[Rafael-SOWNet]

Part of #2139: the real codomain.

The defect: with the real codomain, ModulusSolver.SolveOverTheReals solves an equation in moduli by cases between the kinks, but only where every modulus is of a linear function. A modulus of anything else fell through to Newton's method, and the answer kept non-real entries that solve nothing:

Solve, with the real codomain	2.6.0	this PR
x^2/abs(1-x^2) = x	{ 0, 0.618…, 1.618…, 1.618… + 1.7E-9i, 1.618… + 9.9E-8i }	{ 0, (-1 + sqrt(5)) / 2, (1 + sqrt(5)) / 2 }
abs(x^2 - 4) = 3*x	{ 1, 4, 4.0000000000000062… + 1.6E-7i }	{ 1, 4 }

The change: a polynomial keeps one sign between neighbouring real roots. So a modulus of a polynomial with real numeric coefficients takes its real roots as its kinks.

• The roots come from the analytical solver and are kept exact, so a piece that holds throughout is an exact interval.
• A polynomial with no real root has no kinks, and the whole line is one piece.
• Anything else still declines, so nothing that answered before changes.

Checked:

• ModulusEquationTest has 6 more rows: those above, abs(x^2 - 1) + abs(x - 2) = 3 ({ -1, 0, 2 }), abs(x^2 - 2) = 1, abs(x^2 + 1) = 2, and x^2 + 1 = abs(x) ({ }).
• Unit suite: 17,164 passed, 0 failed, before the six new rows.
• RootCheck 596/596 clean; CasBench 120/121, unchanged; BoundCheck 0 disagreements.
• BREAKING-CHANGES entry added, measured on the 2.6.0 package.

Not in this PR: the complex codomain, which is the issue's own setting, is unchanged. A case split there can miss roots at which the argument is not real: x^2 + 1 = |x| has roots at ±0.618 i, where |x| = 0.618 and x is not ±0.618. And Newton's method in the complex plane assumes a holomorphic function, which |1 - x^2| is not. Which way to go there is asked on #2139.

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Codecov Report

❌ Patch coverage is 65.38462% with 9 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.43%. Comparing base (856b3cb) to head (18c8afa).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...Continuous/Solvers/EquationSolver/ModulusSolver.cs	65.38%	3 Missing and 6 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2178      +/-   ##
==========================================
- Coverage   86.45%   86.43%   -0.03%     
==========================================
  Files         295      295              
  Lines       64969    64988      +19     
  Branches    19092    19099       +7     
==========================================
+ Hits        56171    56172       +1     
- Misses       4770     4783      +13     
- Partials     4028     4033       +5     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.00% <65.38%> (-0.03%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...Continuous/Solvers/EquationSolver/ModulusSolver.cs	73.68% <65.38%> (-5.27%)	⬇️

... and 5 files with indirect coverage changes

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