diff --git a/docs/src/PolyhedralGeometry/Polyhedra/constructions.md b/docs/src/PolyhedralGeometry/Polyhedra/constructions.md index 4eefdeffd57d..fac07af46b3a 100644 --- a/docs/src/PolyhedralGeometry/Polyhedra/constructions.md +++ b/docs/src/PolyhedralGeometry/Polyhedra/constructions.md @@ -26,13 +26,13 @@ julia> P = polyhedron(([-1 0; 1 0], [0,1]), ([0 1], [0])) Polyhedron in ambient dimension 2 julia> facets(P) -2-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^2 described by: +2-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^2 described by: -x_1 <= 0 x_1 <= 1 julia> affine_hull(P) -1-element SubObjectIterator{AffineHyperplane{QQFieldElem}} over the Hyperplanes of R^2 described by: +1-element SubObjectIterator{AffineHyperplane{QQFieldElem}} over the hyperplanes of R^2 described by: x_2 = 0 diff --git a/src/Groups/matrices/MatGrp.jl b/src/Groups/matrices/MatGrp.jl index c74f12f83a54..2c5ab5552258 100644 --- a/src/Groups/matrices/MatGrp.jl +++ b/src/Groups/matrices/MatGrp.jl @@ -559,7 +559,7 @@ compute_order(G::GAPGroup) = ZZRingElem(GAPWrap.Size(G.X)) function compute_order(G::MatrixGroup{T}) where {T <: Union{AbsSimpleNumFieldElem, QQFieldElem}} #= - - For a matrix group G over the Rationals or over a number field, + - For a matrix group G over the rationals or over a number field, the GAP group G.X does usually not store the flag `IsHandledByNiceMonomorphism`. - If we know a reasonable ("nice") faithful permutation action of `G` in advance, we can set this flag in `G.X` to true and store the action homomorphism in `G.X`, diff --git a/src/PolyhedralGeometry/Cone/properties.jl b/src/PolyhedralGeometry/Cone/properties.jl index 7a4d3f964f0f..9aaf989ef0cb 100644 --- a/src/PolyhedralGeometry/Cone/properties.jl +++ b/src/PolyhedralGeometry/Cone/properties.jl @@ -543,7 +543,7 @@ julia> c = positive_hull([1 0 0; 0 1 0; 1 1 1]) Polyhedral cone in ambient dimension 3 julia> f = facets(Halfspace, c) -3-element SubObjectIterator{LinearHalfspace{QQFieldElem}} over the Halfspaces of R^3 described by: +3-element SubObjectIterator{LinearHalfspace{QQFieldElem}} over the halfspaces of R^3 described by: -x_3 <= 0 -x_1 + x_3 <= 0 -x_2 + x_3 <= 0 @@ -616,7 +616,7 @@ $H = \{ (x_1, x_2, x_3) | x_3 = 0 \}$. julia> c = positive_hull([1 0 0; 0 1 0]); julia> linear_span(c) -1-element SubObjectIterator{LinearHyperplane{QQFieldElem}} over the Hyperplanes of R^3 described by: +1-element SubObjectIterator{LinearHyperplane{QQFieldElem}} over the hyperplanes of R^3 described by: x_3 = 0 ``` """ diff --git a/src/PolyhedralGeometry/Polyhedron/properties.jl b/src/PolyhedralGeometry/Polyhedron/properties.jl index 63ecdbbf44cb..a7ad3ae9656a 100644 --- a/src/PolyhedralGeometry/Polyhedron/properties.jl +++ b/src/PolyhedralGeometry/Polyhedron/properties.jl @@ -510,7 +510,7 @@ julia> facets(Polyhedron, C) Polytope in ambient dimension 3 julia> facets(Halfspace, C) -6-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^3 described by: +6-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^3 described by: -x_1 <= 1 x_1 <= 1 -x_2 <= 1 @@ -593,7 +593,7 @@ We can retrieve the six facets of the 3-dimensional cube this way: julia> C = cube(3); julia> facets(C) -6-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^3 described by: +6-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^3 described by: -x_1 <= 1 x_1 <= 1 -x_2 <= 1 @@ -998,7 +998,7 @@ $P = \{ (x_1, x_2, x_3, x_4) | x_3 = 2 ∧ x_4 = 5 \}$. julia> t = convex_hull([0 0 2 5; 1 0 2 5; 0 1 2 5]); julia> affine_hull(t) -2-element SubObjectIterator{AffineHyperplane{QQFieldElem}} over the Hyperplanes of R^4 described by: +2-element SubObjectIterator{AffineHyperplane{QQFieldElem}} over the hyperplanes of R^4 