A union with an empty interval is the other set - #1636
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Two intervals were joined wherever one ended where the other began, before
either was asked whether it was empty: [0; 1] \/ [1; 0] became { 1 },
[3; 1] \/ [1; 2] the empty [3; 2], and [a; b] \/ [b; a] became { b }. An
empty interval now adds nothing, and two intervals with ends that are not
numbers are joined only where neither can be empty -- an end at an
infinity, or a single point closed at both ends -- so [a; b] \/ [b; c] is
left as written. A closed point's union was computed and discarded; it is
returned now.
Closes #1634.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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UniteIntervalAndIntervaljoined two intervals wherever one ended where the other began, before it asked whether either was empty.[1; 0]is empty, and it ends at 0, where[0; 1]begins, so[0; 1] \/ [1; 0]was joined into{ 1 }. The peer session found this on #1633, where a union was the obvious way to write the segment between an integral's limits.The function now asks about emptiness first:
(-oo; x] \/ [x; +oo)is stillRR, and[a; b] \/ [b; c], where either may be empty, is left as written.Simplifyof[0; 1] \/ [1; 0]{ 1 }— wrong[0; 1][3; 1] \/ [1; 2][3; 2], which is empty — wrong[1; 2][a; b] \/ [b; a]{ b }— wrong[a; b] \/ [b; c][a; c]— wrong wherea > borb > c(-oo; x] \/ [x; +oo)RRRRAnEmptyIntervalAddsNothingTestdecides each union by membership, at points on both sides of every end, rather than reading its printed shape. It also pins the symbolic cases.Suite on net10.0, at
1c52ec44on masterfac6ce16: 14196 passed, none failed. The head,2c74c073, differs from it only in its commit message. Every target framework builds.Gate: allocation matches the baseline on all 19 gated benchmarks.
Closes #1634.
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura