consolidate

JuliaMath · Jan 30, 2023 · 0995da3 · 0995da3
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Showing 2 changed files with 26 additions and 16 deletions.
diff --git a/src/common.jl b/src/common.jl
@@ -208,36 +208,43 @@ vander(::Type{<:AbstractPolynomial}, x::AbstractVector, deg::Integer)
 
 
 """
- critical_points(p)
- critical_points(p, lo, hi)
+ critical_points(p, I=domain(p); endpoints::Bool=true)
 
-Return critical points (sorted zeros of derivative) or critical points in `[l,r]` with `l` and `r` included, either possibly infinite.
+Returns critical points (sorted zeros of the derivative) or, if `endpoints=true` critical points in `I` where finite endpoints of `I` are included. `I` defaults to the `p`'s `domain`.
 
-Can be used with `findmax`, `findmin`, `argmax`, `argmin`, `extrema`, etc.
+Can be used in conjuction with `findmax`, `findmin`, `argmax`, `argmin`, `extrema`, etc.
 
 ## Example
 ```
 x = variable()
 p = x^2 - 2
-cps = Polynomials.critical_points(p, -Inf, Inf)
-findmin(p, cps) # (-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}) where {T <: Real}
+function critical_points(p::AbstractPolynomial{T}, I = domain(p); endpoints::Bool=true) where {T <: Real}
+ l, r = extrema(I)
+
  q = Polynomials.ngcd(derivative(p), derivative(p,2)).v
- real.(filter(isreal, roots(q)))
-end
+ pts = sort(real.(filter(isreal, roots(q))))
+ pts = filter(x -> l ≤ x ≤ r, pts)
 
-function critical_points(p::AbstractPolynomial{T}, l, r = -l) where {T <: Real}
- l, r = l < r ? (l,r) : (r,l)
- rs = critical_points(p)
- pts = Iterators.flatten((l, r, rs))
- sort(collect(Iterators.filter(x -> l ≤ x ≤ r, pts)))
+ !endpoints && return pts
+
+ l !== first(pts) && pushfirst!(pts, l)
+ r != last(pts) && push!(pts, r)
+ pts
 end
 
 
+
+
+
+
 """
  integrate(p::AbstractPolynomial)
 

diff --git a/test/StandardBasis.jl b/test/StandardBasis.jl
@@ -903,9 +903,12 @@ end
 @testset "critical points" begin
  for P in (Polynomial, ImmutablePolynomial)
  p = fromroots(P, [-1,-1, 2]) |> integrate
- cps = Polynomials.critical_points(p)
+ cps = Polynomials.critical_points(p, (-5,5); endpoints=false)
  @test all(cps .≈ [-1, 2])
- cps = Polynomials.critical_points(p, -Inf, Inf)
+ 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)