described by: x_3 = 2 x_4 = 5 ``` @@ -1831,7 +1831,7 @@ function Base.show(io::IO, H::SubObjectIterator{<:Halfspace}) print(io, "$s-element $t") if !isempty(H) n = length(normal_vector(H[1])) - print(io, " over the Halfspaces of R^$n described by:\n") + print(io, " over the halfspaces of R^$n described by:\n") if s < d print_constraints(io, H) else @@ -1854,7 +1854,7 @@ function Base.show(io::IO, H::SubObjectIterator{<:Hyperplane}) print(io, "$s-element $t") if !isempty(H) n = length(normal_vector(H[1])) - print(io, " over the Hyperplanes of R^$n described by:\n") + print(io, " over the hyperplanes of R^$n described by:\n") if s < d print_constraints(io, H) else diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl index 9e18a71d8113..29e51665b074 100644 --- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl +++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl @@ -618,7 +618,7 @@ julia> s = simplex(7) Polytope in ambient dimension 7 julia> facets(s) -8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^7 described by: +8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^7 described by: -x_1 <= 0 -x_2 <= 0 -x_3 <= 0 @@ -632,7 +632,7 @@ julia> t = simplex(7, 5) Polytope in ambient dimension 7 julia> facets(t) -8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^7 described by: +8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^7 described by: -x_1 <= 0 -x_2 <= 0 -x_3 <= 0 @@ -674,7 +674,7 @@ julia> C = cross_polytope(3) Polytope in ambient dimension 3 julia> facets(C) -8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^3 described by: +8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^3 described by: x_1 + x_2 + x_3 <= 1 -x_1 + x_2 + x_3 <= 1 x_1 - x_2 + x_3 <= 1 @@ -688,7 +688,7 @@ julia> D = cross_polytope(3, 2) Polytope in ambient dimension 3 julia> facets(D) -8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^3 described by: +8-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^3 described by: x_1 + x_2 + x_3 <= 2 -x_1 + x_2 + x_3 <= 2 x_1 - x_2 + x_3 <= 2 @@ -1408,7 +1408,7 @@ julia> vertices(A) [4, 1, 10, 6] julia> facets(A) -5-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^4 described by: +5-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^4 described by: -x_1 <= -1 -2*x_1 - 2*x_2 <= -10 -x_2 <= -1 @@ -1637,14 +1637,14 @@ julia> G = hypersimplex(3,4,no_facets=true) Polytope in ambient dimension 4 julia> facets(G) -4-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^4 described by: +4-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^4 described by: x_4 <= 1 x_3 <= 1 -x_1 - x_3 - x_4 <= -2 x_1 <= 1 julia> facets(H) -4-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^4 described by: +4-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^4 described by: x_4 <= 1 x_3 <= 1 -x_1 - x_3 - x_4 <= -2 @@ -2253,7 +2253,7 @@ julia> vertices(a) [0, 3, 4, 15, 16] julia> facets(a) -9-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^5 described by: +9-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^5 described by: x_1 - x_2 <= -1 x_1 - x_3 <= -4 x_1 - x_4 <= -9 diff --git a/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon b/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon index cf96a5f18ba5..e15935e9bb47 100644 --- a/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon +++ b/test/book/cornerstones/polyhedral-geometry/pentagon.jlcon @@ -4,7 +4,7 @@ julia> P = convex_hull(points) Polyhedron in ambient dimension 2 julia> facets(P) -5-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the Halfspaces of R^2 described by: +5-element SubObjectIterator{AffineHalfspace{QQFieldElem}} over the halfspaces of R^2 described by: -x_1 <= 1 -x_1 + x_2 <= 1 x_1 - 2*x_2 <= 1