Introduce ZeroVector (#280)

* Move ZeroVector to tangent_space.
* Test coverage; fix/remove arbitrary numbering in the comments.
* add two two further cases.

---------

Co-authored-by: Mateusz Baran <mateuszbaran89@gmail.com>

Author: kellertuer

NEWS.md

@@ -5,6 +5,12 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [2.5.0] 08/07/2026
+
+## Added
+
+* a `ZeroVector` type, to allow for static dispatch and avoid allocating unnecessary zeros similar to the [`Identity`](https://juliamanifolds.github.io/LieGroups.jl/stable/interface/operations/#LieGroups.Identity) on [`LieGroups.jl`](https://github.com/JuliaManifolds/LieGroups.jl).
+
 ## [2.4.0] 03/06/2026
 
 ### Added

Project.toml

@@ -1,6 +1,6 @@
 name = "ManifoldsBase"
 uuid = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
-version = "2.4.0"
+version = "2.5.0"
 authors = ["Seth Axen <seth.axen@gmail.com>", "Mateusz Baran <mateuszbaran89@gmail.com>", "Ronny Bergmann <manopt@ronnybergmann.net>", "Antoine Levitt <antoine.levitt@gmail.com>"]
 
 [workspace]

docs/src/manifolds.md

@@ -5,9 +5,9 @@ helpers to build or create manifolds based on existing manifolds
 
 ## A default manifold
 
-[`DefaultManifold`](@ref ManifoldsBase.DefaultManifold) is a simplified version of [`Euclidean`](https://juliamanifolds.github.io/Manifolds.jl/latest/manifolds/euclidean.html) and demonstrates a basic interface implementation.
+[`DefaultManifold`](@ref ManifoldsBase.DefaultManifold) is a simplified version of [`Euclidean`](@extref `Manifolds.Euclidean`) and demonstrates a basic interface implementation.
 It can be used to perform simple tests.
-Since when using `Manifolds.jl` the [`Euclidean`](https://juliamanifolds.github.io/Manifolds.jl/latest/manifolds/euclidean.html) is available, the `DefaultManifold` itself is not exported.
+Since when using `Manifolds.jl` the [`Euclidean`](@extref `Manifolds.Euclidean`) is available, the [`DefaultManifold`](@ref ManifoldsBase.DefaultManifold) itself is not exported.
 
 ```@docs
 ManifoldsBase.DefaultManifold

src/ManifoldsBase.jl

@@ -8,24 +8,9 @@
 module ManifoldsBase
 
 import Base:
-    isapprox,
-    exp,
-    log,
-    convert,
-    copy,
-    copyto!,
-    angle,
-    eltype,
-    fill,
-    fill!,
-    isempty,
-    length,
-    similar,
-    show,
-    +,
-    -,
-    *,
-    ==
+    isapprox, exp, log,
+    convert, copy, copyto!, angle, eltype, fill, fill!, isempty, length, similar, show,
+    +, -, *, ==
 import LinearAlgebra: ×, dot, norm, det, cross, I, UniformScaling, Diagonal
 import Random: rand, rand!
 
@@ -1229,6 +1214,7 @@ function zero_vector(M::AbstractManifold, p)
     return X
 end
 
+
 #
 #
 # Internal function to set plotting backend
@@ -1266,6 +1252,7 @@ end
 include("errors.jl")
 include("parallel_transport.jl")
 include("vector_transport.jl")
+
 include("shooting.jl")
 include("vector_spaces.jl")
 include("point_vector_fallbacks.jl")
@@ -1332,13 +1319,10 @@ end
 # Export
 # ------
 #
-# (a) Manifolds and general types
+# Manifolds and general types
 export AbstractManifold,
-    AbstractManifoldPoint,
-    AbstractTangentVector,
-    AbstractCotangentVector,
-    TFVector,
-    CoTFVector
+    AbstractManifoldPoint, AbstractTangentVector, AbstractCotangentVector,
+    TFVector, CoTFVector, ZeroVector
 export AbstractAffineConnection, ConnectionManifold, LeviCivitaConnection
 export AbstractMetric, MetricManifold
 export VectorSpaceFiber
@@ -1355,8 +1339,7 @@ export AbstractPowerRepresentation,
     NestedPowerRepresentation, NestedReplacingPowerRepresentation
 export ProductManifold
 
