A cos + i A sin below the bar is written as the exponential it is - #1485
Merged
Merged
Conversation
`cos(x)^2/(a cos(x) + i a sin(x))^3` was declined after twelve seconds. `A cos(y) + i A sin(y)` is `A e^(i y)` and `A cos(y) - i A sin(y)` is `A e^(-i y)`; written so, the integrand is an exponential times a power of a cosine, which the closed rules answer at once. As a sum of a cosine and a sine it has no real rotation -- `A^2 + (i A)^2` is zero -- so the rule for `a cos + b sin` has nothing to do with it. The sibling of the rule for `A + i A tan(y)`, and below the bar only for the same reason. A whole power of the product written is split, `(A e^(i y))^n` as `A^n e^(i n y)`: the rule that distributes such powers takes a constant with a symbol in it and leaves a number, and `cos(x)^2/(2 e^(i x))^3` was declined where `cos(x)^2/(a e^(i x))^3` was not -- found by the tests with numeric coefficients after the corpus rows, which are symbolic, had all passed. Rubi's 4.7.2, all 290 problems: 237 to 249, no row lost, 16 timeouts to 14. Families 1, 4, 5, 6 and 7 and the 1774-problem suite unchanged, row for row. Part of #718. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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
1 participant
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
cos(x)^2/(a cos(x) + i a sin(x))^3was declined after twelve seconds.A cos(y) + i A sin(y)isA e^(i y)andA cos(y) - i A sin(y)isA e^(-i y); written so, the integrand is an exponential times a power of a cosine, which the closed rules answer at once. As a sum of a cosine and a sine it has no real rotation —A^2 + (i A)^2is zero — so the rule fora cos + b sin(#1484) declines it by design. This is the sibling of the rule forA + i A tan(y), and reads below the bar only for the same reason.A second gap under it, found by the tests. A whole power of the product written is split,
(A e^(i y))^nasA^n e^(i n y):SolveByDistributingWholePowersOfProductsdistributes only a constant with a symbol in it, socos(x)^2/(2 e^(i x))^3was declined wherecos(x)^2/(a e^(i x))^3was not. The corpus rows are all symbolic and passed; the tests with numeric coefficients are what failed.Measured
cos(x)^2/(a cos(x) + i a sin(x))^3trig^m (a trig + b trig)^n, all 290 problemsFamily 7 reports two rows as timeouts that the previous run reported as unevaluated, with the same number answered. Both take far longer than the five-second cap on either build, timed alone:
e^(2 acoth(a x)) (c - a^2 c x^2)^(9/2)declines in 26.0 s here and 26.5 s on master, andx^3 (d - c^2 d x^2)^(5/2)(a + b acosh(c x))runs past 50 s on both. Which of the two verdicts a corpus run prints for them is warmth, not this change.A secant above the bar is still declined:
sec(x)^2 e^(-3 i x)is rational ine^(i x)with an imaginary rate, which nothing answers yet. With #1483 and #1484, the 4.7.2 file goes from 199 to 249 of 290.Part of #718.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura