CommutativeAlgebra: fixed bibtool test and docs

Author: YueRen

docs/oscar_references.bib

@@ -2019,7 +2019,7 @@ @Article{Laz92
   pages         = {117--131},
   year          = {1992},
   month         = feb,
-  doi           = {10.1016/S0747-7171(08)80086-7},
+  doi           = {10.1016/S0747-7171(08)80086-7}
 }
 
 @PhDThesis{Lev05,
@@ -2148,7 +2148,7 @@ @Article{Moe93
   pages         = {217--230},
   year          = {1993},
   month         = dec,
-  doi           = {10.1007/BF01200146},
+  doi           = {10.1007/BF01200146}
 }
 
 @Article{Nik79,

docs/src/CommutativeAlgebra/ideals.md

@@ -259,7 +259,7 @@ equidimensional_hull_radical(I::MPolyIdeal)
 ### Triangular Decomposition
 
 ```@docs
-triangular_decomposition(::MPolyIdeal, ::Symbol)
+triangular_decomposition(::MPolyIdeal)
 ```
 
 

src/Rings/mpoly-ideals.jl

@@ -307,8 +307,8 @@ end
 
 # saturation #######################################################
 @doc raw"""
-    saturation(I::MPolyIdeal{T}, 
-               J::MPolyIdeal{T} = ideal(base_ring(I), gens(base_ring(I))); 
+    saturation(I::MPolyIdeal{T},
+               J::MPolyIdeal{T} = ideal(base_ring(I), gens(base_ring(I)));
                iteration::Bool=false) where T
 
 Return the saturation of `I` with respect to `J`.
@@ -372,7 +372,7 @@ _saturation2(I::MPolyIdeal{T}, J::MPolyIdeal{T} = ideal(base_ring(I), gens(base_
 
 #######################################################
 @doc raw"""
-    saturation_with_index(I::MPolyIdeal{T}, 
+    saturation_with_index(I::MPolyIdeal{T},
                           J::MPolyIdeal{T} = ideal(base_ring(I), gens(base_ring(I)))) where T
 
 Return $I:J^{\infty}$ together with the smallest integer $m$ such that $I:J^m = I:J^{\infty}$ (saturation index).
@@ -509,7 +509,7 @@ function eliminate(I::MPolyIdeal, o::MonomialOrdering, l::Int)
   @req is_elimination_ordering(o, R_gens) "Given ordering is not an elimination ordering"
   gb = get(I.gb, o, nothing)
   isnothing(gb) && return eliminate(I, R_gens)
-  
+
   elimination_ideal_gens_indices = findall(x -> cmp(o, R_gens[end], leading_monomial(x; ordering=o)) > 0, gens(gb))
   isempty(elimination_ideal_gens_indices) && return ideal(R, [])
   ideal(IdealGens(gens(gb)[elimination_ideal_gens_indices], o; isGB=true))
@@ -530,7 +530,7 @@ Return the radical of `I`.
 
 # Implemented Algorithms
 
-  * If the base ring of `I` is a polynomial ring over a the field of rational numbers or a finite field, a combination of the algorithms of Krick and Logar (with modifications by Laplagne) and Kemper is used. 
+  * If the base ring of `I` is a polynomial ring over a the field of rational numbers or a finite field, a combination of the algorithms of Krick and Logar (with modifications by Laplagne) and Kemper is used.
   * If the `base_ring` of `I` is a number field, then we first expand the minimal polynomials to reduce to a computation over the rationals.
   * For polynomial rings over the integers, the algorithm proceeds as suggested by Pfister, Sadiq, and Steidel. See [KL91](@cite), [Kem02](@cite), and [PSS11](@cite).
 
