Yet another attempt to revise printing for modules (#4251)

* Revise printing of modules

* Adjust test case in test/Modules/ExteriorPowers.jl for new printing

* update jldoctest

* Also adjust printing of ideals

* update doctests

* Also update README.md

* Update code snippet, change to jldoctest

* Update code snippets which are not doctests

* Update booktests

README.md

@@ -70,34 +70,28 @@ Free module of rank 1 over R
 
 julia> s = sub(F, [f*F[1]])[1]
 Submodule with 1 generator
-1 -> (x1^2 + x2)*e[1]
-represented as subquotient with no relations.
+  1: (x1^2 + x2)*e[1]
+represented as subquotient with no relations
 
 julia> H, mH = hom(s, quo(F, s)[1])
-(hom of (s, Subquotient of
-1 -> e[1]
-by
-1 -> (x1^2 + x2)*e[1]), Map: H -> set of all homomorphisms from s to subquotient of Submodule with 1 generator
-1 -> e[1]
-by Submodule with 1 generator
-1 -> (x1^2 + x2)*e[1])
+(hom of (s, Subquotient of submodule with 1 generator
+  1: e[1]
+by submodule with 1 generator
+  1: (x1^2 + x2)*e[1]), Map: H -> set of all homomorphisms from s to subquotient of submodule with 1 generator
+  1: e[1]
+by submodule with 1 generator
+  1: (x1^2 + x2)*e[1])
 
 julia> mH(H[1])
-Map with following data
-Domain:
-=======
-Submodule with 1 generator
-1 -> (x1^2 + x2)*e[1]
-represented as subquotient with no relations.
-Codomain:
-=========
-Subquotient of Submodule with 1 generator
-1 -> e[1]
-by Submodule with 1 generator
-1 -> (x1^2 + x2)*e[1]
+Module homomorphism
+  from s
+  to subquotient of submodule with 1 generator
+    1: e[1]
+  by submodule with 1 generator
+    1: (x1^2 + x2)*e[1]
 ```
 
-Of course, the cornerstones are also available directly:
+Of course, the cornerstones are also available directly. For example:
 
 ```
 julia> C = Polymake.polytope.cube(3);

docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases_integers.md

@@ -60,11 +60,11 @@ Ideal generated by
 
 julia> G = groebner_basis(I, ordering = lex(R))
 Gröbner basis with elements
-  1 -> 28*y^3 - 35*y
-  2 -> 4*x*y^2 - 5*x
-  3 -> 15*x^2 + 28*y^2
-  4 -> 3*x^2*y + 7*y
-  5 -> x^2*y^2 - 5*x^2 - 7*y^2
+  1: 28*y^3 - 35*y
+  2: 4*x*y^2 - 5*x
+  3: 15*x^2 + 28*y^2
+  4: 3*x^2*y + 7*y
+  5: x^2*y^2 - 5*x^2 - 7*y^2
 with respect to the ordering
   lex([x, y])
 ```

docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/complexes.md

@@ -50,25 +50,15 @@ julia> range(C)
 5:-1:3
 
 julia> C[5]
-Subquotient of Submodule with 1 generator
-1 -> e[1]
-by Submodule with 1 generator
-1 -> x^4*e[1]
+Subquotient of submodule with 1 generator
+  1: e[1]
+by submodule with 1 generator
+  1: x^4*e[1]
 
 julia> delta = map(C, 5)
-Map with following data
-Domain:
-=======
-Subquotient of Submodule with 1 generator
-1 -> e[1]
-by Submodule with 1 generator
-1 -> x^4*e[1]
-Codomain:
-=========
-Subquotient of Submodule with 1 generator
-1 -> e[1]
-by Submodule with 1 generator
-1 -> x^3*e[1]
+Module homomorphism
+  from A
+  to B
 
 julia> matrix(delta)
 [x^2]

docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md

@@ -96,13 +96,13 @@ julia> B = R[x^2; y^3; z^4]
 [z^4]
 
 julia> M = SubquoModule(F, A, B)
-Subquotient of Submodule with 2 generators
-1 -> x*e[1]
-2 -> y*e[1]
-by Submodule with 3 generators
-1 -> x^2*e[1]
-2 -> y^3*e[1]
-3 -> z^4*e[1]
+Subquotient of submodule with 2 generators
+  1: x*e[1]
+  2: y*e[1]
+by submodule with 3 generators
+  1: x^2*e[1]
+  2: y^3*e[1]
+  3: z^4*e[1]
 
 julia> base_ring(M)
 Multivariate polynomial ring in 3 variables x, y, z
@@ -134,12 +134,12 @@ julia> relations(M)
  z^4*e[1]
 
 julia> ambient_module(M)
-Subquotient of Submodule with 1 generator
-1 -> e[1]
-by Submodule with 3 generators
-1 -> x^2*e[1]
-2 -> y^3*e[1]
-3 -> z^4*e[1]
+Subquotient of submodule with 1 generator
+  1: e[1]
+by submodule with 3 generators
+  1: x^2*e[1]
+  2: y^3*e[1]
+  3: z^4*e[1]
 ```
 
