Merge branch 'main' into pr/629

Author: PBrdng

.github/dependabot.yml

@@ -0,0 +1,7 @@
+# https://docs.github.com/github/administering-a-repository/configuration-options-for-dependency-updates
+version: 2
+updates:
+  - package-ecosystem: "github-actions"
+    directory: "/" # Location of package manifests
+    schedule:
+      interval: "weekly"

.github/workflows/TagBot.yml

@@ -4,6 +4,11 @@ on:
     types:
       - created
   workflow_dispatch:
+    inputs:
+      lookback:
+        default: 3
+permissions:
+  contents: write
 jobs:
   TagBot:
     if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'

.github/workflows/documentation.yml

@@ -11,7 +11,7 @@ jobs:
   docs:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@latest
         with:
           version: "^1.4"

.github/workflows/format_check.yml

@@ -15,7 +15,7 @@ jobs:
       - uses: julia-actions/setup-julia@latest
         with:
           version: "^1.4"
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - name: Install JuliaFormatter and format
         run: |
           julia  -e 'using Pkg; Pkg.add(PackageSpec(name="JuliaFormatter", version="1.0.33"))'

.github/workflows/run_tests.yml

@@ -19,12 +19,13 @@ jobs:
         julia-version: ["^1.10"]
         os: [ubuntu-latest]
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@latest
         with:
           version: ${{ matrix.julia-version }}
+      - uses: julia-actions/cache@v2
       - uses: julia-actions/julia-buildpkg@latest
       - uses: julia-actions/julia-runtest@latest
-      - uses: julia-actions/julia-uploadcodecov@latest
+      - uses: codecov/codecov-action@v5
         env:
           CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}

.github/workflows/run_tests_modelkit.yml

@@ -18,12 +18,13 @@ jobs:
         julia-version: ["^1.6.0-0"]
         os: [ubuntu-latest]
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@latest
         with:
           version: ${{ matrix.julia-version }}
+      - uses: julia-actions/cache@v2
       - uses: julia-actions/julia-buildpkg@latest
       - uses: julia-actions/julia-runtest@latest
-      - uses: julia-actions/julia-uploadcodecov@latest
+      - uses: codecov/codecov-action@v5
         env:
           CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}

Project.toml

@@ -1,7 +1,7 @@
 name = "HomotopyContinuation"
 uuid = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
 authors = ["Sascha Timme <sascha@timme.xyz>", "Paul Breiding <pbrdng@gmail.com>"]
-version = "2.12.0"
+version = "2.14"
 
 [deps]
 Arblib = "fb37089c-8514-4489-9461-98f9c8763369"

README.md

@@ -1,6 +1,7 @@
 <img src="https://www.juliahomotopycontinuation.org/images/logo_transparent_bg.png" width="320px">
 
-[![][docs-stable-img]][docs-stable-url] ![Run tests](https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/workflows/Run%20tests/badge.svg?branch=main)
+[![][docs-stable-img]][docs-stable-url] [![Run tests](https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/actions/workflows/run_tests.yml/badge.svg)](https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/actions/workflows/run_tests.yml)
+
 
 **HomotopyContinuation.jl** is a Julia package for solving systems of polynomial equations by numerical homotopy continuation.
 

src/certification.jl

@@ -41,9 +41,13 @@ abstract type AbstractSolutionCertificate end
 """
     SolutionCertificate
 
-Result of [`certify`](@ref) for a single solution. Contains the initial solutions
-and if the certification was successfull a vector of complex intervals where the true
-solution is contained in.
+Result of [`certify`](@ref) for a single solution. Contains the initial solutions and if the certification was successfull a vector of complex intervals where the true solution is contained in.
+The complex intervals are given as an `Arblib.AcbMatrix`.
+The `Arblib.AcbMatrix` is printed in the default format of `Arblib`. This means that, if the midpoint of an interval can't be represented with sufficiently many correct digits, `Arblib` will not print the midpoint. Instead, it will print an interval of the form `[+/- r]`, where `r` will be an upper bound for the absolute value of the ball. An enclosure of the correct interval can be printed as follows.
+```julia
+Base.show(certificate::SolutionCertificate; digits = 16, more = true)
+```
+This uses the [`ARB_STR_MORE`](https://flintlib.org/doc/arb.html#c.arb_get_str) functionality in `Flint` with `16` digits.
 """
 Base.@kwdef struct SolutionCertificate <: AbstractSolutionCertificate
     solution_candidate::AbstractVector
@@ -145,8 +149,7 @@ end
     certified_solution_interval(certificate::AbstractSolutionCertificate)
 
