Repository navigation
Integrate an exponential of a quadratic over the linear through its vertex - #1951
Merged
Rafael-SOWNet merged 1 commit intoOct 19, 2026
Conversation
…ertex f^(a + b x + c x^2)/(b + 2 c x)^n was declined. Under u = b + 2 c x the exponent is u^2/(4 c) + a - b^2/(4 c), with no linear part, and the integrand is a moment about 0 of the Gaussian, which the integrator answers: the exponential integral of the square for an odd n, the error function for an even one. The exponent in u is written from the coefficients, and the vertex condition 2 A p = q B is decided as a value. Rubi's 2.3: 6 rows go from unevaluated to solved, 0 wrong. Families 0 and 1 and samples of 2-8 otherwise identical; gate and suite pass. Part of #233. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
Rafael-SOWNet
deleted the
an-exponential-of-a-quadratic-over-the-linear-through-its-vertex
branch
October 29, 2026 00:43
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Part of #233.
f^(a + b x + c x^2)/(b + 2 c x)^nwas declined. Underu = b + 2 c xthe exponent isu^2/(4 c) + a - b^2/(4 c), with no linear part, and the integrand is a moment about 0 of the Gaussian, which the integrator answers. An oddngives the exponential integral of the square, and an even one the error function. The new rule,SolveAnExponentialOfAQuadraticOverTheLinearThroughItsVertex, takes only a linear whose root is the vertex (2 A p = q B, decided as a value). Elsewhere the shift leaves a linear part:e^(x^2 + 2 x)/(x + 2)is still declined, and is pinned by a test.Measured against master
8a1ef454:Rebased onto #1950 without conflict. Both together put family 2 at 635 of 650. All six rows were declined by 2.5.0 too, and
BREAKING-CHANGES.mdhas the entry.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura