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Add intersection for smodule (#725)
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Such a method is used in Oscar right now
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fingolfin authored Nov 6, 2023
1 parent e7f649d commit f10823a
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62 changes: 62 additions & 0 deletions src/module/module.jl
Original file line number Diff line number Diff line change
Expand Up @@ -115,6 +115,68 @@ function lead(M::smodule)
return z
end

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#
# Intersection
#
###############################################################################

@doc raw"""
intersection(I::smodule{S}, J::smodule{S}) where S <: SPolyUnion
Returns the intersection of the two given modules.
# Examples
```jldoctest
julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"])
(Singular polynomial ring (QQ),(x,y),(dp(2),C), spoly{n_Q}[x, y])
julia> v1 = vector(R, x + 1, x*y + 1, y)
x*y*gen(2)+x*gen(1)+y*gen(3)+gen(2)+gen(1)
julia> v2 = vector(R, x^2 + 1, 2x + 3y, x)
x^2*gen(1)+x*gen(3)+2*x*gen(2)+3*y*gen(2)+gen(1)
julia> v3 = x*v1 + y*v2 + vector(R, x, y + 1, y^2)
x^2*y*gen(2)+x^2*y*gen(1)+x^2*gen(1)+2*x*y*gen(3)+2*x*y*gen(2)+y^2*gen(3)+3*y^2*gen(2)+x*gen(2)+2*x*gen(1)+y*gen(2)+y*gen(1)+gen(2)
julia> M1 = Singular.Module(R, v1, v2);
julia> M2 = Singular.Module(R, v2, v3);
julia> M3 = intersection(M1, M2)
Singular Module over Singular polynomial ring (QQ),(x,y),(dp(2),C), with Generators:
x^2*gen(1)+x*gen(3)+2*x*gen(2)+3*y*gen(2)+gen(1)
julia> ngens(M3)
1
julia> M3[1] == v2
true
```
"""
function intersection(I::smodule{S}, J::smodule{S}) where S <: SPolyUnion
check_parent(I, J)
R = base_ring(I)
ptr = GC.@preserve I J R libSingular.id_Intersection(I.ptr, J.ptr, R.ptr)
return Module(R, ptr)
end

function intersection(I::smodule{S}, Js::smodule{S}...) where S <: SPolyUnion
R = base_ring(I)
GC.@preserve I Js R begin
CC = Ptr{Nothing}[I.ptr.cpp_object]
for J in Js
push!(CC, J.ptr.cpp_object)
end
GC.@preserve CC begin
C_ptr = reinterpret(Ptr{Nothing}, pointer(CC))
ptr = libSingular.id_MultSect(C_ptr, length(CC), R.ptr)
end
return smodule{S}(R, ptr)
end
end

###############################################################################
#
# Groebner basis
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