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Remove polynomials #203

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6f63963
Remove Polynomials
blegat Apr 17, 2026
73a511a
Algebra in term
blegat Apr 17, 2026
13e58ee
Remove monomial
blegat Apr 17, 2026
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114 changes: 58 additions & 56 deletions src/DynamicPolynomials.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -8,85 +8,87 @@ import MutableArithmetics as MA
import StarAlgebras as SA

include("var.jl")
#const CommutativeVariable{O,M} = Variable{Commutative{O},M}
#const NonCommutativeVariable{O,M} = Variable{NonCommutative{O},M}
include("mono.jl")
const DMonomialLike{V,M} = Union{Monomial{V,M},Variable{V,M}}
MA.mutability(::Type{<:Monomial{<:Commutative}}) = MA.IsMutable()
MA.mutability(::Type{<:Monomial{<:NonCommutative}}) = MA.IsNotMutable()
const _Term{V,M,T} = MP.Term{T,Monomial{V,M}}
function __add_variables!(t::_Term, allvars, map)
return __add_variables!(MP.monomial(t), allvars, map)
end
include("monomial_vector.jl")
include("poly.jl")
MA.mutability(::Type{<:Polynomial}) = MA.IsMutable()
const TermPoly{V,M,T} = Union{_Term{V,M,T},Polynomial{V,M,T}}
const PolyType{V,M} =
Union{Polynomial{V,M},_Term{V,M},Monomial{V,M},Variable{V,M}}

# Monomials are now MP.Polynomial{MP.Monomial, V, E}
# No separate Monomial struct — variables and exponents live in the basis element.

# The monomial type for DP variables
const DMonomialLike{V} = Union{MP.Polynomial{MP.Monomial,V},Variable{V}}
# Convenience alias for the specific monomial type with DP variables
const DPMonomial{V,M} = MP.Polynomial{MP.Monomial,Vector{Variable{V,M}},Vector{Int}}

function MP.variable_union_type(
::Union{PolyType{V,M},Type{<:PolyType{V,M}}},
::Union{Variable{V,M},Type{<:Variable{V,M}}},
) where {V,M}
return Variable{V,M}
end
MP.constant_monomial(::Type{<:PolyType{V,M}}) where {V,M} = Monomial{V,M}()
function MP.constant_monomial(p::PolyType)
return Monomial(copy(MP.variables(p)), zeros(Int, nvariables(p)))
end
MP.monomial_type(::Type{<:PolyType{V,M}}) where {V,M} = Monomial{V,M}
MP.monomial_type(::PolyType{V,M}) where {V,M} = Monomial{V,M}
MP.ordering(p::PolyType) = MP.ordering(MP.variable_union_type(p))
#function MP.constant_monomial(::Type{Monomial{V,M}}, vars=Variable{V,M}[]) where {V,M}
# return Monomial{V,M}(vars, zeros(Int, length(vars)))
#end
function MP.term_type(
::Union{TermPoly{V,M,T},Type{<:TermPoly{V,M,T}}},
) where {V,M,T}
return _Term{V,M,T}
function MP.variable_union_type(
::Union{DPMonomial{V,M},Type{<:DPMonomial{V,M}}},
) where {V,M}
return Variable{V,M}
end

MP.constant_monomial(::Type{DPMonomial{V,M}}) where {V,M} = MP.Polynomial(
MP.Variables{MP.Monomial}(Variable{V,M}[]),
Int[],
)
MP.monomial_type(::Type{<:DPMonomial{V,M}}) where {V,M} = DPMonomial{V,M}
MP.monomial_type(::DPMonomial{V,M}) where {V,M} = DPMonomial{V,M}
MP.monomial_type(::Type{<:Variable{V,M}}) where {V,M} = DPMonomial{V,M}
MP.monomial_type(::Variable{V,M}) where {V,M} = DPMonomial{V,M}
# MP.ordering for Variable is in var.jl