@@ -639,27 +639,27 @@ Ideal generated by
 ```
 """
 @attr MPolyIdeal{T} function radical(
-    I::MPolyIdeal{T}; 
+    I::MPolyIdeal{T};
     preprocessing::Bool=true,
     eliminate_variables::Bool=true,
     factor_generators::Bool=true
   ) where {T <: MPolyRingElem}
   is_known(is_radical, I) && is_radical(I) && return I
-  # We first check for the squarefree flag. 
-  # Elimination of variables will probably affect how the generators factor. 
+  # We first check for the squarefree flag.
+  # Elimination of variables will probably affect how the generators factor.
   if preprocessing && factor_generators
-    # Replace every generator by its squarefree part to get closer to the actual radical 
+    # Replace every generator by its squarefree part to get closer to the actual radical
     # even before passing computations on to Singular.
     return radical(_squarefree_generator_ideal(I); preprocessing, eliminate_variables, factor_generators=false)
   end
   if preprocessing && eliminate_variables
     is_known(is_radical, I) && is_radical(I) && return I
-    # Call `elimpart` (within `simplify`) in order to substitute variables. 
+    # Call `elimpart` (within `simplify`) in order to substitute variables.
     # This turns out to significantly speed things up in many cases.
     R = base_ring(I)
     Q, pr = quo(R, I)
     S, iso, iso_inv = simplify(Q)
-    is_zero(ngens(S)) && return I # This only happens when all variables can be eliminated. 
+    is_zero(ngens(S)) && return I # This only happens when all variables can be eliminated.
     # Then the ideal defines a reduced point.
     J = modulus(S)
     pre_res = radical(J; preprocessing, eliminate_variables=false, factor_generators)
@@ -704,7 +704,7 @@ function _compute_radical(I::T) where {T <: MPolyIdeal}
   return Irad
 end
 
-# Go through the generators of I and replace each generator by its squarefree part. 
+# Go through the generators of I and replace each generator by its squarefree part.
 # This is a heuristic preprocessing method for radical computations.
 function _squarefree_generator_ideal(I::MPolyIdeal)
   R = base_ring(I)
@@ -723,18 +723,18 @@ end
 @attr MPolyIdeal{T} function radical(
     I::MPolyIdeal{T};
     preprocessing::Bool=true,
-    factor_generators::Bool=true, 
+    factor_generators::Bool=true,
     eliminate_variables::Bool=true
   ) where {U<:Hecke.RelSimpleNumFieldElem, T<:MPolyRingElem{U}}
   is_known(is_radical, I) && is_radical(I) && return I
   R = base_ring(I)
   preprocessing && factor_generators && return radical(_squarefree_generator_ideal(I); preprocessing, eliminate_variables, factor_generators=false)
   R_flat, iso, iso_inv = _expand_coefficient_field_to_QQ(R)
   I_flat = ideal(R_flat, iso_inv.(gens(I)))
-  I_flat_rad = radical(I_flat; 
+  I_flat_rad = radical(I_flat;
                        preprocessing,
-                       eliminate_variables, 
-                       factor_generators=false) # Taking the squarefree part of generators only pays off on the top level. 
+                       eliminate_variables,
+                       factor_generators=false) # Taking the squarefree part of generators only pays off on the top level.
   Irad = iso(I_flat_rad)
   set_attribute!(Irad, :is_radical => true)
   @hassert :IdealSheaves 2 !is_one(Irad)
@@ -875,7 +875,7 @@ end
 is_known(::typeof(primary_decomposition), I::MPolyIdeal) = has_attribute(I, :primary_decomposition)
 
 function primary_decomposition(
-    I::MPolyIdeal{T}; 
+    I::MPolyIdeal{T};
     algorithm::Symbol=:GTZ, cache::Bool=true
   ) where {U<:Hecke.RelSimpleNumFieldElem, T<:MPolyRingElem{U}}
   if has_attribute(I, :primary_decomposition)
@@ -887,7 +887,7 @@ function primary_decomposition(
   dec = primary_decomposition(I_flat; algorithm, cache)
   result = Vector{Tuple{typeof(I), typeof(I)}}()
   for (P, Q) in dec
-    push!(result, (ideal(R, unique!([x for x in iso.(gens(P)) if !iszero(x)])), 
+    push!(result, (ideal(R, unique!([x for x in iso.(gens(P)) if !iszero(x)])),
                    ideal(R, unique!([x for x in iso.(gens(Q)) if !iszero(x)]))))
   end
 
@@ -1010,7 +1010,7 @@ Ideal generated by
   x + _a*y
 
 julia> RAP = base_ring(AP)
-Multivariate polynomial ring in 2 variables over number field graded by 
+Multivariate polynomial ring in 2 variables over number field graded by
   x -> [1]
   y -> [1]
 ```
@@ -1225,12 +1225,12 @@ end
 
 is_known(::typeof(minimal_primes), I::MPolyIdeal) = has_attribute(I, :minimal_primes)
 
-# rerouting the procedure for minimal primes this way leads to 
+# rerouting the procedure for minimal primes this way leads to
 # much longer computations compared to the flattening of the coefficient
 # field implemented above.
 function minimal_primes(
-    I::MPolyIdeal{T}; 
-    algorithm::Symbol=:GTZ, 
+    I::MPolyIdeal{T};
+    algorithm::Symbol=:GTZ,
     eliminate_variables::Bool=true,
     cache::Bool=true
   ) where {U<:Union{AbsSimpleNumFieldElem, <:Hecke.RelSimpleNumFieldElem}, T<:MPolyRingElem{U}}
@@ -1347,7 +1347,7 @@ end
 
 Return a vector of equidimensional radical ideals increasingly ordered by dimension.
 For each dimension, the returned radical ideal is the intersection of the associated primes
-of `I` of that dimension. 
+of `I` of that dimension.
 
 # Implemented Algorithms
 
@@ -1614,7 +1614,8 @@ julia> triangular_decomposition(I; algorithm=:lazard_factorized)
  Ideal (x5 - 1, x4^4 + x4^3 + x4^2 + x4 + 1, -x3 + x4^2, -x2 + x4^3, x1 + x4^3 + x4^2 + x4 + 1)
  Ideal (x5^2 + 3*x5 + 1, x4 - 1, x3 - 1, x2 - 1, x1 + x5 + 3)
  Ideal (x5^2 + 3*x5 + 1, x4 + x5 + 3, x3 - 1, x2 - 1, x1 - 1)
- ⋮
+ Ideal with 5 generators
+ Ideal (x5^4 + x5^3 + x5^2 + x5 + 1, x4 - 1, x3 + x5^3 + x5^2 + x5 + 1, -x2 + x5^3, -x1 + x5^2)
  Ideal (x5^4 + x5^3 + x5^2 + x5 + 1, x4 - x5, x3 - x5, x2^2 + 3*x2*x5 + x5^2, x1 + x2 + 3*x5)
  Ideal (x5^4 + x5^3 + x5^2 + x5 + 1, x4 - x5, x3^2 + 3*x3*x5 + x5^2, x2 + x3 + 3*x5, x1 - x5)
  Ideal with 5 generators
@@ -2072,7 +2073,7 @@ end
 
 # In general this depends on the ring, ...
 is_known(::typeof(is_zero), I::MPolyIdeal) = true
-# but for specific rings we can do more. 
+# but for specific rings we can do more.
 is_known(::typeof(is_zero), I::MPolyIdeal{QQMPolyRingElem}) = true
 
 @doc raw"""
@@ -2109,7 +2110,7 @@ end
 function is_known(::typeof(is_one), I::MPolyIdeal)
   has_attribute(I, :is_one) && return true
   !is_empty(I.gb) && return true # a Groebner basis has already been computed
-  if any(is_unit, gens(I)) 
+  if any(is_unit, gens(I))
     set_attribute!(I, :is_one=>true)
     return true
   end
@@ -2260,7 +2261,7 @@ function small_generating_set(
     # than the original one!!!
     return_value = filter(!iszero, (R).(gens(sing_min)))
 
-    # The following is a common phenomenon which we can not fully explain yet. So far nothing but a 
+    # The following is a common phenomenon which we can not fully explain yet. So far nothing but a
     # restart really seems to help, unfortunately.
     if is_zero(length(return_value))
       !is_zero(I) && error("singular crashed in the background; please restart your session!")
@@ -2290,7 +2291,7 @@ small_generating_set(I::MPolyIdeal{<:MPolyDecRingElem}; algorithm::Symbol=:simpl
 ################################################################################
 #returns Pluecker ideal in ring with standard grading
 function grassmann_pluecker_ideal(subspace_dimension::Int, ambient_dimension::Int)
-  I = convert(MPolyIdeal{QQMPolyRingElem}, 
+  I = convert(MPolyIdeal{QQMPolyRingElem},
 	      Polymake.ideal.pluecker_ideal(subspace_dimension, ambient_dimension))
   base = base_ring(I)
   base2, x = graded_polynomial_ring(coefficient_ring(base), :x=> sort(subsets(ambient_dimension, subspace_dimension)))
@@ -2310,8 +2311,8 @@ generated by the Plücker relations. If the input ring is not graded, return the
 If the ring is not specified return the ideal in a multivariate polynomial ring over the rationals with variables indexed by
 elements of ${[n]\choose d}$ with the standard grading.
 
