Extend is_invertible_with_inverse to rings of type `MPolyQuoRing{<:…

…MPolyDecRingElem}` (oscar-system#4226)

* Extend `is_invertible_with_inverse` to rings of type `MPolyQuoRing{<:MPolyDecRingElem}`

* correction

* Adressing remark by @joschmitt

* correction

* add extended function to docu

* correction

docs/src/CommutativeAlgebra/affine_algebras.md

@@ -171,6 +171,10 @@ simplify(f::MPolyQuoRingElem)
 ==(f::MPolyQuoRingElem{T}, g::MPolyQuoRingElem{T}) where T
 ```
 
+```@docs
+is_invertible_with_inverse(f::MPolyQuoRingElem)
+```
+
 In the graded case, we additionally have:
 
 ```@docs

experimental/IntersectionTheory/docs/src/AbstractBundles.md

@@ -39,7 +39,7 @@ top_chern_class(F::AbstractBundle)
 ```
 
 ```@docs
-segre_class(F::AbstractBundle)
+total_segre_class(F::AbstractBundle)
 ```
 
 ```@docs

experimental/IntersectionTheory/src/IntersectionTheory.jl

@@ -55,6 +55,7 @@ export pushforward
 export schubert_class
 export schubert_classes
 export schur_functor
+export total_segre_class
 export segre_class
 export structure_map
 export tangent_bundle
@@ -134,6 +135,7 @@ export pushforward
 export schubert_class
 export schubert_classes
 export schur_functor
+export total_segre_class
 export segre_class
 export structure_map
 export tangent_bundle

experimental/IntersectionTheory/src/Main.jl

@@ -90,6 +90,12 @@ AbstractBundle of rank 2 on AbstractVariety of dim 6
 julia> total_chern_class(Q)
 c[1]^2 - c[1] - c[2] + 1
 
+julia> chern_class(Q, 1)
+-c[1]
+
+julia> chern_class(Q, 2)
+c[1]^2 - c[2]
+
 ```
 """
 total_chern_class(F::AbstractBundle) = (
@@ -161,18 +167,37 @@ julia> top_chern_class(F)
 top_chern_class(F::AbstractBundle) = chern_class(F, F.rank)
 
 @doc raw"""
-    segre_class(F::AbstractBundle)
+    total_segre_class(F::AbstractBundle)
 
 Return the total Segre class of `F`.
+
+# Examples
+```jldoctest
+julia> G = abstract_grassmannian(3,5)
+AbstractVariety of dim 6
+
+julia> Q = tautological_bundles(G)[2]
+AbstractBundle of rank 2 on AbstractVariety of dim 6
+
+julia> C = total_chern_class(Q)
+c[1]^2 - c[1] - c[2] + 1
+
+julia> S = total_segre_class(Q)
+c[1] + c[2] + c[3] + 1
+
+julia> C*S
+1
+
+```
 """
-segre_class(F::AbstractBundle) = inv(total_chern_class(F))
+total_segre_class(F::AbstractBundle) = inv(total_chern_class(F))
 
 @doc raw"""
     segre_class(F::AbstractBundle, k::Int)
 
-Retuen the `k`-th Segre class of `F`.
+Return the `k`-th Segre class of `F`.
 """
-segre_class(F::AbstractBundle, k::Int) = segre_class(F)[k]
+segre_class(F::AbstractBundle, k::Int) = total_segre_class(F)[k]
 
 @doc raw"""
     todd_class(F::AbstractBundle)

src/Rings/MPolyQuo.jl

@@ -1100,6 +1100,33 @@ end
 
 one(Q::MPolyQuoRing) = Q(1)
 
+@doc raw"""
+    is_invertible_with_inverse(f::MPolyQuoRingElem)
+
+If `f` is invertible with inverse `g`, say, return `(true, g)`. Otherwise, return `(false, f)`.
+
+# Examples
+
+```jldoctest
+julia> R, c = polynomial_ring(QQ, :c => (1:3));
+
+julia> R, c = grade(R, [1, 2, 3]);
+
+julia> I = ideal(R, [  -c[1]^3 + 2*c[1]*c[2] - c[3], c[1]^4 - 3*c[1]^2*c[2] + 2*c[1]*c[3] + c[2]^2,-c[1]^5 + 4*c[1]^3*c[2] - 3*c[1]^2*c[3] - 3*c[1]*c[2]^2 + 2*c[2]*c[3]]);
+
+julia> A, _ = quo(R, I);
+
+julia> f = A(c[1]^2 - c[1] - c[2] + 1)
+c[1]^2 - c[1] - c[2] + 1
+
+julia> tt, g = is_invertible_with_inverse(f)
+(true, c[1] + c[2] + c[3] + 1)
+
+julia> f*g
+1
+
+```
+"""
 function is_invertible_with_inverse(a::MPolyQuoRingElem)
   # TODO:
   # Eventually, the code below should be replaced
@@ -1111,6 +1138,11 @@ function is_invertible_with_inverse(a::MPolyQuoRingElem)
   Q = parent(a)
   J = oscar_groebner_basis(Q)
   J = vcat(J, [a.f])
+
+  if Q isa MPolyQuoRing{<:MPolyDecRingElem}
+     J = [x.f for x in J]
+  end
+
   j, T = standard_basis_with_transformation_matrix(ideal(J))
   if is_constant(j[1]) && is_unit(first(coefficients(j[1])))
     @assert ncols(T) == 1
@@ -1121,6 +1153,28 @@ end
 
 is_unit(a::MPolyQuoRingElem) = is_invertible_with_inverse(a)[1]
 
+@doc raw"""
+    inv(f::MPolyQuoRingElem)
+
+If `f` is invertible, return its inverse. Otherwise, throw an error.
+
+# Examples
+
+```jldoctest
+julia> R, c = polynomial_ring(QQ, :c => (1:3));
+
+julia> I = ideal(R, [  -c[1]^3 + 2*c[1]*c[2] - c[3], c[1]^4 - 3*c[1]^2*c[2] + 2*c[1]*c[3] + c[2]^2,-c[1]^5 + 4*c[1]^3*c[2] - 3*c[1]^2*c[3] - 3*c[1]*c[2]^2 + 2*c[2]*c[3]]);
+
+julia> A, _ = quo(R, I);
+
+julia> f = A(c[1]^2 - c[1] - c[2] + 1)
+c[1]^2 - c[1] - c[2] + 1
+
+julia> inv(f)
+c[1] + c[2] + c[3] + 1
+
+```
+"""
 function inv(a::MPolyQuoRingElem)
   fl, b = is_invertible_with_inverse(a)
   fl || error("Element not invertible")