add unexported critical points (#458)

* add unexported critical points

* consolidate

* clean up

* add precompiles

Project.toml

@@ -2,7 +2,7 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "3.2.3"
+version = "3.2.4"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/Polynomials.jl

@@ -35,4 +35,6 @@ include("rational-functions/plot-recipes.jl")
 # compat; opt-in with `using Polynomials.PolyCompat`
 include("polynomials/Poly.jl")
 
+include("precompiles.jl")
+
 end # module

src/common.jl

@@ -205,6 +205,55 @@ Calculate the pseudo-Vandermonde matrix of the given polynomial type with the gi
 """
 vander(::Type{<:AbstractPolynomial}, x::AbstractVector, deg::Integer)
 
+
+"""
+ critical_points(p::AbstractPolynomial{<:Real}, I=domain(p); endpoints::Bool=true)
+
+Return the critical points of `p` (real zeros of the derivative) within `I` in sorted order.
+
+* `p`: a polynomial
+
+* `I`: a specification of a closed or infinite domain, defaulting to `Polynomials.domain(p)`. When specified, the values of `extrema(I)` are used with closed endpoints when finite.
+
+* `endpoints::Bool`: if `true`, return the endpoints of `I` along with the critical points
+
+
+Can be used in conjuction with `findmax`, `findmin`, `argmax`, `argmin`, `extrema`, etc.
+
+## Example
+```
+x = variable()
+p = x^2 - 2
+cps = Polynomials.critical_points(p)
+findmin(p, cps) # (-2.0, 2.0)
+argmin(p, cps) # 0.0
+extrema(p, cps) # (-2.0, Inf)
+cps = Polynomials.critical_points(p, (0, 2))
+extrema(p, cps) # (-2.0, 2.0)
+```
+"""
+function critical_points(p::AbstractPolynomial{T}, I = domain(p);
+ endpoints::Bool=true) where {T <: Real}
+
+ I′ = Interval(I)
+ l, r = extrema(I′)
+
+ q = Polynomials.ngcd(derivative(p), derivative(p,2)).v
+ pts = sort(real.(filter(isreal, roots(q))))
+ pts = filter(in(I′), pts)
+
+ !endpoints && return pts
+
+ l !== first(pts) && pushfirst!(pts, l)
+ r != last(pts) && push!(pts, r)
+ pts
+end
+
+
+
+
+
+
 """
  integrate(p::AbstractPolynomial)
 

src/contrib.jl

@@ -174,6 +174,8 @@ struct Interval{T, L <: Bound, R <: Bound}
  end
  Interval(f, l) = Interval{Closed, Closed}(f, l)
 end
+Interval(I::Interval) = I
+Interval(I) = Interval(extrema(I)...)
 
 bounds_types(x::Interval{T,L,R}) where {T,L,R} = (L, R)
 

src/precompiles.jl

@@ -0,0 +1,6 @@
+# precompiles
+
+p = fromroots(Polynomial, [1,1,2])
+Multroot.multroot(p)
+gcd(p, derivative(p); method=:numerical)
+uvw(p, derivative(p); method=:numerical)

test/StandardBasis.jl

@@ -900,6 +900,24 @@ end
  end
 end
 
+@testset "critical points" begin
+ for P in (Polynomial, ImmutablePolynomial)
+ p = fromroots(P, [-1,-1, 2]) |> integrate
+ cps = Polynomials.critical_points(p, (-5,5); endpoints=false)
+ @test all(cps .≈ [-1, 2])
+ cps = Polynomials.critical_points(p, (0,5); endpoints=false)
+ @test all(cps .≈ [2])
+
+ cps = Polynomials.critical_points(p)
+ m, i = findmin(p, cps)
+ @test m ≈ -6.0
+ x = argmin(p, cps)
+ @test x ≈ 2.0
+ mn, mx = extrema(p, cps)
+ @test mn ≈ -6.0 && isinf(mx)
+ end
+end
+
 @testset "Integrals and Derivatives" begin
  # Integrals derivatives
  @testset for P in Ps