[Rafael-SOWNet]

Every root a solver finds goes back into the equation as written, and the ones that fail are dropped. Where all of them failed, the empty set was left, and the empty set claims there's no root. For a polynomial of degree one or more over the complex numbers that is never true, so what failed was the solver. Such a polynomial is now left as the set of the x that satisfy it, which claims only that its roots weren't found.

Solve("x"), with neither #2314 nor #2315	before	now
(x + 1)^3 = 2	{ }	{ x : (x + 1) ^ 3 = 2 }
31x^4 - 62x^3 + 33x^2 - 2x - 1 = 0	{ }	{ x : 31 * x ^ 4 - … = 0 }
sqrt(x) = -1	{ }	{ }: not a polynomial, and it has no root

• It applies only to a polynomial with numbers for coefficients, over the complex numbers. An equation that isn't a polynomial can have no root, and so can a polynomial over the reals: x^2 + 1 = 0.
• It's a guard, not a fix. The two { } answers above come from defects A quartic that is biquadratic once depressed is solved #2314 and A cube shifted is solved #2315 fix, and with those merged no equation I know of reaches this, so no answer changes and there's no BREAKING-CHANGES.md entry. It turns the next such defect into "unsolved" rather than a wrong answer. The tests ask WithoutSpuriousRoots directly, with candidates that fail.
• The suite, the trio, F#, AOT and the eight harnesses pass.

No issue was filed.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 75.00000% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.75%. Comparing base (5f7a0de) to head (6477079).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...ontinuous/Solvers/EquationSolver/SolveStatement.cs	75.00%	0 Missing and 3 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2317      +/-   ##
==========================================
- Coverage   86.76%   86.75%   -0.02%     
==========================================
  Files         311      311              
  Lines       68216    68225       +9     
  Branches    19827    19832       +5     
==========================================
- Hits        59191    59189       -2     
- Misses       4882     4891       +9     
- Partials     4143     4145       +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.30% <75.00%> (-0.02%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...ontinuous/Solvers/EquationSolver/SolveStatement.cs	83.69% <75.00%> (-0.88%)	⬇️

... and 2 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.