PolyhedralGeometry: simplified operations with PolyhedralFan and PolyhedralComplex

Author: YueRen

src/PolyhedralGeometry/PolyhedralComplex/standard_constructions.jl

@@ -81,7 +81,7 @@ end
 ## Scalar product
 ###############################################################################
 
-function *(c::QQFieldElem, Sigma::PolyhedralComplex)
+function *(c::scalar_types_extended, Sigma::PolyhedralComplex)
     # if scalar is zero, return polyhedral complex consisting only of the origin
     if iszero(c)
         return polyhedral_complex(convex_hull(zero_matrix(QQ,1,ambient_dim(Sigma))))
@@ -92,10 +92,9 @@ function *(c::QQFieldElem, Sigma::PolyhedralComplex)
     SigmaRayIndices = findall(vr -> vr isa RayVector, SigmaVertsAndRays)
     SigmaLineality = lineality_space(Sigma)
     SigmaIncidence = maximal_polyhedra(IncidenceMatrix,Sigma)
-    return polyhedral_complex(SigmaIncidence, multiply_by_nonzero_scalar.(SigmaVertsAndRays,c), SigmaRayIndices, SigmaLineality)
+    return polyhedral_complex(coefficient_field(Sigma), SigmaIncidence, SigmaVertsAndRays .*c, SigmaRayIndices, SigmaLineality)
 end
-*(c::RationalUnion, Sigma::PolyhedralComplex) = QQ(c)*Sigma
-*(Sigma::PolyhedralComplex, c::RationalUnion) = c*Sigma
+*(Sigma::PolyhedralComplex, c::scalar_types_extended) = c*Sigma
 
 
 ###############################################################################
@@ -114,27 +113,23 @@ end
 ## Translation
 ###############################################################################
 
-function translate_by_vector(u::PointVector{QQFieldElem}, v::Vector{QQFieldElem})
-    return u .+ v
+# requires separate function because to ensure that translation does not change ray vectors
+function translate_by_vector(u::PointVector{<:scalar_types_extended}, v::Vector{<:scalar_types_extended})
+    return u + v
 end
-function translate_by_vector(u::RayVector{QQFieldElem}, ::Vector{QQFieldElem})
+function translate_by_vector(u::RayVector{<:scalar_types_extended}, ::Vector{<:scalar_types_extended})
     return u
 end
-function +(v::Vector{QQFieldElem}, Sigma::PolyhedralComplex)
+function +(v::Vector{<:scalar_types_extended}, Sigma::PolyhedralComplex)
     @req length(v)==ambient_dim(Sigma) "ambient dimension mismatch"
     SigmaVertsAndRays = vertices_and_rays(Sigma)
     SigmaRayIndices = findall(vr -> vr isa RayVector, SigmaVertsAndRays)
     SigmaLineality = lineality_space(Sigma)
     SigmaIncidence = maximal_polyhedra(IncidenceMatrix,Sigma)
-    return polyhedral_complex(SigmaIncidence, translate_by_vector.(SigmaVertsAndRays,Ref(v)), SigmaRayIndices, SigmaLineality)
+    return polyhedral_complex(coefficient_field(Sigma), SigmaIncidence, translate_by_vector.(SigmaVertsAndRays,Ref(v)), SigmaRayIndices, SigmaLineality)
 end
-+(v::Vector{ZZRingElem}, Sigma::PolyhedralComplex) = QQ.(v)+Sigma
-+(v::Vector{Rational}, Sigma::PolyhedralComplex) = QQ.(v)+Sigma
-+(v::Vector{Int}, Sigma::PolyhedralComplex) = QQ.(v)+Sigma
-
-+(Sigma::PolyhedralComplex, v::Vector{QQFieldElem}) = v+Sigma
-+(Sigma::PolyhedralComplex, v::Vector{<:RationalUnion}) = QQ.(v)+Sigma
++(Sigma::PolyhedralComplex, v::Vector{<:scalar_types_extended}) = v+Sigma
 
 # Vector addition for polyhedral fans
-+(Sigma::PolyhedralFan, v::Vector) = polyhedral_complex(Sigma)+v
-+(v::Vector, Sigma::PolyhedralFan) = v+polyhedral_complex(Sigma)
++(Sigma::PolyhedralFan, v::Vector{<:scalar_types_extended}) = polyhedral_complex(Sigma)+v
++(v::Vector{<:scalar_types_extended}, Sigma::PolyhedralFan) = v+polyhedral_complex(Sigma)

src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl

@@ -411,35 +411,26 @@ end
 ## Scalar multiplication
 ###############################################################################
 
-function multiply_by_nonzero_scalar(u::PointVector{QQFieldElem}, c::QQFieldElem)
-  return u .* c
-end
-function multiply_by_nonzero_scalar(u::RayVector{QQFieldElem}, c::QQFieldElem)
-  return (c<0 ? -u : u)
-end
-
-function *(c::QQFieldElem, Sigma::PolyhedralFan)
-  # if scalar is zero, return polyhedral complex consisting only of the origin
+function *(c::scalar_types_extended, Sigma::PolyhedralFan)
+  # if scalar is zero, return polyhedral fan consisting only of the origin
   if iszero(c)
-    return polyhedral_complex(convex_hull(zero_matrix(QQ,1,ambient_dim(Sigma))))
+    return polyhedral_fan(positive_hull(zero_matrix(coefficient_field(Sigma),1,ambient_dim(Sigma))))
   end
 
-  # if scalar is non-zero, multiple all vertices and rays by said scalar
+  # if scalar is non-zero, multiple all rays by said scalar
   SigmaRays = first(rays_modulo_lineality(Sigma))
   SigmaLineality = lineality_space(Sigma)
   SigmaIncidence = maximal_cones(IncidenceMatrix,Sigma)
-  return polyhedral_fan(SigmaIncidence, multiply_by_nonzero_scalar.(SigmaRays,c), SigmaLineality)
+  return polyhedral_fan(coefficient_field(Sigma), SigmaIncidence, SigmaRays .* c, SigmaLineality)
 end
-*(c::RationalUnion, Sigma::PolyhedralFan) = QQ(c)*Sigma
-*(Sigma::PolyhedralFan,c::RationalUnion) = c*Sigma
+*(Sigma::PolyhedralFan,c::scalar_types_extended) = c*Sigma
 
 ###############################################################################
 ## Negation
 ###############################################################################
 
 function -(Sigma::PolyhedralFan)
-  SigmaRays = first(rays_modulo_lineality(Sigma))
-  SigmaLineality = lineality_space(Sigma)
+  SigmaRays, SigmaLineality = first(rays_modulo_lineality(Sigma))
   SigmaIncidence = maximal_cones(IncidenceMatrix,Sigma)
-  return polyhedral_fan(SigmaIncidence, -SigmaRays, SigmaLineality)
+  return polyhedral_fan(coefficient_field(Sigma), SigmaIncidence, -SigmaRays, SigmaLineality)
 end