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Write an exponent given expanded as the power of a shifted linear it is - #2097
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Rafael-SOWNet merged 1 commit intoOct 23, 2026
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e^(a^3 + 3 a^2 b x + 3 a b^2 x^2 + b^3 x^3) x^k was declined, where e^((a + b x)^3) x^k is answered by the rule for a polynomial beside a function of one shifted linear. An exponential of a polynomial of degree 3 to 12, given expanded, is now written as p (x + s)^n plus a constant, where p is the leading coefficient and s = p_(n - 1)/(n p), exactly when each lower coefficient is p C(n, j) s^(n - j). Then it is asked again as the same question, at the same depth, so that the rules scoped to the question asked or one below still read it. Part of #2075. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Writes an exponent given expanded back as the power of a shifted linear it is. Part of #2075.
The rule.
e^(a^3 + 3 a^2 b x + 3 a b^2 x^2 + b^3 x^3) x^kwas declined, thoughe^((a + b x)^3) x^kis answered by #2087's rule for a polynomial beside a function of one shifted linear.An exponential of a polynomial of degree 3 to 12, given expanded, is now written as
p (x + s)^nplus a constant. Herepis the leading coefficient ands = p_(n - 1)/(n p). That holds exactly when each lower coefficient isp C(n, j) s^(n - j). The respelled integrand is then asked again as the same question, at the same depth, so that the rules scoped to the question asked, or one below it, still read it.The shift is simplified, and the
provided p != 0that comes with it is dropped: reading the polynomial at its degree already assumes it. Left in, it hid the linear from the rule that substitutes for it.Measured on Rubi's suite, with the harness that reads
GAMMA, against68211405, the whole corpus each side. This branch was measured on2be40bad, which adds #2088 to that base, and is rebased onto master now.68211405The gains are
2.3:239-243. The other 5 are #2088's. Time per stream is 1.015, 0.999 and 0.918 of the base's, and allocation 1.0007, 1.0004 and 0.9977. One row's allocation grew in the run,6.1.7:196, which is the same alone on both builds, as before.Three integrals differentiate back in the tests, a quartic among them. The suite passes (16,955), and so do the MCP tests (329).
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura