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A quotient of logarithms tends to the logarithms of its arguments' limits - #2276
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Rafael-SOWNet merged 2 commits intoOct 31, 2026
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…mits limit(ln(y + x) / ln(z + x), x, 0) was y / z, where it is ln(y) / ln(z), while the same limit with numbers, ln(x + 2) / ln(x + 3), was ln(2) / ln(3). SolveAsLogarithmDivision builds the quotient of the limits' logarithms, and returns it where it evaluates to a number; its last arm, reached for a symbolic limit, returned the quotient of the limits themselves. It now returns the quotient of their logarithms. LogarithmsOfSymbolicLimitsTest takes six symbolic quotients and one numeric one; the six fail on master. ln(1 + x) / ln(y + x) at 0, which was 1 / y, is 0 provided not ln(y) = 0. The suite, the trio, F#, AOT and the eight harnesses pass. Fixes #2271. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## master #2276 +/- ##
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+ Coverage 86.70% 86.71% +0.01%
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Files 310 310
Lines 67869 67872 +3
Branches 19701 19701
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+ Hits 58843 58857 +14
+ Misses 4903 4891 -12
- Partials 4123 4124 +1
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…-the-limits Both this branch and #2268 add a header rule after ModulusPhaseTest's; each keeps its own. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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limitright(ln(x^x), x, -1) was ln(-1), which is i pi, where it is -i pi: x^x comes to -1 from below as x comes down to -1, and the principal logarithm is continuous on its cut from above only. The value on the cut is the limit along the real line and from above, so it was given as the limit from either side. ArrivesOnTheCutOffTheRealLine asks whether a logarithm's argument, or the base of a power to an exponent that is not whole, tends to a negative real and is not known to be real on the approach; a power's base and a logarithm's argument count as positive where their values at the destination are. Which side such an argument comes from is not decided, so a limit there is declined: by substitution, by the logarithm's and the power's descent, by SolveAsLogarithm, by the quotient of logarithms, and by Gruntz, whose series took the principal logarithm of a negative coefficient. A limit from above, whose answer was right, is declined too. LimitOnABranchCutTest takes eight limits from below the cut, three two-sided ones that do not exist, and nine along the real line, which are answered as before; eleven fail on master. The suite, the trio, F#, AOT and the eight harnesses pass. Composed with #2268, #2275 and #2276, work/limitcheck finds none of the 56 limits it found answered with another value on master, of 600 expressions. Part of #2266. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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limit(ln(y + x) / ln(z + x), x, 0)wasy / z, where it isln(y) / ln(z), while the same limit with numbers,ln(x + 2) / ln(x + 3), wasln(2) / ln(3).SolveAsLogarithmDivisionbuilds the quotient of the limits' logarithms and returns it when it evaluates to a number. Its last arm, reached for a symbolic limit, returned the quotient of the limits themselves. It now returns the quotient of their logarithms.limit(ln(y + x) / ln(z + x), x, 0)y / zln(y) / ln(z)limit(ln(a + 1/x) / ln(b + 1/x), x, +oo)a / bln(a) / ln(b)limit(ln(1 + x) / ln(y + x), x, 0)1 / y0 provided not ln(y) = 0LogarithmsOfSymbolicLimitsTest: its six symbolic cases fail on master, and the numeric one passes on both. The suite (18,236), the trio, F#, AOT and the eight harnesses pass locally.This touches the same function as #2275, in a different hunk.
Fixes #2271.
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