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Provide a root of a raised radical equation with a parameter with being one - #2337

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Rafael-SOWNet merged 2 commits into
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a-raised-root-with-a-parameter-is-provided-it-is-one
Nov 3, 2026
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Rafael-SOWNet merged 2 commits into
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a-raised-root-with-a-parameter-is-provided-it-is-one

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Found while working on #2335. No issue was filed.

An equation in a radical is raised to a power, which adds roots. Each root is then put back into the equation and dropped where it fails. With another name in the equation that can't be decided, so every root of the raised equation was answered:

sqrt(x + 1) + a + x = 0, then a given 2.6.0 and master this PR
a = -5 { 3, 8 }, and 8 is not a root { 3 }
a = 0 two roots, one of them not a root { (1 - sqrt(5)) / 2 }
a = 2 two roots, neither a root { }

Each root is now provided it is one, with the equation at that root as its condition, so giving the name a value keeps the roots and drops the rest. An equation in x alone is unchanged, since there the roots are decided when they're put back.

This touches the same place in FractionedPolynoms as #2335, so whichever merges second gets a conflict round.

Tests: the four cases in ARaisedRootWithAParameterTest fail on master. The 1,611 solve tests pass. There is a BREAKING entry, A root of a raised radical equation with a parameter is provided it is one.

🤖 Generated with Claude Code

…ng one

An equation in a radical is raised to a power, which adds roots, and each
root is put back into the equation to be dropped where it fails. With
another name in the equation that cannot be decided, and every root of the
raised equation was answered: sqrt(x + 1) + a + x = 0 had both roots of
its square, and for each a one of them is not a root. At a = -5 they are 3
and 8, and 8 is not a root; at a = 2 neither is. 2.6.0 answered the same.

Each is now provided it is one, the equation at that root, so giving the
name a value keeps the roots and drops the rest. An equation in x alone is
unchanged: its roots are decided where they are put back.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
@Rafael-SOWNet Rafael-SOWNet added this to the 2.7.0 milestone Nov 2, 2026
@Rafael-SOWNet Rafael-SOWNet moved this from Todo to In review in AngouriMath Nov 2, 2026
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codecov Bot commented Nov 2, 2026 •

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.76%. Comparing base (0a58c74) to head (f78e54d).
⚠️ Report is 1 commits behind head on master.

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@@            Coverage Diff             @@
##           master    #2337      +/-   ##
==========================================
- Coverage   86.77%   86.76%   -0.01%     
==========================================
  Files         312      312              
  Lines       68540    68542       +2     
  Branches    19938    19939       +1     
==========================================
- Hits        59474    59473       -1     
- Misses       4906     4908       +2     
- Partials     4160     4161       +1     
Flag Coverage Δ
cpp 37.77% <ø> (ø)
csharp 87.31% <100.00%> (-0.01%) ⬇️
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
...nuous/Solvers/EquationSolver/FractionedPolynoms.cs 85.91% <100.00%> (+0.40%) ⬆️

... and 5 files with indirect coverage changes

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@Rafael-SOWNet
Rafael-SOWNet merged commit 77ed372 into master Nov 3, 2026
37 of 38 checks passed
@github-project-automation github-project-automation Bot moved this from In review to Done in AngouriMath Nov 3, 2026
@Rafael-SOWNet
Rafael-SOWNet deleted the a-raised-root-with-a-parameter-is-provided-it-is-one branch November 3, 2026 01:13
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