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Split a biquadratic with surds in it by its roots in the square - #1903
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Rafael-SOWNet merged 3 commits intoOct 16, 2026
Merged
Rafael-SOWNet merged 3 commits into
Rafael-SOWNet merged 3 commits into
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The rule for an even polynomial over a + b x^2 + c x^4 took symbolic coefficients only, and left numbers to the partial fractions, which factor over the rationals: Rubi's 1.2.2.3 (sqrt(2) - x^2)/(1 - sqrt(2) x^2 + x^4) and (sqrt(2) + x^2)/(1 + sqrt(2) x^2 + x^4) were declined. Part of #718 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…surds-is-split-by-its-roots-in-the-square
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Part of #718.
SolveAnEvenPolynomialOverASymbolicBiquadraticsplits an even polynomial overa + b x^2 + c x^4by the two roots inx^2. It declined unless the denominator held a symbol, leaving numbers to the partial fractions. Those factor over the rationals, so(sqrt(2) - x^2)/(1 - sqrt(2) x^2 + x^4)was declined by both. The guard now also passes a denominator with a coefficient that is not rational. Rational biquadratics still go to the partial fractions as before.Checks
x^2and three with real ones: 150/150.ABiquadraticWithSurdsIntegralTest: 6 cases; the existing biquadratic tests pass alongside, 49 in all.Corpus, measured against master 55a8044 (this branch then merged bab8c75):
A third move, 3.2.3:30, is solved on both arms re-run alone. One row read as slow, 3.2.3:42 (1.6 s → 6.8 s). Re-timed alone twice per arm while another chain ran, master took 6.0 and 7.0 s and this branch 6.5 and 9.3 s. It sits near the budget on both, and this change does not reach a logarithm. Gate passed; suite 15,419 passed, 0 failed.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura