http://wiki.googology.top/index.php?action=history&feed=atom&title=UPS
UPS - 版本历史
2026-07-22T06:12:11Z
本wiki上该页面的版本历史
MediaWiki 1.43.1
http://wiki.googology.top/index.php?title=UPS&diff=3441&oldid=prev
2026年7月10日 (五) 02:57 CGoL
2026-07-10T02:57:55Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月10日 (五) 10:57的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l93">第93行：</td>
<td colspan="2" class="diff-lineno">第93行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>展开结果的基本列第 <math>m</math> 项为 <chem>S' + B^{+1} + B^{+2} + ... + B^{+m}</chem> , 其中 <math>+</math> 为序列拼接。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>展开结果的基本列第 <math>m</math> 项为 <chem>S' + B^{+1} + B^{+2} + ... + B^{+m}</chem> , 其中 <math>+</math> 为序列拼接。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>若表达式无坏根或坏根为 <math>-1</math> , <del style="font-weight: bold; text-decoration: none;">则该表达式无法展开。</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>若表达式无坏根或坏根为 <math>-1</math> , <ins style="font-weight: bold; text-decoration: none;">则该表达式无法展开，表示后继序数。</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== 展开器 ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== 展开器 ==</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3439:rev-3441:php=table -->
</table>
CGoL
http://wiki.googology.top/index.php?title=UPS&diff=3439&oldid=prev
2026年7月10日 (五) 02:38 Alice
2026-07-10T02:38:02Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月10日 (五) 10:38的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">第1行：</td>
<td colspan="2" class="diff-lineno">第1行：</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>UPS（Upward Projection Sequence, 向上投影序列）是由 Optimism 最初创作，Alice <del style="font-weight: bold; text-decoration: none;">完善的记号，旨在以序列形式模拟向上投影。</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>UPS（Upward Projection Sequence, 向上投影序列）是由 Optimism 最初创作，Alice <ins style="font-weight: bold; text-decoration: none;">完善的记号，旨在以序列形式模拟向上投影。然而，UPS 在 [[SSO]] 以上是不理想的。</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其极限表达式为 <math>0, 1, 2*, 3*, 4*, ...</math> 。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其极限表达式为 <math>0, 1, 2*, 3*, 4*, ...</math> 。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3438:rev-3439:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3438&oldid=prev
Alice：/* 坏根寻找 */
2026-07-08T14:06:17Z
<p><span class="autocomment">坏根寻找</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 22:06的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l64">第64行：</td>
<td colspan="2" class="diff-lineno">第64行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>令 <math>a = \mathrm{ps}(L-1), d = \mathrm{drop}(a)</math> 。若 <math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> 。若 <math>a = -1</math> , 表达式无坏根。</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>令 <math>a = \mathrm{ps}(L-1), d = \mathrm{drop}(a)</math> 。若 <math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math> 。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> 。若 <math>a = -1</math> , 表达式无坏根。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3437:rev-3438:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3437&oldid=prev
Alice：/* 直接集与直接段 */
2026-07-08T11:20:32Z
<p><span class="autocomment">直接集与直接段</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 19:20的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17">第17行：</td>
<td colspan="2" class="diff-lineno">第17行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>一个索引 <math>i</math> 的直接集定义为：</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>一个索引 <math>i</math> 的直接集定义为：</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># <math>i \in D(i)</math>;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># <math>i \in D(i)</math> ;</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 若 <math>p(j) \in D(i), s_j = 1</math> , 则 <math>j \in D(i)</math> 。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 若 <math>p(j) \in D(i), s_j = 1</math> , 则 <math>j \in D(i)</math> 。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>定义直接段结尾：令 <math>M(i) = \max(t | t \in D(i))</math> 。若存在 <math>k</math> 使得 <math>k > M(i), p(k) \in D(i)</math> 且 <math>v_k = \min (v_j | j > M(i), p(j) \in D(i))</math> , 找到其中索引最小的 <math>k_0</math> , 定义 <math>\mathrm{end}(i) = k_0</math> ; 否则，定义 <math>\mathrm{end}(i) = M(i)</math> 。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>定义直接段结尾：令 <math>M(i) = \max(t | t \in D(i))</math> 。若存在 <math>k</math> 使得 <math>k > M(i), p(k) \in D(i)</math> 且 <math>v_k = \min (v_j | j > M(i), p(j) \in D(i))</math> , 找到其中索引最小的 <math>k_0</math> , 定义 <math>\mathrm{end}(i) = k_0</math> ; 否则，定义 <math>\mathrm{end}(i) = M(i)</math> 。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3430:rev-3437:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3430&oldid=prev
2026年7月8日 (三) 10:09 Alice
2026-07-08T10:09:58Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 18:09的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">第1行：</td>
<td colspan="2" class="diff-lineno">第1行：</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">UPS（Upper </del>Projection Sequence, 向上投影序列）是由 Optimism 最初创作，Alice 完善的记号，旨在以序列形式模拟向上投影。</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">UPS（Upward </ins>Projection Sequence, 向上投影序列）是由 Optimism 最初创作，Alice 完善的记号，旨在以序列形式模拟向上投影。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其极限表达式为 <math>0, 1, 2*, 3*, 4*, ...</math> 。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>其极限表达式为 <math>0, 1, 2*, 3*, 4*, ...</math> 。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3428:rev-3430:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3428&oldid=prev
2026年7月8日 (三) 09:50 Alice
2026-07-08T09:50:56Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 17:50的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l97">第97行：</td>
