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fix: univariate polynomial rings over zero rings #1911

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Nov 26, 2024
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fix: univariate polynomial rings over zero rings #1911

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5 changes: 3 additions & 2 deletions src/Poly.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -200,7 +200,7 @@ number_of_generators(R::PolyRing) = 1

iszero(a::PolynomialElem) = length(a) == 0

isone(a::PolynomialElem) = length(a) == 1 && isone(coeff(a, 0))
isone(a::PolynomialElem) = length(a) <= 1 && isone(coeff(a, 0))
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does coeff(a, 0) even work for length(a) == 0 or does that error?

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Yes it works. This is part of the interface https://nemocas.github.io/AbstractAlgebra.jl/stable/poly_interface/#Basic-manipulation-of-rings-and-elements.


@doc raw"""
is_gen(a::PolynomialElem)
Expand Down Expand Up @@ -780,6 +780,7 @@ function ^(a::PolyRingElem{T}, b::Int) where T <: RingElement
b < 0 && throw(DomainError(b, "exponent must be >= 0"))
# special case powers of x for constructing polynomials efficiently
R = parent(a)
is_trivial(R) && return zero(R)
if is_gen(a)
z = R()
fit!(z, b + 1)
Expand Down Expand Up @@ -1352,7 +1353,7 @@ end

function divexact(f::PolyRingElem{T}, g::PolyRingElem{T}; check::Bool=true) where T <: RingElement
check_parent(f, g)
iszero(g) && throw(DivideError())
is_trivial(parent(f)) || (iszero(g) && throw(DivideError()))
if iszero(f)
return zero(parent(f))
end
Expand Down
3 changes: 2 additions & 1 deletion src/generic/GenericTypes.jl
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Expand Up @@ -260,10 +260,11 @@ end
@attributes mutable struct PolyRing{T <: RingElement} <: AbstractAlgebra.PolyRing{T}
base_ring::Ring
S::Symbol
istrivial::Bool

function PolyRing{T}(R::Ring, s::Symbol, cached::Bool = true) where T <: RingElement
return get_cached!(PolyID, (R, s), cached) do
new{T}(R, s)
new{T}(R, s, is_trivial(R))
end::PolyRing{T}
end
end
Expand Down
3 changes: 3 additions & 0 deletions src/generic/Poly.jl
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Expand Up @@ -20,6 +20,8 @@ parent(a::Poly) = a.parent

var(a::PolyRing) = a.S

is_trivial(a::PolyRing) = a.istrivial

###############################################################################
#
# Basic manipulation
Expand Down Expand Up @@ -199,6 +201,7 @@ function zero!(c::Poly{T}) where T <: RingElement
end

function one!(c::Poly{T}) where T <: RingElement
is_trivial(parent(c)) && return zero!(c)
fit!(c, 1)
c = set_length!(c, 1)
c.coeffs[1] = one(base_ring(c))
Expand Down
1 change: 1 addition & 0 deletions src/generic/imports.jl
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Expand Up @@ -154,6 +154,7 @@ import ..AbstractAlgebra: is_square
import ..AbstractAlgebra: is_square_with_sqrt
import ..AbstractAlgebra: is_term
import ..AbstractAlgebra: is_terse
import ..AbstractAlgebra: is_trivial
import ..AbstractAlgebra: is_unit
import ..AbstractAlgebra: is_univariate
import ..AbstractAlgebra: is_zero_divisor
Expand Down
7 changes: 7 additions & 0 deletions test/generic/Poly-test.jl
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Expand Up @@ -3034,3 +3034,10 @@ end
@test collect(Base.Iterators.take(V, d)) == collect(Base.Iterators.take(W, d))
end
end

@testset "Generic.Poly.zero_rings" begin
R, = residue_ring(ZZ, 1)
Rx, = R[:x]
@test is_zero(gen(Rx)) && is_one(gen(Rx))
test_Ring_interface_recursive(Rx)
end
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