function MP.term_type(
::Union{PolyType{V,M},Type{<:PolyType{V,M}}},
::Union{Variable{V,M},Type{<:Variable{V,M}}},
::Type{T},
) where {V,M,T}
return _Term{V,M,T}
# Create a term via the convenience constructor
# term_type needs to return a constructible type...
# For now just return SA.Term{T} since concrete type depends on algebra
return SA.Term{T}
end
MP.term_type(::Type{Polynomial{V,M}}) where {V,M} = _Term{V,M}
MP.polynomial_type(::Type{_Term{V,M}}) where {V,M} = Polynomial{V,M}
MP.polynomial_type(::Type{_Term{V,M,T}}) where {T,V,M} = Polynomial{V,M,T}
function MP.polynomial_type(
::Union{PolyType{V,M},Type{<:PolyType{V,M}}},
::Type{T},
) where {V,M,T}
return Polynomial{V,M,T}
end
MP.variables(p::AbstractArray{<:PolyType}) = mergevars(MP.variables.(p))[1]
function MP.nvariables(
p::Union{PolyType,MonomialVector,AbstractArray{<:PolyType}},
)

MP.variables(p::AbstractArray{<:Variable}) = mergevars(MP.variables.(p))[1]
function MP.nvariables(p::Union{Variable,AbstractArray{<:Variable}})
return length(MP.variables(p))
end
function MP.similar_variable(
P::Union{PolyType{V,M},Type{<:PolyType{V,M}}},
P::Union{Variable{V,M},Type{<:Variable{V,M}}},
::Type{Val{S}},
) where {V,M,S}
return MP.similar_variable(P, S)
end
function MP.similar_variable(p::PolyType{V,M}, s::Symbol) where {V,M}
function MP.similar_variable(p::Variable{V,M}, s::Symbol) where {V,M}
return Variable(string(s), V, M, isreal(p) ? REAL : COMPLEX)
end
function MP.similar_variable(::Type{<:PolyType{V,M}}, s::Symbol) where {V,M}
return Variable(string(s), V, M, REAL) # we cannot infer this from the type
function MP.similar_variable(::Type{<:Variable{V,M}}, s::Symbol) where {V,M}
return Variable(string(s), V, M, REAL)
end

include("promote.jl")
# Create monomial from variable: Variable → Polynomial{Monomial,...}
function Base.convert(::Type{DPMonomial{V,M}}, x::Variable{V,M}) where {V,M}
return MP.Polynomial{MP.Monomial}(x)
end

# monomial(vars, exps) constructs a Polynomial{Monomial,...}
function MP.monomial(vars::Vector{Variable{V,M}}, z::Vector{Int}) where {V,M}
@assert !iscomm(V) || issorted(vars, rev = true)
return MP.Polynomial(MP.Variables{MP.Monomial}(vars), z)
end

# exponents for variables is in var.jl

include("operators.jl")
include("comp.jl")
include("promote.jl")

include("anti_diff.jl")
include("diff.jl")
include("subs.jl")
# Variable power → monomial
Base.:(^)(x::Variable{V,M}, i::Int) where {V,M} = MP.Polynomial(
MP.Variables{MP.Monomial}([x]),
[i],
)

include("div.jl")
# Variable + Variable → uses term + term → AlgebraElement
Base.:(+)(x::Variable, y::Variable) = MP.term(x) + MP.term(y)
Base.:(-)(x::Variable, y::Variable) = MP.term(x) - MP.term(y)

end # module
82 changes: 1 addition & 81 deletions src/comp.jl
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@@ -1,12 +1,10 @@
import Base.==

# TODO This should be in Base with T instead of Variable{V,M}.
# See https://github.com/blegat/MultivariatePolynomials.jl/issues/3
# Comparison of Variable vectors
function Base.:(==)(x::Vector{Variable{V,M}}, y::Vector{Variable{V,M}}) where {V,M}
if length(x) != length(y)
false
else
#for (xi, yi) in zip(x, y)
for i in 1:length(x)
if x[i] != y[i]
return false
Expand All @@ -17,7 +15,6 @@ function Base.:(==)(x::Vector{Variable{V,M}}, y::Vector{Variable{V,M}}) where {V
end

