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linesweeper: docs/sweep.typ spells "conditions" and names q(i+1)
Two typos in docs/sweep.typ are corrected: "condi0.2tions" reads "conditions", and the insertion-position argument says q(i+1) is false instead of q(i+i). SOURCE.json records the new sha256 of docs/sweep.typ and the change in local_patches, and README.craft.md lists it.
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Vendored
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@@ -14,6 +14,8 @@ and, for every file kept, the hash in the package (`source_sha256`) and the hash
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- `docs/sweep.typ`: the intersection scan to the left compares each segment with `alpha^(i+1)`
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instead of `alpha^i`. With `alpha^i`, its first pass compared `alpha^i` with itself, and the lemma
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after it is stated for `alpha^(i+1)`.
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- `docs/sweep.typ`: two typos are corrected. "condi0.2tions" reads "conditions", and `q(i+i)` reads
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`q(i+1)`, the first index for which `q` is false.
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`omitted_files` lists the 43 files of the package left out here, with their hashes:
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Vendored
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@@ -8,7 +8,8 @@
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"upstream_revision": "824b0791a750f7b27b8edcbb6c6244d0e629875e",
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"upstream_directory": "",
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"local_patches": [
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"In `docs/sweep.typ`, the intersection scan to the left compares each segment with `alpha^(i+1)`, the segment the lemma after it is stated for, instead of `alpha^i`."
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"In `docs/sweep.typ`, the intersection scan to the left compares each segment with `alpha^(i+1)`, the segment the lemma after it is stated for, instead of `alpha^i`.",
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"In `docs/sweep.typ`, the typo \"condi0.2tions\" reads \"conditions\", and `q(i+i)` reads `q(i+1)`, the first index for which `q` is false."
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],
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"files": [
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{ "path": ".cargo_vcs_info.json", "source_sha256": "47fba6a9dbdf445a5c97f783c9be62093035f9d5e5cdc2cf3216ad8259bcd8fc", "source_git_blob": null, "sha256": "47fba6a9dbdf445a5c97f783c9be62093035f9d5e5cdc2cf3216ad8259bcd8fc" },
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@@ -23,7 +24,7 @@
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{ "path": "benches/linebender_logo.rs", "source_sha256": "d10867f43439d37f0e1da5d30eaed9ab3bfbe655ed47212f65dc20ab4db65cb3", "source_git_blob": null, "sha256": "d10867f43439d37f0e1da5d30eaed9ab3bfbe655ed47212f65dc20ab4db65cb3" },
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{ "path": "benches/painted_dreams.rs", "source_sha256": "073008db93840d380710e13ed3ae38e08cb823f10c12e5f838dac1ccf37eaecf", "source_git_blob": null, "sha256": "073008db93840d380710e13ed3ae38e08cb823f10c12e5f838dac1ccf37eaecf" },
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{ "path": "benches/synthetic.rs", "source_sha256": "7ce59bef2e1c4f28b00cb89feb15bc71ca4b098a8d27e7b02ea699aca9bcc810", "source_git_blob": null, "sha256": "7ce59bef2e1c4f28b00cb89feb15bc71ca4b098a8d27e7b02ea699aca9bcc810" },
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{ "path": "docs/sweep.typ", "source_sha256": "4766082c8672a7bb4356b5581043489c13b4e3fb8931ba3a5f0a473fab0172f3", "source_git_blob": null, "sha256": "571f227f4b43eaba8060c48344e26b639a4fea8787e5c63bd3f826836c5e4806" },
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{ "path": "docs/sweep.typ", "source_sha256": "4766082c8672a7bb4356b5581043489c13b4e3fb8931ba3a5f0a473fab0172f3", "source_git_blob": null, "sha256": "b9bb12076458469869e3e7723598d35ae391307bf22ea312f1b989949e9829a1" },
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{ "path": "examples/boolean_op.rs", "source_sha256": "3b38a1ccda7e736cce4b191a3a45ab4824c4c365190e3eb637b2fb39b5996c9f", "source_git_blob": null, "sha256": "3b38a1ccda7e736cce4b191a3a45ab4824c4c365190e3eb637b2fb39b5996c9f" },
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{ "path": "examples/bus.rs", "source_sha256": "e206a08be73899f564188052c8ecc15526b54606e52ee2935a64ce6b5723da33", "source_git_blob": null, "sha256": "e206a08be73899f564188052c8ecc15526b54606e52ee2935a64ce6b5723da33" },
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{ "path": "examples/curve_metrics.rs", "source_sha256": "0db6a5327fd2119a03a9a66624fea3e04b6bbb519655667ad30487aee6c787d2", "source_git_blob": null, "sha256": "0db6a5327fd2119a03a9a66624fea3e04b6bbb519655667ad30487aee6c787d2" },
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Vendored
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@@ -555,7 +555,7 @@ height. Note that because the sweep line changes at a discrete set of heights,
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at every important height $y$ we actually have two weakly-ordered sweep line:
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the "old" one from infinitesmally before $y$ height and the "new" one from $y$
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onwards. Because everything is continuous and the weak ordering conditions are
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closed, both the old and new sweep lines satisfy the weak ordering condi0.2tions
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closed, both the old and new sweep lines satisfy the weak ordering conditions
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at $y$.
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The algorithm goes like this: at every important height we use
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@@ -623,7 +623,7 @@ Let's check that this insertion position is valid: for every $j <= i$ we have
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either $j <= i_-$ or $i_- < j <= i$. In the first case, we already observed
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that $alpha^j_-(y) <= beta(y)$; in the second case, $q(j)$ returned `true` and
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so $alpha^j_-(y) <= beta^j^+ (y)$. In either case, $alpha^j prec.tilde beta$.
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On the other hand, $q(i+i)$ being `false` implies that $alpha^(i+1)_- (y) >=
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On the other hand, $q(i+1)$ being `false` implies that $alpha^(i+1)_- (y) >=
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beta(y)$. This implies that for all $j >= i+1$, $alpha^j_+ (y) >= beta(y)$ and
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so $alpha^j succ.tilde_y beta$.
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