 In the graded case, we also have:
@@ -191,13 +191,13 @@ julia> B = R[x^2; y^3; z^4]
 [z^4]
 
 julia> M = SubquoModule(F, A, B)
-Subquotient of Submodule with 2 generators
-1 -> x*e[1]
-2 -> y*e[1]
-by Submodule with 3 generators
-1 -> x^2*e[1]
-2 -> y^3*e[1]
-3 -> z^4*e[1]
+Subquotient of submodule with 2 generators
+  1: x*e[1]
+  2: y*e[1]
+by submodule with 3 generators
+  1: x^2*e[1]
+  2: y^3*e[1]
+  3: z^4*e[1]
 
 julia> m = M(sparse_row(R, [(1,z),(2,one(R))]))
 (x*z + y)*e[1]
@@ -247,25 +247,25 @@ julia> B = R[x^2; y^3; z^4]
 [z^4]
 
 julia> M = SubquoModule(F, A, B)
-Subquotient of Submodule with 2 generators
-1 -> x*e[1]
-2 -> y*e[1]
-by Submodule with 3 generators
-1 -> x^2*e[1]
-2 -> y^3*e[1]
-3 -> z^4*e[1]
+Subquotient of submodule with 2 generators
+  1: x*e[1]
+  2: y*e[1]
+by submodule with 3 generators
+  1: x^2*e[1]
+  2: y^3*e[1]
+  3: z^4*e[1]
 
 julia> m = z*M[1] + M[2]
 (x*z + y)*e[1]
 
 julia> parent(m)
-Subquotient of Submodule with 2 generators
-1 -> x*e[1]
-2 -> y*e[1]
-by Submodule with 3 generators
-1 -> x^2*e[1]
-2 -> y^3*e[1]
-3 -> z^4*e[1]
+Subquotient of submodule with 2 generators
+  1: x*e[1]
+  2: y*e[1]
+by submodule with 3 generators
+  1: x^2*e[1]
+  2: y^3*e[1]
+  3: z^4*e[1]
 
 julia> coordinates(m)
 Sparse row with positions [1, 2] and values QQMPolyRingElem[z, 1]

experimental/GroebnerWalk/src/common.jl

@@ -30,31 +30,31 @@ julia> I = ideal([y^4+ x^3-x^2+x,x^4]);
 
 julia> groebner_walk(I, lex(R))
 Gröbner basis with elements
-  1 -> x + y^12 - y^8 + y^4
-  2 -> y^16
+  1: x + y^12 - y^8 + y^4
+  2: y^16
 with respect to the ordering
   lex([x, y])
 
 julia> groebner_walk(I, lex(R); algorithm=:generic)
 Gröbner basis with elements
-  1 -> y^16
-  2 -> x + y^12 - y^8 + y^4
+  1: y^16
+  2: x + y^12 - y^8 + y^4
 with respect to the ordering
   lex([x, y])
 
 julia> set_verbosity_level(:groebner_walk, 1);
 
 julia> groebner_walk(I, lex(R))
 Results for standard_walk
-Crossed Cones in: 
+Crossed Cones in:
 ZZRingElem[1, 1]
 ZZRingElem[4, 3]
 ZZRingElem[4, 1]
 ZZRingElem[12, 1]
 Cones crossed: 4
 Gröbner basis with elements
-  1 -> x + y^12 - y^8 + y^4
-  2 -> y^16
+  1: x + y^12 - y^8 + y^4
+  2: y^16
 with respect to the ordering
   lex([x, y])
 

experimental/Schemes/src/Tjurina.jl

@@ -769,17 +769,17 @@ Spectrum
     at complement of maximal ideal of point (0, 0, 0)
 
