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Implement maxdegree for vector of polynomials #279

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Nov 23, 2023
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Implement maxdegree for vector of polynomials #279

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29 changes: 19 additions & 10 deletions src/polynomial.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -272,23 +272,29 @@ end

#$(SIGNATURES)
"""
mindegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractTermLike}})
mindegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractPolynomialLike}})

Returns the minimal total degree of the monomials of `p`, i.e. `minimum(degree, terms(p))`.

mindegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractTermLike}}, v::AbstractVariable)
mindegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractPolynomialLike}}, v::AbstractVariable)

Returns the minimal degree of the monomials of `p` in the variable `v`, i.e. `minimum(degree.(terms(p), v))`.

### Examples
Calling `mindegree` on on ``4x^2y + xy + 2x`` should return 1, `mindegree(4x^2y + xy + 2x, x)` should return 1 and `mindegree(4x^2y + xy + 2x, y)` should return 0.
"""
function mindegree(X::AbstractVector{<:AbstractTermLike}, args...)
return isempty(X) ? 0 : minimum(t -> degree(t, args...), X)
function mindegree(
X::AbstractVector{<:AbstractPolynomialLike},
args::Vararg{Any,N},
) where {N}
return isempty(X) ? 0 : minimum(t -> mindegree(t, args...), X)
end
function mindegree(p::AbstractPolynomialLike, args...)
function mindegree(p::AbstractPolynomialLike, args::Vararg{Any,N}) where {N}
return mindegree(terms(p), args...)
end
function mindegree(t::AbstractTermLike, args::Vararg{Any,N}) where {N}
return degree(t, args...)
end

#$(SIGNATURES)
"""
Expand All @@ -304,30 +310,33 @@ Returns the maximal degree of the monomials of `p` in the variable `v`, i.e. `ma
Calling `maxdegree` on ``4x^2y + xy + 2x`` should return 3, `maxdegree(4x^2y + xy + 2x, x)` should return 2 and `maxdegree(4x^2y + xy + 2x, y)` should return 1.
"""
function maxdegree(
X::AbstractVector{<:AbstractTermLike},
X::AbstractVector{<:AbstractPolynomialLike},
args::Vararg{Any,N},
) where {N}
return mapreduce(t -> degree(t, args...), max, X, init = 0)
return mapreduce(t -> maxdegree(t, args...), max, X, init = 0)
end
function maxdegree(p::AbstractPolynomialLike, args::Vararg{Any,N}) where {N}
return maxdegree(terms(p), args...)
end
function maxdegree(t::AbstractTermLike, args::Vararg{Any,N}) where {N}
return degree(t, args...)
end

#$(SIGNATURES)
"""
extdegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractTermLike}})
extdegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractPolynomialLike}})

Returns the extremal total degrees of the monomials of `p`, i.e. `(mindegree(p), maxdegree(p))`.

extdegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractTermLike}}, v::AbstractVariable)
extdegree(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractPolynomialLike}}, v::AbstractVariable)

Returns the extremal degrees of the monomials of `p` in the variable `v`, i.e. `(mindegree(p, v), maxdegree(p, v))`.

### Examples
Calling `extdegree` on ``4x^2y + xy + 2x`` should return `(1, 3)`, `extdegree(4x^2y + xy + 2x, x)` should return `(1, 2)` and `maxdegree(4x^2y + xy + 2x, y)` should return `(0, 1)`.
"""
function extdegree(
p::Union{AbstractPolynomialLike,AbstractVector{<:AbstractTermLike}},
p::Union{AbstractPolynomialLike,AbstractVector{<:AbstractPolynomialLike}},
args...,
)
return (mindegree(p, args...), maxdegree(p, args...))
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57 changes: 36 additions & 21 deletions test/polynomial.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -72,29 +72,44 @@ const MP = MultivariatePolynomials
@test Tuple(variables([x + 1, y^2])) == (x, y)
@test Tuple(variables([y^2, x + 1])) == (x, y)

@test maxdegree(x^2 - x^2) == 0
@test maxdegree(x^2 - x^2, x) == 0
@test maxdegree(x^2 - x^2, y) == 0
@test mindegree(x^2 - x^2) == 0
@test mindegree(x^2 - x^2, x) == 0
@test mindegree(x^2 - x^2, y) == 0
@test extdegree(x^2 - x^2) == (0, 0)
@test extdegree(x^2 - x^2, x) == (0, 0)
@test extdegree(x^2 - x^2, y) == (0, 0)
@test maxdegree(x * y + 2 + x^2 * y + x + y) == 3
@test maxdegree(x * y + 2 + x^2 * y + x + y, x) == 2
@test maxdegree(x * y + 2 + x^2 * y + x + y, y) == 1
@test mindegree(x * y + 2 + x^2 * y + x + y) == 0
@test mindegree(x * y + 2 + x^2 * y + x + y, x) == 0
@test mindegree(x * y + 2 + x^2 * y + x + y, y) == 0
@test extdegree(x * y + 2 + x^2 * y + x + y) == (0, 3)
@test extdegree(x * y + 2 + x^2 * y + x + y, x) == (0, 2)
@test extdegree(x * y + 2 + x^2 * y + x + y, y) == (0, 1)
@test extdegree(x * y + x^2 * y, x) == (1, 2)
@test extdegree(x * y + x^2 * y, y) == (1, 1)
@test leading_term(x * y + 2 + x^2 * y + x + y) == x^2 * y
p = x^2 - x^2
@test maxdegree(p) == 0
@test maxdegree(p, x) == 0
@test maxdegree(p, y) == 0
@test mindegree(p) == 0
@test mindegree(p, x) == 0
@test mindegree(p, y) == 0
@test extdegree(p) == (0, 0)
@test extdegree(p, x) == (0, 0)
@test extdegree(p, y) == (0, 0)
q = x * y + 2 + x^2 * y + x + y
@test maxdegree(q) == 3
@test maxdegree(q, x) == 2
@test maxdegree(q, y) == 1
@test mindegree(q) == 0
@test mindegree(q, x) == 0
@test mindegree(q, y) == 0
@test extdegree(q) == (0, 3)
@test extdegree(q, x) == (0, 2)
@test extdegree(q, y) == (0, 1)
r = x * y + x^2 * y
@test extdegree(r, x) == (1, 2)
@test extdegree(r, y) == (1, 1)
@test leading_term(q) == x^2 * y
@test nvariables(x + y - x) == 2
@test nvariables(x + x^2) == 1
@test mindegree([p, q, r]) == 0
@test mindegree([p, q, r], x) == 0
@test mindegree([p, q, r], y) == 0
@test mindegree([p, q], y) == 0
@test mindegree([q], y) == 0
@test mindegree([r], y) == 1
@test maxdegree([p, q, r]) == 3
@test maxdegree([p, q, r], x) == 2
@test maxdegree([p, q, r], y) == 1
@test extdegree([p, q, r]) == (0, 3)
@test extdegree([p, q, r], x) == (0, 2)
@test extdegree([p, q, r], y) == (0, 1)

@test collect(
coefficients(
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