# Comparison of Variable

const AnyCommutative{O} = Union{Commutative{O},NonCommutative{O}}

function Base.cmp(
Expand All @@ -31,81 +28,4 @@ function Base.cmp(
end
end

# TODO remove
Base.:(==)(x::Variable, y::Variable) = iszero(cmp(x, y))
Base.:(==)(x::Monomial, y::Monomial) = iszero(cmp(x, y))

# Comparison of MonomialVector
function (==)(x::MonomialVector{V,M}, y::MonomialVector{V,M}) where {V,M}
if length(x.Z) != length(y.Z)
return false
end
allvars, maps = mergevars([MP.variables(x), MP.variables(y)])
# Should be sorted in the same order since the non-common
# polyvar should have exponent 0
for (a, b) in zip(x.Z, y.Z)
A = zeros(Int, length(allvars))
B = zeros(Int, length(allvars))
A[maps[1]] = a
B[maps[2]] = b
if A != B
return false
end
end
return true
end
(==)(mv::AbstractVector, x::MonomialVector) = monomial_vector(mv) == x
(==)(x::MonomialVector, mv::AbstractVector) = x == monomial_vector(mv)

# Comparison of Term
function _compare(p::Polynomial{V,M}, q::Polynomial{V,M}, comparator) where {V,M}
# terms should be sorted and without zeros
if MP.nterms(p) != MP.nterms(q)
return false
end
for i in eachindex(p.a)
if !comparator(p.x[i], q.x[i])
# There should not be zero terms
@assert p.a[i] != 0
@assert q.a[i] != 0
return false
end
if !comparator(p.a[i], q.a[i])
return false
end
end
return true
end

(==)(p::Polynomial{V, M}, q::Polynomial{V, M}) where {V, M} = _compare(p, q, (==))
Base.isequal(p::Polynomial{V, M}, q::Polynomial{V, M}) where {V, M} = _compare(p, q, isequal)

function Base.isapprox(
p::Polynomial{V,M,S},
q::Polynomial{V,M,T};
rtol::Real = Base.rtoldefault(S, T, 0),
atol::Real = 0,
ztol::Real = iszero(atol) ? Base.rtoldefault(S, T, 0) : atol,
) where {V,M,S,T}
i = j = 1
while i <= length(p.x) || j <= length(q.x)
if i > length(p.x) || (j <= length(q.x) && q.x[j] < p.x[i])
if !isapproxzero(q.a[j], ztol = ztol)
return false
end
j += 1
elseif j > length(q.x) || p.x[i] < q.x[j]
if !isapproxzero(p.a[i], ztol = ztol)
return false
end
i += 1
else
if !isapprox(p.a[i], q.a[j], rtol = rtol, atol = atol)
return false
end
i += 1
j += 1
end
end
return true
end
18 changes: 0 additions & 18 deletions src/diff.jl
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Expand Up @@ -8,21 +8,3 @@ function MP.differentiate(m::Monomial{V,M}, x::Variable{V,M}) where {V,M}
m.z[i] * Monomial(MP.variables(m), z)
end
end

function MP.differentiate(p::Polynomial{V,M,T}, x::Variable{V,M}) where {V,M,T}
# grlex order preserved
i = something(findfirst(isequal(x), MP.variables(p)), 0)
S = typeof(zero(T) * 0)
if iszero(i)
zero(Polynomial{V,M,S})
else
keep = findall(z -> z[i] > 0, p.x.Z)
Z = copy.(p.x.Z[keep])
a = Vector{S}(undef, length(keep))
for j in 1:length(Z)
a[j] = p.a[keep[j]] * Z[j][i]
Z[j][i] -= 1
end
Polynomial(a, MonomialVector(MP.variables(p), Z))
end
end
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