-# (b) Generic Estimation Types
-
+# Generic Estimation Types
 export GeodesicInterpolationWithinRadius,
     CyclicProximalPointEstimation,
     ExtrinsicEstimation,
@@ -1365,8 +1348,7 @@ export GeodesicInterpolationWithinRadius,
     AbstractApproximationMethod,
     GeodesicInterpolation
 
-
-# (b) Retraction Types
+# Retraction Types
 export AbstractRetractionMethod,
     ApproximateRetraction,
     ApproximateExponentialRetraction,
@@ -1385,7 +1367,7 @@ export AbstractRetractionMethod,
     SoftmaxRetraction,
     StabilizedRetraction
 
-# (c) Inverse Retraction Types
+# Inverse Retraction Types
 export AbstractInverseRetractionMethod,
     ApproximateInverseRetraction,
     ApproximateLogarithmicInverseRetraction,
@@ -1402,7 +1384,7 @@ export AbstractInverseRetractionMethod,
     SoftmaxInverseRetraction,
     StabilizedInverseRetraction
 
-# (d) Vector Transport Types
+# Vector Transport Types
 export AbstractVectorTransportMethod,
     DifferentiatedRetractionVectorTransport,
     EmbeddedVectorTransport,
@@ -1416,7 +1398,7 @@ export AbstractVectorTransportMethod,
     VectorTransportTo,
     VectorTransportWithKeywords
 
-# (e) Basis Types
+# Basis Types
 export CachedBasis,
     DefaultBasis,
     DefaultOrthogonalBasis,
@@ -1427,12 +1409,12 @@ export CachedBasis,
     ProjectedOrthonormalBasis,
     VeeOrthogonalBasis
 
-# (f) Error Messages
+# Error Messages
 export OutOfInjectivityRadiusError, ManifoldDomainError
 export ApproximatelyError
 export CompositeManifoldError, ComponentManifoldError, ManifoldDomainError
 
-# (g) Functions on Manifolds
+# Functions on Manifolds
 export ×,
     ℝ,
     ℂ,

src/bases.jl

@@ -298,20 +298,14 @@ function allocate_coordinates(M::AbstractManifold, p::Int, T, n::Int)
     return (representation_size(M) == () && n == 0) ? zero(T) : zeros(T, n)
 end
 function allocate_result(
-        M::AbstractManifold,
-        f::typeof(get_coordinates),
-        p,
-        X,
-        basis::AbstractBasis{𝔽},
+        M::AbstractManifold, f::typeof(get_coordinates), p, X, basis::AbstractBasis{𝔽},
     ) where {𝔽}
     T = coordinate_eltype(M, p, 𝔽)
     return allocate_coordinates(M, p, T, number_of_coordinates(M, basis))
 end
 
 @inline function allocate_result_type(
-        M::AbstractManifold,
-        f::typeof(get_vector),
-        args::Tuple{Any, Vararg{Any}},
+        M::AbstractManifold, f::typeof(get_vector), args::Tuple{Any, Vararg{Any}},
     )
     apf = allocation_promotion_function(M, f, args)
     return apf(
@@ -369,12 +363,7 @@ function change_basis(M::AbstractManifold, p, c, B_in::AbstractBasis, B_out::Abs
 end
 
 function change_basis!(
-        M::AbstractManifold,
-        c_out,
-        p,
-        c,
-        B_in::AbstractBasis,
-        B_out::AbstractBasis,
+        M::AbstractManifold, c_out, p, c, B_in::AbstractBasis, B_out::AbstractBasis,
     )
     return get_coordinates!(M, c_out, p, get_vector(M, p, c, B_in), B_out)
 end
@@ -561,10 +550,7 @@ requires either a dual basis or the cached basis to be selfdual, for example ort
 See also: [`get_vector`](@ref), [`get_basis`](@ref)
 """
 function get_coordinates(
-        M::AbstractManifold,
-        p,
-        X,
-        B::AbstractBasis = default_basis(M, typeof(p)),
+        M::AbstractManifold, p, X, B::AbstractBasis = default_basis(M, typeof(p)),
     )
     return _get_coordinates(M, p, X, B)
 end
@@ -681,25 +667,13 @@ function _get_coordinates!(M::AbstractManifold, Y, p, X, B::CachedBasis)
     return get_coordinates_cached!(M, number_system(M), Y, p, X, B, number_system(B))
