Answer a polynomial with its roots, not with one per starting point

[Rafael-SOWNet]

"x^5 + 3*x + 1".SolveEquation("x")   // master: 28 roots
"x^6 + x + 1".SolveEquation("x")     // master: 23 roots

Four of those 28:

-0.83907243306660750
-0.83907243306660761
-0.83907243306660773
-0.83907243306660784

They are one root. The numeric search starts from a grid and iterates in double precision, so the same root reached from different starting points comes back agreeing to about sixteen significant digits and differing after that — and each starting point contributed an answer of its own. The rounding that was already there only zeroes components near zero, so it collapses a stray 1e-19 imaginary part but has nothing to say about these.

What it does now

Candidates closer together than the iteration can tell apart are one root, and the one kept from each group is whichever leaves the equation closest to zero.

The threshold is measured. Candidates for a single root lie within 1e-15 of each other relative to their size; the nearest two genuinely distinct roots over the twelve polynomials I tried are 0.42 apart. The threshold is 1e-13 — a hundred times above the noise, and twelve orders below the closest two roots that were ever told apart.

polynomial	before	after
x^5 + 3x + 1	28	5
x^6 + x + 1	23	6
x^9 - x - 1	33	9
x^5 - 5x + 2	19	5

Every one of the twelve now comes back with exactly as many roots as its degree, and every root satisfies its equation. The polynomials solved exactly, by radicals rather than by iteration — x^5 - 1, x^8 - 1, x^7 - 2 — never had the problem and are untouched.

One existing test changed

FromStringTest.TestFormula8 asserted which of the two roots of x^2 + 1 a HashSet hands back first. That was never the solver's to decide, and it changed here: the candidates are now ordered before being collapsed, so that which one is compared against which does not depend on the order the grid produced them in. The test now asks for both roots, which is what it was checking.

Verification

19 new tests, 9 of which fail without the change. 4015 unit tests and 127 F# tests on both target frameworks, none failing. 117-problem self-verifying corpus at 101/117 with nothing wrong, in error or timing out; 1320 property checks over 151 expressions, none failing.

No issue is filed for this — I found it while checking the answers of #685.

[codecov-commenter]

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Codecov Report

❌ Patch coverage is 96.66667% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 80.41%. Comparing base (90c00a8) to head (6f3050a).
⚠️ Report is 56 commits behind head on master.

Files with missing lines	Patch %	Lines
...ontinuous/Solvers/NumericalSolving/NewtonSolver.cs	96.66%	1 Missing ⚠️
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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #686      +/-   ##
==========================================
- Coverage   80.99%   80.41%   -0.59%     
==========================================
  Files         155      156       +1     
  Lines       13687    12923     -764     
  Branches     1957     2123     +166     
==========================================
- Hits        11086    10392     -694     
+ Misses       1990     1923      -67     
+ Partials      611      608       -3     

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