Changes in direct sums construction

docs/src/quad_forms/Zgenera.md

@@ -41,7 +41,7 @@ Zgenera(sig_pair::Tuple{Int,Int}, determinant::Union{Int,ZZRingElem})
 ```
 ### From other genus symbols
 ```@docs
-orthogonal_sum(G1::ZGenus, G2::ZGenus)
+direct_sum(G1::ZGenus, G2::ZGenus)
 ```
 
 ## Attributes of the genus
@@ -127,9 +127,9 @@ gram_matrix(S::ZpGenus)
 rescale(S::ZpGenus, a::RationalUnion)
 ```
 
-### Orthogonal sums
+### Direct sums
 ```@docs
-orthogonal_sum(S1::ZpGenus, S2::ZpGenus)
+direct_sum(S1::ZpGenus, S2::ZpGenus)
 ```
 
 ### Embeddings/Representations

docs/src/quad_forms/basics.md

@@ -211,13 +211,35 @@ is_represented_by(H2, H)
 ```
 ---
 
+## Categorical constructions
+One can construct direct sums of spaces of the same kind. Since those are also
+direct products, they are called biproducts in this context. Depending on the user
+usage, one of the following three methods can be called to obtain the direct
+sum of a finite collection of spaces. Note that the corresponding copies
+of the original spaces in the direct sum are pairwise orthogonal.
+
+```@docs
+direct_sum(x::Vector{AbstractSpace})
+direct_product(x::Vector{AbstractSpace})
+biproduct(x::Vector{AbstractSpace})
+```
+
+### Example
+
+```@repl 2
+using Hecke # hide
+E, b = cyclotomix_field_as_cm_extensions(7);
+H = hermitian_space(E, 3);
+H2 = hermitian_space(E, E[-1 0 0; 0 1 0; 0 0 -1]);
+H3, inj, proj = biproduct(H, H2)
+isone(compose(inj[1], proj[1]))
+iszero(compose(inj[1], proj[2]))
+```
 ## Orthogonality operations
 
 ```@docs
 orthogonal_complement(::AbstractSpace, ::MatElem)
 orthogonal_projection(::AbstractSpace, ::MatElem)
-orthogonal_sum(::AbstractSpace, ::AbstractSpace)
-direct_sum(x::Vararg{QuadSpace})
 ```
 
 ### Example
@@ -226,15 +248,8 @@ direct_sum(x::Vararg{QuadSpace})
 using Hecke # hide
 K, a = CyclotomicRealSubfield(7);
 Kt, t = K["t"];
-E, b = number_field(t^2-a*t+1, "b");
 Q = quadratic_space(K, K[0 1; 1 0]);
-H = hermitian_space(E, 3);
-H2 = hermitian_space(E, E[-1 0 0; 0 1 0; 0 0 -1]);
 orthogonal_complement(Q, matrix(K, 1, 2, [1 0]))
-H3, map1, map2 = orthogonal_sum(H, H2);
-H3
-map1
-map2
 ```
 ---
 

docs/src/quad_forms/discriminant_group.md

@@ -123,8 +123,9 @@ brown_invariant(T::TorQuadModule)
 is_genus(T::TorQuadModule, signature_pair::Tuple{Int, Int})
 ```
 
-### Orthogonal sums
+### Categorical constructions
 ```@docs
-orthogonal_sum(T::TorQuadModule, U::TorQuadModule)
-direct_sum(x::Vararg{TorQuadModule})
+direct_sum(x::Vector{TorQuadModule})
+direct_product(x::Vector{TorQuadModule})
+biproduct(x::Vector{TorQuadModule})
 ```

docs/src/quad_forms/genusherm.md

@@ -435,8 +435,8 @@ length(representatives(G1))
 ## Sum of genera
 
 ```@docs
-orthogonal_sum(::HermLocalGenus, ::HermLocalGenus)
-orthogonal_sum(::HermGenus, ::HermGenus)
+direct_sum(::HermLocalGenus, ::HermLocalGenus)
+direct_sum(::HermGenus, ::HermGenus)
 ```
 
 ### Examples
@@ -458,8 +458,8 @@ gens = Vector{Hecke.NfRelElem{nf_elem}}[map(E, [1, 0, 0]), map(E, [a, 0, 0]), ma
 L = hermitian_lattice(E, gens, gram = D);
 g2 = genus(L, p);
 G2 = genus(L);
-orthogonal_sum(g1, g2)
-orthogonal_sum(G1, G2)
+direct_sum(g1, g2)
+direct_sum(G1, G2)
 ```
 
 ---

docs/src/quad_forms/integer_lattices.md

@@ -132,11 +132,16 @@ divisibility(::ZLat, ::Union{Vector, QQMatrix})
 
 ## Embeddings
 
+### Categorical constructions
+```@docs
+direct_sum(x::Vector{ZLat})
+direct_product(x::Vector{ZLat})
+biproduct(x::Vector{ZLat})
+```
+
 ### Orthogonal sublattices
 ```@docs
-orthogonal_sum(::ZLat, ::ZLat)
 orthogonal_submodule(::ZLat, ::ZLat)
-direct_sum(x::Vararg{ZLat})
 irreducible_components(::ZLat)
 ```
 

docs/src/quad_forms/lattices.md

@@ -256,6 +256,17 @@ ambient_space(rescale(Lquad,3*a))
 pseudo_matrix(Lquad)
 ```
 
+## Categorical constructions
+Given finite collections of lattices, one can construct their direct sums, which
+are also direct products in this context. They are also sometimes called biproducts.
+Depending on the user usage, it is possible to call one of the following functions.
+
+```@docs
+direct_sum(x::Vector{AbstractLat})
+direct_product(x::Vector{AbstractLat})
+biproduct(x::Vector{AbstractLat})
+```
+
 ---
 
 ## Invariants

src/Deprecations.jl

@@ -32,6 +32,10 @@
 
 @deprecate automorphisms(x::LocalField, y::Union{FlintPadicField, FlintQadicField, LocalField}) automorphism_list(x, y)
 
+# Deprecated during 0.18.*
+
+@deprecate orthogonal_sum(x::T, y::T) where T <: Union{AbstractSpace, ZGenus, ZpGenus, HermGenus, HermLocalGenus, QuadGenus, QuadLocalGenus, JorDec, LocalQuadSpaceCls, QuadSpaceCls} direct_sum(x, y)
+
 # Things that moved to Nemo
 
 # > 0.18.1