 Returns an `Arblib.AcbMatrix` representing a vector of complex intervals where a unique
-zero of the system is contained in.
-Returns `nothing` if `is_certified(certificate)` is `false`.
+zero of the system is contained in. Returns `nothing` if `is_certified(certificate)` is `false`.
 """
 certified_solution_interval(certificate::AbstractSolutionCertificate) = certificate.I
 @deprecate certified_solution(certificate) certified_solution_interval(certificate)
@@ -156,8 +159,7 @@ certified_solution_interval(certificate::AbstractSolutionCertificate) = certific
 
 Returns an `Arblib.AcbMatrix` representing a vector of complex intervals where a unique
 zero of the system is contained in.
-This is the result of applying the Krawczyk operator to `certified_solution_interval(certificate)`.
-Returns `nothing` if `is_certified(certificate)` is `false`.
+This is the result of applying the Krawczyk operator to `certified_solution_interval(certificate)`. Returns `nothing` if `is_certified(certificate)` is `false`.
 """
 certified_solution_interval_after_krawczyk(certificate::ExtendedSolutionCertificate) =
     certificate.I′
@@ -193,7 +195,14 @@ Returns a `NamedTuple` `(x, Y)` with the parameters of the Krawczyk operator fol
 """
 krawczyk_operator_parameters(cert::ExtendedSolutionCertificate) = (x = cert.x̃, Y = cert.Y)
 
-function Base.show(f::IO, cert::AbstractSolutionCertificate)
+Base.show(cert::AbstractSolutionCertificate; digits::Int = 16, more::Bool = false) =
+    Base.show(stdout, cert; digits = digits, more = more)
+function Base.show(
+    f::IO,
+    cert::AbstractSolutionCertificate;
+    digits::Int = 16,
+    more::Bool = false,
+)
     println(f, "SolutionCertificate:")
     println(f, "solution_candidate = [")
     for z in solution_candidate(cert)
@@ -208,7 +217,7 @@ function Base.show(f::IO, cert::AbstractSolutionCertificate)
         println(f, "certified_solution_interval = [")
         for z in certified_solution_interval(cert)
             print(f, "  ")
-            print(f, z)
+            print(f, string(z; digits = digits, more = more))
             println(f, ",")
         end
         println(f, "]")
@@ -1397,6 +1406,7 @@ function certify(
     p::Union{Nothing,AbstractArray} = nothing,
     cache::CertificationCache = CertificationCache(F);
     target_parameters = nothing,
+    max_precision::Int = 256,
     kwargs...,
 )
     cert_params =
@@ -1410,6 +1420,7 @@ function certify(
     p::Union{Nothing,AbstractArray} = nothing,
     cache::CertificationCache = CertificationCache(F);
     target_parameters = nothing,
+    max_precision::Int = 256,
     kwargs...,
 )
     cert_params =
@@ -1423,6 +1434,7 @@ function certify(
     p::Union{Nothing,AbstractArray} = nothing,
     cache::CertificationCache = CertificationCache(F);
     target_parameters = nothing,
+    max_precision::Int = 256,
     kwargs...,
 )
     cert_params =

src/endgame_tracker.jl

@@ -35,11 +35,12 @@ These parameters control the behaviour during the endgame.
    endgame strategy is considered to be applied.
 * `min_coord_growth = 100`: The minimal relative growth of a coordinate necessary to
   to be considered going to infininity (resp. zero).
+* `singular_min_accuracy = 1e-6`: A solution can be treated with a singular endgame method only if its [`accuracy`](@ref) is below this threshold. Otherwise, the solution will either be refined or labeled as unsuccessfully terminated.
 * `val_at_infinity_tol = 1e-3`: Tolerance on the valuation which has to be
   satisfied before a path is considered to diverge / go to infinity.
 * `val_finite_tol = 1e-3`: Tolerance on the valuation which has to be satisfied before the endgame is started.
 * `sing_cond = 1e14`: value for the condition number above which a solution is considered singular.
-* `sing_accuracy = 1e-12`: value for the accuracy number above which a solution is considered singular.
+* `sing_accuracy = 1e-12`: value for the [`accuracy`](@ref) above which a solution is considered singular.
 * `scaling_threshold = -30.0`: Row scaling of matrices is only applied to rows with `e < scaling_threshold`, where is the norm of the row is estimated to be `2^e`. See [`skeel_row_scaling`](@skeel_row_scaling) for details.
 * `refine_steps = 3`: number of steps for refining solutions at the end.
 """