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Take the real root in the sampled checks where the library's power takes it - #2092
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Rafael-SOWNet merged 2 commits intoOct 23, 2026
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…kes it The checks at sampled points evaluate both sides in intervals, doubles and then forty and eighty digits, and both tiers took every power's principal branch. The library takes the real root for a negative real base and an exact exponent of odd denominator below 10: (-8)^(1/3) is -2 (#204). So on the negative axis the check could disagree with the values it was checking. The derivative of (-x^3)^(1/3) is -x^2 (-x^3)^(-2/3), which is -1. At the points right of 0 the check read it as -e^(-2 i pi/3), and turned the right answer away. Equally it could accept an answer that is right only on the principal branch, where the library's value is another. Both tiers now take the real root under the conditions Number.Pow takes it: the exponent an exact fraction in the tree, not whole, of odd denominator below 10, and the base's interval real and negative. An even denominator, a decimal exponent and a base off the real line keep the principal branch, as the library's power does. Fixes #2089. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…t resolve as a cref Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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…s it (#2099) The precise evaluation read gamma(a, z) with its order as a decimal, which is the principal branch on the negative axis. The function itself takes the power's real root there for an exact order of odd denominator below 10, as the sampled checks' powers now do (#2092): gamma(1/3, -2) is 10.21, and the check read it as complex. Such an order is now handed to the function as it is written. Part of #2075. Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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The checks at sampled points take the real root where the library's power takes it. Fixes #2089.
The defect. Both interval tiers, doubles and then forty and eighty digits, took every power's principal branch. The library takes the real root for a negative real base and an exact exponent of odd denominator below 10:
(-8)^(1/3)is-2(#204). On the negative axis the check could therefore disagree with the values it checks:The change. Both tiers take the real root under the conditions
Number.Powdoes: the exponent an exact fraction in the tree, not whole, of odd denominator below 10, and the base's interval real and negative. An even denominator, a decimal exponent and a base off the real line keep the principal branch, as the library's power does.Measured on Rubi's suite, with the harness that reads
GAMMA, against this branch's base68211405, the whole corpus each side: 48,907 solved on both, 0 rows moved, 0 wrong. Time per stream is 1.017, 1.010 and 1.003 of the base's, and allocation 1.0001 in each.Tests: the interval holds the real root's value in both tiers,
(-8)^(1/3) + (-2)^(2/5)and(-3/2)^(-4/7) + (-5)^(1/2), and the derivative above holds against-1and not against-1 + 1/1000. The suite passes (16,948), and so do the MCP tests (329).🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura