服务:Spring Boot 3.2 + docx4j 8.3.9,POST /api/v3/server_office_file/file/parse
接受 .docx,返回 HTML(公式 → LaTeX,图片 → RustFS 外链)
公式支持三类来源:
- OMML(Word 2007+ 公式) → Python omml_mathml2latex
- MathType OLE 对象 → Ruby mathtype2mathml → MathML → LaTeX
- Word EQ 域(老教辅主力) → EqToLatexUtil(本次新增)
本次改动:
1. 新增 java-svc/.../core/EqToLatexUtil.java:
移植自 jby backend-services office-core,EQ 语法 → LaTeX
(\f→\dfrac、\r→\sqrt、\i→\int/\sum/\prod、\s→^{}/_{}、\b→\left\right、
\a→array、\x→\boxed/\overline、\o\al 堆叠、圈码、化学符号、极限、连等式)
品牌标记 JBYU* → WPU*,与采集端一致
2. CtoMathFinder:接上 EQ 分支(原为 not-ported 桩),域代码经
EqToLatexUtil.convert 转 LaTeX 写入 eqLatexMap(WPEQNUM 占位符)
3. WordParseUtil.dealPlaceholder:EQ 的 LaTeX 同样加 \( \) 包裹
(原先因 WPEQNUM 例外不加包裹,前端/MathJax 不渲染)
修前症状:教辅 Word 里分式/方程组/上下标整段丢失(如 {−1/3, 1} 变成 {-,1})
修后实测:46 份教辅 2908 处 EQ 域全部还原,公式总数 2954 处、零未包裹残留
安全:application.yml(含 RustFS 密钥)不入库,提供 application.yml.example;
OssService 的 @Value 默认密钥已清空
15 lines
51 KiB
JSON
15 lines
51 KiB
JSON
{
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xmlns:c16=\"http://schemas.microsoft.com/office/drawing/2014/chart\" xmlns:dgm=\"http://schemas.openxmlformats.org/drawingml/2006/diagram\" xmlns:thm15=\"http://schemas.microsoft.com/office/thememl/2012/main\" xmlns:we=\"http://schemas.microsoft.com/office/webextensions/webextension/2010/11\" xmlns:w10=\"urn:schemas-microsoft-com:office:word\" xmlns:ns39=\"http://www.w3.org/2003/InkML\" xmlns:wp=\"http://schemas.openxmlformats.org/drawingml/2006/wordprocessingDrawing\" xmlns:sl=\"http://schemas.openxmlformats.org/schemaLibrary/2006/main\" xmlns:ns38=\"http://www.w3.org/1998/Math/MathML\" xmlns:w15=\"http://schemas.microsoft.com/office/word/2012/wordml\" xmlns:w14=\"http://schemas.microsoft.com/office/word/2010/wordml\" xmlns:dgm14=\"http://schemas.microsoft.com/office/drawing/2010/diagram\" xmlns:c16ac=\"http://schemas.microsoft.com/office/drawing/2014/chart/ac\" xmlns:a=\"http://schemas.openxmlformats.org/drawingml/2006/main\" xmlns:b=\"http://schemas.openxmlformats.org/officeDocument/2006/bibliography\" xmlns:c=\"http://schemas.openxmlformats.org/drawingml/2006/chart\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\" xmlns:wne=\"http://schemas.microsoft.com/office/word/2006/wordml\" xmlns:o=\"urn:schemas-microsoft-com:office:office\" xmlns:cs=\"http://schemas.microsoft.com/office/drawing/2012/chartStyle\" xmlns:r=\"http://schemas.openxmlformats.org/officeDocument/2006/relationships\" xmlns:cx=\"http://schemas.microsoft.com/office/drawing/2014/chartex\" xmlns:v=\"urn:schemas-microsoft-com:vml\" xmlns:pic14=\"http://schemas.microsoft.com/office/drawing/2010/picture\" xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\" xmlns:lc=\"http://schemas.openxmlformats.org/drawingml/2006/lockedCanvas\" xmlns:wetp=\"http://schemas.microsoft.com/office/webextensions/taskpanes/2010/11\"><m:sSubSup><m:sSubSupPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sSubSupPr><m:e><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>C</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:e><m:sub><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sub><m:sup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>3</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sup></m:sSubSup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>(</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>3</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:num><m:den><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:den></m:f><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>)</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:e><m:sup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>3</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sup></m:sSup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>(</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>1</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:num><m:den><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:den></m:f><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>)+</m:t></m:r><m:sSubSup><m:sSubSupPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sSubSupPr><m:e><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>C</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:e><m:sub><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sub><m:sup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sup></m:sSubSup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>(</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>3</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:num><m:den><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:den></m:f><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>)</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:e><m:sup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>4</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:sup></m:sSup><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>=</m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>189</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:num><m:den><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr><m:t>256</m:t></m:r><m:ctrlPr><w:rPr><w:rFonts w:hint=\"eastAsia\" w:ascii=\"DejaVu Math TeX Gyre\" w:hAnsi=\"DejaVu Math TeX Gyre\" w:eastAsia=\"微软雅黑\" w:cs=\"微软雅黑\"/><w:kern w:val=\"2\"/><w:sz w:val=\"18\"/><w:szCs w:val=\"18\"/><w:lang w:val=\"en-US\" w:eastAsia=\"zh-CN\" w:bidi=\"ar-SA\"/></w:rPr></m:ctrlPr></m:den></m:f></m:oMath>",
|
||
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|
||
"x6" : "<m:oMath xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\" xmlns:wpc=\"http://schemas.microsoft.com/office/word/2010/wordprocessingCanvas\" xmlns:cx=\"http://schemas.microsoft.com/office/drawing/2014/chartex\" xmlns:cx1=\"http://schemas.microsoft.com/office/drawing/2015/9/8/chartex\" xmlns:cx2=\"http://schemas.microsoft.com/office/drawing/2015/10/21/chartex\" xmlns:cx3=\"http://schemas.microsoft.com/office/drawing/2016/5/9/chartex\" xmlns:cx4=\"http://schemas.microsoft.com/office/drawing/2016/5/10/chartex\" xmlns:cx5=\"http://schemas.microsoft.com/office/drawing/2016/5/11/chartex\" xmlns:cx6=\"http://schemas.microsoft.com/office/drawing/2016/5/12/chartex\" xmlns:cx7=\"http://schemas.microsoft.com/office/drawing/2016/5/13/chartex\" xmlns:cx8=\"http://schemas.microsoft.com/office/drawing/2016/5/14/chartex\" xmlns:mc=\"http://schemas.openxmlformats.org/markup-compatibility/2006\" xmlns:aink=\"http://schemas.microsoft.com/office/drawing/2016/ink\" xmlns:am3d=\"http://schemas.microsoft.com/office/drawing/2017/model3d\" xmlns:o=\"urn:schemas-microsoft-com:office:office\" xmlns:oel=\"http://schemas.microsoft.com/office/2019/extlst\" xmlns:r=\"http://schemas.openxmlformats.org/officeDocument/2006/relationships\" xmlns:v=\"urn:schemas-microsoft-com:vml\" xmlns:wp14=\"http://schemas.microsoft.com/office/word/2010/wordprocessingDrawing\" xmlns:wp=\"http://schemas.openxmlformats.org/drawingml/2006/wordprocessingDrawing\" xmlns:w10=\"urn:schemas-microsoft-com:office:word\" xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\" xmlns:w14=\"http://schemas.microsoft.com/office/word/2010/wordml\" xmlns:w15=\"http://schemas.microsoft.com/office/word/2012/wordml\" xmlns:w16cex=\"http://schemas.microsoft.com/office/word/2018/wordml/cex\" xmlns:w16cid=\"http://schemas.microsoft.com/office/word/2016/wordml/cid\" xmlns:w16=\"http://schemas.microsoft.com/office/word/2018/wordml\" xmlns:w16du=\"http://schemas.microsoft.com/office/word/2023/wordml/word16du\" xmlns:w16sdtdh=\"http://schemas.microsoft.com/office/word/2020/wordml/sdtdatahash\" xmlns:w16sdtfl=\"http://schemas.microsoft.com/office/word/2024/wordml/sdtformatlock\" xmlns:w16se=\"http://schemas.microsoft.com/office/word/2015/wordml/symex\" xmlns:wpg=\"http://schemas.microsoft.com/office/word/2010/wordprocessingGroup\" xmlns:wpi=\"http://schemas.microsoft.com/office/word/2010/wordprocessingInk\" xmlns:wne=\"http://schemas.microsoft.com/office/word/2006/wordml\" xmlns:wps=\"http://schemas.microsoft.com/office/word/2010/wordprocessingShape\"><m:r><w:rPr><w:rFonts w:ascii=\"Cambria Math\" w:hAnsi=\"Cambria Math\"/></w:rPr><m:t>∄x∈</m:t></m:r><m:r><m:rPr><m:sty m:val=\"b\"/></m:rPr><w:rPr><w:rFonts w:ascii=\"Cambria Math\" w:hAnsi=\"Cambria Math\"/></w:rPr><m:t>R</m:t></m:r></m:oMath>",
|
||
"x7" : "<m:oMath xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\" xmlns:wpc=\"http://schemas.microsoft.com/office/word/2010/wordprocessingCanvas\" xmlns:cx=\"http://schemas.microsoft.com/office/drawing/2014/chartex\" xmlns:cx1=\"http://schemas.microsoft.com/office/drawing/2015/9/8/chartex\" xmlns:cx2=\"http://schemas.microsoft.com/office/drawing/2015/10/21/chartex\" xmlns:cx3=\"http://schemas.microsoft.com/office/drawing/2016/5/9/chartex\" xmlns:cx4=\"http://schemas.microsoft.com/office/drawing/2016/5/10/chartex\" xmlns:cx5=\"http://schemas.microsoft.com/office/drawing/2016/5/11/chartex\" xmlns:cx6=\"http://schemas.microsoft.com/office/drawing/2016/5/12/chartex\" xmlns:cx7=\"http://schemas.microsoft.com/office/drawing/2016/5/13/chartex\" xmlns:cx8=\"http://schemas.microsoft.com/office/drawing/2016/5/14/chartex\" xmlns:mc=\"http://schemas.openxmlformats.org/markup-compatibility/2006\" xmlns:aink=\"http://schemas.microsoft.com/office/drawing/2016/ink\" xmlns:am3d=\"http://schemas.microsoft.com/office/drawing/2017/model3d\" xmlns:o=\"urn:schemas-microsoft-com:office:office\" xmlns:oel=\"http://schemas.microsoft.com/office/2019/extlst\" xmlns:r=\"http://schemas.openxmlformats.org/officeDocument/2006/relationships\" xmlns:v=\"urn:schemas-microsoft-com:vml\" xmlns:wp14=\"http://schemas.microsoft.com/office/word/2010/wordprocessingDrawing\" xmlns:wp=\"http://schemas.openxmlformats.org/drawingml/2006/wordprocessingDrawing\" xmlns:w10=\"urn:schemas-microsoft-com:office:word\" xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\" xmlns:w14=\"http://schemas.microsoft.com/office/word/2010/wordml\" xmlns:w15=\"http://schemas.microsoft.com/office/word/2012/wordml\" xmlns:w16cex=\"http://schemas.microsoft.com/office/word/2018/wordml/cex\" xmlns:w16cid=\"http://schemas.microsoft.com/office/word/2016/wordml/cid\" xmlns:w16=\"http://schemas.microsoft.com/office/word/2018/wordml\" xmlns:w16du=\"http://schemas.microsoft.com/office/word/2023/wordml/word16du\" xmlns:w16sdtdh=\"http://schemas.microsoft.com/office/word/2020/wordml/sdtdatahash\" xmlns:w16sdtfl=\"http://schemas.microsoft.com/office/word/2024/wordml/sdtformatlock\" xmlns:w16se=\"http://schemas.microsoft.com/office/word/2015/wordml/symex\" xmlns:wpg=\"http://schemas.microsoft.com/office/word/2010/wordprocessingGroup\" xmlns:wpi=\"http://schemas.microsoft.com/office/word/2010/wordprocessingInk\" xmlns:wne=\"http://schemas.microsoft.com/office/word/2006/wordml\" xmlns:wps=\"http://schemas.microsoft.com/office/word/2010/wordprocessingShape\"><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:ascii=\"Cambria Math\" w:hAnsi=\"Cambria Math\"/></w:rPr><m:t>∃</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii=\"Cambria Math\" w:hAnsi=\"Cambria Math\"/></w:rPr><m:t>x</m:t></m:r><m:r><m:rPr><m:sty m:val=\"p\"/></m:rPr><w:rPr><w:rFonts w:ascii=\"Cambria Math\" w:hAnsi=\"Cambria Math\"/></w:rPr><m:t>∉</m:t></m:r><m:r><w:rPr><w:rFonts w:ascii=\"Cambria Math\" w:hAnsi=\"Cambria Math\"/></w:rPr><m:t>R</m:t></m:r></m:oMath>",
|
||