 julia> T = tjurina_module(X)
-Subquotient of Submodule with 2 generators
-1 -> e[1]
-2 -> e[2]
-by Submodule with 7 generators
-1 -> 2*x*e[1] + y*e[2]
-2 -> 2*y*e[1] + x*e[2]
-3 -> -2*z*e[1]
-4 -> (x^2 + y^2 - z^2)*e[1]
-5 -> (x^2 + y^2 - z^2)*e[2]
-6 -> x*y*e[1]
-7 -> x*y*e[2]
+Subquotient of submodule with 2 generators
+  1: e[1]
+  2: e[2]
+by submodule with 7 generators
+  1: 2*x*e[1] + y*e[2]
+  2: 2*y*e[1] + x*e[2]
+  3: -2*z*e[1]
+  4: (x^2 + y^2 - z^2)*e[1]
+  5: (x^2 + y^2 - z^2)*e[2]
+  6: x*y*e[1]
+  7: x*y*e[2]
 
 julia> vector_space_basis(T)
 5-element Vector{Any}:

src/AlgebraicGeometry/Schemes/Sheaves/CoherentSheaves.jl

@@ -264,10 +264,10 @@ Coherent sheaf of modules
     3: [(s0//s2), (s1//s2), (s3//s2)]   affine 3-space
     4: [(s0//s3), (s1//s3), (s2//s3)]   affine 3-space
 with restrictions
-  1: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
-  2: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
-  3: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
-  4: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+  1: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
+  2: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
+  3: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
+  4: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
 ```
 """
 function twisting_sheaf(IP::AbsProjectiveScheme{<:Field}, d::Int)
@@ -325,10 +325,10 @@ Coherent sheaf of modules
     3: [(s0//s2), (s1//s2), (s3//s2)]   affine 3-space
     4: [(s0//s3), (s1//s3), (s2//s3)]   affine 3-space
 with restrictions
-  1: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
-  2: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
-  3: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
-  4: free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ
+  1: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
+  2: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
+  3: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
+  4: free module of rank 1 over multivariate polynomial ring in 3 variables over QQ
 ```
 """
 function tautological_bundle(IP::AbsProjectiveScheme{<:Field})

src/AlgebraicGeometry/Surfaces/AdjunctionProcess/AdjunctionProcess.jl

@@ -141,18 +141,17 @@ Given a smooth projective variety `X`, return a module whose sheafification is t
 
 # Examples
 
-```
+```jldoctest
 julia> R, x = graded_polynomial_ring(QQ, :x => (1:6));
 
 julia> I = ideal(R, [x[1]*x[6] - x[2]*x[5] + x[3]*x[4]]);
 
-julia> GRASSMANNIAN = variety(I);  
+julia> GRASSMANNIAN = variety(I);
 
 julia> Omega = canonical_bundle(GRASSMANNIAN)
-Graded subquotient of submodule of R^1 generated by
-1 -> e[1]
-by submodule of R^1 generated by
-1 -> (x[1]*x[6] - x[2]*x[5] + x[3]*x[4])*e[1]
+Graded submodule of R^1 with 1 generator
+  1: e[1]
+represented as subquotient with no relations
 
 julia> degrees_of_generators(Omega)
 1-element Vector{FinGenAbGroupElem}:
@@ -167,10 +166,9 @@ julia> I = ideal(R, [y^2*z + x*y*z - x^3 - x*z^2 - z^3]);
 julia> ELLCurve = variety(I);
 
 julia> Omega = canonical_bundle(ELLCurve)
-Graded subquotient of submodule of R^1 generated by
-1 -> e[1]
-by submodule of R^1 generated by
-1 -> (x^3 - x*y*z + x*z^2 - y^2*z + z^3)*e[1]
+Graded submodule of R^1 with 1 generator
+  1: e[1]
+represented as subquotient with no relations
 
 julia> degrees_of_generators(Omega)
 1-element Vector{FinGenAbGroupElem}:

src/Modules/ModuleTypes.jl

@@ -294,14 +294,14 @@ julia> B = R[x^2; x*y; y^2; z^4]
 [z^4]
 
 julia> M = SubquoModule(A, B)
-Subquotient of Submodule with 2 generators
-1 -> x*e[1]
-2 -> y*e[1]
-by Submodule with 4 generators
-1 -> x^2*e[1]
-2 -> x*y*e[1]
-3 -> y^2*e[1]
-4 -> z^4*e[1]
+Subquotient of submodule with 2 generators
+  1: x*e[1]
+  2: y*e[1]
+by submodule with 4 generators
+  1: x^2*e[1]
+  2: x*y*e[1]
+  3: y^2*e[1]
+  4: z^4*e[1]
 
 julia> f = SubquoModuleElem(sparse_row(R, [(1,z),(2,one(R))]),M)
 (x*z + y)*e[1]