-The Grassmann-Plücker ideal is the homogeneous ideal generated by the relations defined by 
-the Plücker Embedding of the Grassmannian. That is given Gr$(k, n)$ the Moduli 
+The Grassmann-Plücker ideal is the homogeneous ideal generated by the relations defined by
+the Plücker Embedding of the Grassmannian. That is given Gr$(k, n)$ the Moduli
 space of all $k$-dimensional subspaces of an $n$-dimensional vector space, the relations
 are given by all $d \times d$ minors of a $d \times n$ matrix. For the algorithm see
 [Stu93](@cite).
@@ -2332,7 +2333,7 @@ Ideal generated by
 """
 function grassmann_pluecker_ideal(ring::MPolyRing,
                                  subspace_dimension::Int,
-                                 ambient_dimension::Int) 
+                                 ambient_dimension::Int)
   I = grassmann_pluecker_ideal(subspace_dimension, ambient_dimension)
   coeff_ring = base_ring(ring)
   o = degrevlex(ring)
@@ -2374,7 +2375,7 @@ _pluecker_sgn(a::Vector{Int}, b::Vector{Int}, t::Int)::Int =
 @doc raw"""
     flag_pluecker_ideal(F::Union{Field, MPolyRing}, dimensions::Vector{Int}, n::Int; minimal::Bool=true)
 
-Return the generators of the defining ideal for the complete flag variety 
+Return the generators of the defining ideal for the complete flag variety
 $\text{Fl}(\mathbb{F}, (d_1,\dots,d_k), n)$, where $(d_1,\dots,d_k)
 =$`dimensions`, with $d_j\leq n-1$,  denotes the rank.  That is, the vanishing
 set of this ideal corresponds to the space of $k$-step flags of linear
@@ -2391,7 +2392,7 @@ Evaluating this function with the parameter `minimal = true` returns the reduced
 the flag Plücker ideal with respect to the degree reverse lexicographical order. For more details, see Theorem 14.6 [MS05](@cite)
 # Examples
 
-Complete flag variety $\text{Fl}(\mathbb{Q}, (1,2,3), 4)$. 
+Complete flag variety $\text{Fl}(\mathbb{Q}, (1,2,3), 4)$.
 ```jldoctest
 julia> flag_pluecker_ideal(QQ,[1,2,3],4)
 Ideal generated by
@@ -2435,7 +2436,7 @@ flag_pluecker_ideal(dimensions::Vector{Int}, n::Int; minimal::Bool=true) = flag_
 
 function flag_pluecker_ideal(ring::MPolyRing{<: FieldElem}, dimensions::Vector{Int}, n::Int; minimal::Bool=true)
   dimensions = unique(dimensions)
-   
+
   @req maximum(dimensions) <= n-1 "The dimensions must be at most n-1"
   @req sum(binomial(n, d) for d in dimensions) == ngens(ring) "The ring doesn't have the right number of variables"
   @req issorted(dimensions) "The dimensions must be increasing"
@@ -2462,7 +2463,7 @@ function flag_pluecker_ideal(ring::MPolyRing{<: FieldElem}, dimensions::Vector{I
   gg = unique(x ->  divexact(x, canonical_unit(x)), genz)
   I  = ideal(gg)
 
-  !minimal && return I 
+  !minimal && return I
 
   o = degrevlex(ring)
   converted_generators = collect(groebner_basis(I; ordering = o))
@@ -2473,7 +2474,7 @@ function flag_pluecker_ideal(ring::MPolyRing{<: FieldElem}, dimensions::Vector{I
 end
 
 # Since most ideals implement `==`, they have to implement the hash function.
-# See issue #4143 for problems entailed. Interestingly, this does not yet fix 
+# See issue #4143 for problems entailed. Interestingly, this does not yet fix
 # the failure of unique! on lists of ideals.
 function hash(I::Ideal, c::UInt)
   return hash(base_ring(I), c)