"x8" : "<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\"><mi>P</mi><mo>(</mo><mi>X</mi><mo>=</mo><mn>1</mn><mo>)</mo><mo>=</mo><msubsup><mrow><mi mathvariant=\"normal\">C</mi></mrow><mrow><mn>4</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><msup><mrow><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><msup><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>27</mn></mrow><mrow><mn>64</mn></mrow></mfrac></math>",
|
||
"x9" : "<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\"><msup><mrow><mi mathvariant=\"normal\">e</mi></mrow><mrow><mi>x</mi></mrow></msup><mo>+</mo><mi>x</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>y</mi></mrow></mfrac><mo>+</mo><mi mathvariant=\"normal\">l</mi><mi mathvariant=\"normal\">n</mi><mfrac><mrow><mn>1</mn></mrow><mrow><mi>y</mi></mrow></mfrac><mo>=</mo><mi mathvariant=\"normal\">l</mi><mi mathvariant=\"normal\">n</mi><mfrac><mrow><mn>1</mn></mrow><mrow><mi>y</mi></mrow></mfrac><mo>+</mo><msup><mrow><mi mathvariant=\"normal\">e</mi></mrow><mrow><mi mathvariant=\"normal\">l</mi><mi mathvariant=\"normal\">n</mi><mfrac><mrow><mn>1</mn></mrow><mrow><mi>y</mi></mrow></mfrac></mrow></msup></math>",
|
||
"x10" : "<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\"><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msubsup><mrow><mi mathvariant=\"normal\">C</mi></mrow><mrow><mn>6</mn></mrow><mrow><mi>r</mi></mrow></msubsup><msup><mrow><mn>2</mn></mrow><mrow><mn>6</mn><mo>-</mo><mi>r</mi></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><mn>6</mn><mo>-</mo><mfrac><mrow><mn>3</mn><mi>r</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math>",
|
||
"x11" : "<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\"><mi>P</mi><mo>(</mo><mover accent=\"false\"><mrow><mi>B</mi></mrow><mo>¯</mo></mover><mo>|</mo><mi>A</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>P</mi><mo>(</mo><mover accent=\"false\"><mrow><mi>B</mi></mrow><mo>¯</mo></mover><mo>)</mo><mi>P</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><mi>P</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mi>P</mi><mo>(</mo><mover accent=\"false\"><mrow><mi>B</mi></mrow><mo>¯</mo></mover><mo>)</mo><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math>",
|
||
"x12" : "<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\"><msub><mrow><mi>T</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msubsup><mrow><mi mathvariant=\"normal\">C</mi></mrow><mrow><mn>8</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><mn>2</mn><mi>x</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>8</mn><mo>-</mo><mi>r</mi></mrow></msup><mo>(</mo><mo>-</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></mfrac><msup><mrow><mo>)</mo></mrow><mrow><mi>r</mi></mrow></msup><mo>=</mo><mo>(</mo><mo>-</mo><mi>a</mi><msup><mrow><mo>)</mo></mrow><mrow><mi>r</mi></mrow></msup><msup><mrow><mn>2</mn></mrow><mrow><mn>8</mn><mo>-</mo><mi>r</mi></mrow></msup><msubsup><mrow><mi mathvariant=\"normal\">C</mi></mrow><mrow><mn>8</mn></mrow><mrow><mi>r</mi></mrow></msubsup><msup><mrow><mi>x</mi></mrow><mrow><mn>8</mn><mo>-</mo><mn>2</mn><mi>r</mi></mrow></msup></math>",
|
||
"x13" : "<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\" xmlns:m=\"http://schemas.openxmlformats.org/officeDocument/2006/math\"><msubsup><mrow><mi mathvariant=\"normal\">C</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>×</mo><mo>(</mo><mn>1</mn><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo><mo>×</mo><mo>(</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><msup><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mo>[</mo><mn>1</mn><mo>-</mo><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><msup><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>]</mo><mo>=</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>36</mn></mrow></mfrac></math>"
|
||
} |