: x*y^2*z*e[1]
+  4: x^2*z^2*e[1]
+  5: x*y*z^2*e[1]
+  6: y^2*z^2*e[1]
 
 julia> fitting_ideal(conorm, 1)
 Ideal generated by