<td colspan="2" class="diff-lineno">第97行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== 展开器 ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== 展开器 ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://smilelee-lyx.github.io/ne-rewritten/ NE Rewritten] 上可进行 UPS 的展开。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://smilelee-lyx.github.io/ne-rewritten/ NE Rewritten] 上可进行 UPS 的展开。</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{默认排序:个人记号}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[分类:记号]]</ins></div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3424:rev-3428:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3424&oldid=prev
2026年7月8日 (三) 06:13 Alice
2026-07-08T06:13:00Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 14:13的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l40">第40行：</td>
<td colspan="2" class="diff-lineno">第40行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 父段与 Dropping 祖先段 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 父段与 Dropping 祖先段 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>定义索引 <math>i</math> 的父段起始索引为：<math>\mathrm{ps}(i) = \begin{cases}-1 ,&p(i) = -1;\\ p(i),&s_{p(i)} = 0;\\ \mathrm{ps}(p(i)),&s_{p(i)} = 1.\end{cases}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>定义索引 <math>i</math> 的父段起始索引为：<math>\mathrm{ps}(i) = \begin{cases}-1 ,&p(i) = -1;\\ p(i),&s_{p(i)} = 0;\\ \mathrm{ps}(p(i)),&s_{p(i)} = 1.\end{cases}</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">定义索引 <math>i</math> 的父段为 <math>\mathrm{seg}(\mathrm{ps}(i))</math> 。</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_i = 0</math> , 通过以下流程计算出索引 <math>i</math> 的 Dropping 祖先段：初始状态下定义 <math>c_0 = i, r_0 = i</math> 。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_i = 0</math> , 通过以下流程计算出索引 <math>i</math> 的 Dropping 祖先段：初始状态下定义 <math>c_0 = i, r_0 = i</math> 。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3423:rev-3424:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3423&oldid=prev
2026年7月8日 (三) 06:11 Alice
2026-07-08T06:11:41Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 14:11的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66">第66行：</td>
<td colspan="2" class="diff-lineno">第66行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>令 <math>a = \mathrm{ps}(L-1), d = \mathrm{drop}(a)</math> 。若 <math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> <del style="font-weight: bold; text-decoration: none;">。</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>令 <math>a = \mathrm{ps}(L-1), d = \mathrm{drop}(a)</math> 。若 <math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> <ins style="font-weight: bold; text-decoration: none;">。若 <math>a = -1</math> , 表达式无坏根。</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3422:rev-3423:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3422&oldid=prev
2026年7月8日 (三) 06:08 Alice
2026-07-08T06:08:37Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 14:08的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66">第66行：</td>
<td colspan="2" class="diff-lineno">第66行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>令 <math><del style="font-weight: bold; text-decoration: none;">l > 0</math> 为最小的自然数使得 <math>s_</del>{<del style="font-weight: bold; text-decoration: none;">p^l(L-1)</del>} <del style="font-weight: bold; text-decoration: none;">= 0</math> 。定义 <math>a = p^l</del>(L-1), d = \mathrm{drop}(a)</math> <del style="font-weight: bold; text-decoration: none;">。</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>令 <math><ins style="font-weight: bold; text-decoration: none;">a = \mathrm</ins>{<ins style="font-weight: bold; text-decoration: none;">ps</ins>}(L-1), d = \mathrm{drop}(a)</math> <ins style="font-weight: bold; text-decoration: none;">。若 </ins><math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> 。</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">若 </del><math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> 。</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3421:rev-3422:php=table -->
</table>
Alice
http://wiki.googology.top/index.php?title=UPS&diff=3421&oldid=prev
2026年7月8日 (三) 06:05 Alice
2026-07-08T06:05:52Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hans-CN">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年7月8日 (三) 14:05的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66">第66行：</td>
<td colspan="2" class="diff-lineno">第66行：</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>若 <math>s_{L-1} = 1</math> , 以此流程确定坏根。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>令 <math>l > 0</math> 为最小的自然数使得 <math>s_{p^l(L-1)} = 0</math> 。定义 <math>a = p^l(L-1), d = \mathrm{drop}(a)</math> <del style="font-weight: bold; text-decoration: none;">。若 </del><math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> <del style="font-weight: bold; text-decoration: none;">。若 </del><math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>令 <math>l > 0</math> 为最小的自然数使得 <math>s_{p^l(L-1)} = 0</math> 。定义 <math>a = p^l(L-1), d = \mathrm{drop}(a)</math> <ins style="font-weight: bold; text-decoration: none;">。</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">若 </ins><math>\mathrm{ps}^{m+1}(a) = -1</math> , 则构建祖先段链 <math>A = [\mathrm{ps}(a), \mathrm{ps}^2(a), ..., \mathrm{ps}^m(a)]</math>。定义参考段 <math>R = [\alpha_d, \alpha_{d+1}, ..., \alpha_{L-1}]</math> <ins style="font-weight: bold; text-decoration: none;">。</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">若 </ins><math>d = \mathrm{ps}^k(a)</math> , 则将 <math>\mathrm{ps}(a)</math> 到 <math>\mathrm{ps}^k(a)</math> 预先标记为跳过。</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>按顺序枚举祖先段链。</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>按顺序枚举祖先段链。</div></td></tr>
<!-- diff cache key my_wiki:diff:1.41:old-3420:rev-3421:php=table -->
</table>
Alice