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Write a symbolic cubic with a repeated root over its roots - #1933
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Rafael-SOWNet merged 3 commits intoOct 17, 2026
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A cubic below the bar whose discriminant vanishes identically is a (x - r)^2 (x - s), with r and s rational in its coefficients, or a cube where b^2 - 3ac vanishes too. 1/(9x^3 - 9bx + 2 sqrt(3) b^(3/2)) was left unevaluated (Rubi's 1.3.1:8) and so written is answered in half a second. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…ated-root-is-split-over-it # Conflicts: # Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs # Sources/AngouriMath/Functions/Continuous/Integration/Integration.Definition.cs
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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A cubic below the bar with symbolic coefficients and a discriminant that vanishes identically is
a (x - r)^2 (x - t), with the double rootr = (9ad - bc)/(2(b² - 3ac))and the simple roott = (4abc - 9a²d - b³)/(a(b² - 3ac))(a triple roota (x + b/3a)^3whereb² - 3acvanishes too). It is written so before the partial fractions; each candidate is checked by expanding it back against the cubic.1/(x^3 - 3b x + 2b^(3/2))was left unevaluated and is answered in 84 ms.Part of #718 — Rubi's 1.3.1:8.
Measured against master b2ef509, both arms in one chain:
Recorded in BREAKING-CHANGES.md.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura