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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 intoNov 3, 2026
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…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>
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## master #2337 +/- ##
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- Coverage 86.77% 86.76% -0.01%
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Files 312 312
Lines 68540 68542 +2
Branches 19938 19939 +1
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- Misses 4906 4908 +2
- Partials 4160 4161 +1
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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, thenagivena = -5{ 3, 8 }, and 8 is not a root{ 3 }a = 0{ (1 - sqrt(5)) / 2 }a = 2{ }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
FractionedPolynomsas #2335, so whichever merges second gets a conflict round.Tests: the four cases in
ARaisedRootWithAParameterTestfail 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