 end
 function get_coordinates_cached!(
-        M::AbstractManifold,
-        ::ComplexNumbers,
-        Y,
-        p,
-        X,
-        B::CachedBasis,
-        ::ComplexNumbers,
+        M::AbstractManifold, ::ComplexNumbers, Y, p, X, B::CachedBasis, ::ComplexNumbers,
     )
     map!(vb -> conj(inner(M, p, X, vb)), Y, get_vectors(M, p, B))
     return Y
 end
 function get_coordinates_cached!(
-        M::AbstractManifold,
-        ::𝔽,
-        Y,
-        p,
-        X,
-        C::CachedBasis,
-        ::RealNumbers,
+        M::AbstractManifold, ::𝔽, Y, p, X, C::CachedBasis, ::RealNumbers,
     ) where {𝔽}
     map!(vb -> real(inner(M, p, X, vb)), Y, get_vectors(M, p, C))
     return Y
@@ -721,10 +695,7 @@ requires either a dual basis or the cached basis to be selfdual, for example ort
 See also: [`get_coordinates`](@ref), [`get_basis`](@ref), [`default_basis`](@ref)
 """
 @inline function get_vector(
-        M::AbstractManifold,
-        p,
-        c,
-        B::AbstractBasis = default_basis(M, typeof(p)),
+        M::AbstractManifold, p, c, B::AbstractBasis = default_basis(M, typeof(p)),
     )
     return _get_vector(M, p, c, B)
 end
@@ -830,11 +801,7 @@ end
 function get_vector_orthonormal! end
 
 @inline function _get_vector!(
-        M::AbstractManifold,
-        Y,
-        p,
-        c,
-        B::DiagonalizingOrthonormalBasis,
+        M::AbstractManifold, Y, p, c, B::DiagonalizingOrthonormalBasis,
     )
     return get_vector_diagonalizing!(M, Y, p, c, B)
 end
@@ -917,33 +884,21 @@ When a set of vectors is orthonormalized a set of vectors is returned.
 When an [`AbstractBasis`](@ref) is orthonormalized, a [`CachedBasis`](@ref) is returned.
 """
 function gram_schmidt(
-        M::AbstractManifold{𝔽},
-        p,
-        B::AbstractBasis{𝔽};
-        warn_linearly_dependent = false,
-        return_incomplete_set = false,
-        skip_linearly_dependent = false,
+        M::AbstractManifold{𝔽}, p, B::AbstractBasis{𝔽};
+        warn_linearly_dependent = false, return_incomplete_set = false, skip_linearly_dependent = false,
         kwargs...,
     ) where {𝔽}
     V = gram_schmidt(
-        M,
-        p,
-        get_vectors(M, p, B);
-        warn_linearly_dependent = warn_linearly_dependent,
-        skip_linearly_dependent = skip_linearly_dependent,
-        return_incomplete_set = return_incomplete_set,
-        kwargs...,
+        M, p, get_vectors(M, p, B);
+        warn_linearly_dependent = warn_linearly_dependent, skip_linearly_dependent = skip_linearly_dependent,
+        return_incomplete_set = return_incomplete_set, kwargs...,
     )
     return CachedBasis(GramSchmidtOrthonormalBasis(𝔽), V)
 end
 function gram_schmidt(
-        M::AbstractManifold,
-        p,
-        V::AbstractVector;
-        atol = eps(number_eltype(first(V))),
-        warn_linearly_dependent = false,
-        return_incomplete_set = false,
-        skip_linearly_dependent = false,
+        M::AbstractManifold, p, V::AbstractVector;
+        atol = eps(number_eltype(first(V))), warn_linearly_dependent = false,
+        return_incomplete_set = false, skip_linearly_dependent = false,
         kwargs...,
     )
     N = length(V)

src/exp_log_geo.jl

@@ -18,7 +18,7 @@ function exp(M::AbstractManifold, p, X)
 end
 
 @doc raw"""
-    exp_fused(M::AbstractManifold, p, X, t::Number = 1)
+    exp_fused(M::AbstractManifold, p, X, t::Number)
 
 Compute the exponential map of tangent vector `X` scaled by `t` at point `p`.
 Compared to [`exp`](@ref), this method provides the opportunity to