init: WordFileParse docx→HTML 解析服务（含 Word EQ 域公式修复）
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
This commit is contained in:
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scripts/omml_mathml2latex/data/symbols.py
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scripts/omml_mathml2latex/data/symbols.py
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"""
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Unicode to LaTeX symbol mappings for OMML/MathML to LaTeX conversion.
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This module provides comprehensive Unicode symbol to LaTeX command mappings
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for mathematical notation, chemical symbols, and special characters.
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Architecture
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============
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This module defines three primary dictionaries that work together to handle
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symbol conversion with MathJax compatibility:
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1. UNICODE_TO_LATEX (dict[str, str])
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- Maps Unicode symbols → LaTeX commands
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- Used for symbols that SHOULD be converted to LaTeX
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- Contains ~430 symbol mappings organized by category:
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* Greek letters (lowercase and uppercase)
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* Mathematical operators and relations
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* Arrows and directional symbols
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* Set theory and logic symbols
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* Calculus and analysis symbols (basic integrals)
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* Chemistry symbols and arrows
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* Geometric shapes and special characters
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2. UNICODE_PASSTHROUGH (set[str])
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- Unicode symbols that should NEVER be converted to LaTeX
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- These symbols are kept as-is for MathJax compatibility
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- Contains ~64 advanced mathematical symbols whose LaTeX commands
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are not supported or render poorly in MathJax
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- Examples: advanced integrals (∯, ∰), special operators (⊛, ⊚)
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- IMPORTANT: Symbols in this set are NOT in UNICODE_TO_LATEX
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3. MATHJAX_UNSUPPORTED_TO_UNICODE (dict[str, str])
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- Inverse of UNICODE_PASSTHROUGH: LaTeX command → Unicode
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- Used in post-processing to convert unsupported LaTeX back to Unicode
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- Should be exact inverse of symbols in UNICODE_PASSTHROUGH
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Conversion Flow
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===============
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Input Unicode Symbol
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↓
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Is it in UNICODE_PASSTHROUGH?
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├─ YES → Keep as Unicode (don't convert)
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└─ NO → Look up in UNICODE_TO_LATEX
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↓
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Convert to LaTeX command
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↓
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Post-process: If command in MATHJAX_UNSUPPORTED_TO_UNICODE
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↓
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Convert back to Unicode for MathJax rendering
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Design Principles
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=================
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1. **No Overlap**: Symbols should be in EITHER UNICODE_TO_LATEX OR
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UNICODE_PASSTHROUGH, never both.
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2. **Consistency**: MATHJAX_UNSUPPORTED_TO_UNICODE values must exactly
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match UNICODE_PASSTHROUGH contents (they are inverses).
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3. **Inverse Mapping**: For any symbol in UNICODE_PASSTHROUGH, if there
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exists a LaTeX command in MATHJAX_UNSUPPORTED_TO_UNICODE, the command
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names must be consistent.
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4. **Special Patterns**:
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- Empty braces ({}) only for radical symbols (√, ∛, ∜)
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- Placeholders (__DDOT__, __DDDOT__) only for accent detection
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- Regional preferences handled separately (see REGIONAL_SYMBOL_PREFERENCES)
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Testing
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=======
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Symbol dictionary integrity is validated by:
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- tests/test_symbol_dictionaries.py
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This test suite ensures:
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- No duplicate keys in any dictionary
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- No overlap between UNICODE_TO_LATEX and UNICODE_PASSTHROUGH
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- Consistency between MATHJAX_UNSUPPORTED and UNICODE_PASSTHROUGH
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- Valid mappings and inverse consistency
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"""
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# Centralized symbol mappings to eliminate duplication
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UNICODE_TO_LATEX = {
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# Greek letters (lowercase)
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"α": "\\alpha", "β": "\\beta", "γ": "\\gamma", "δ": "\\delta",
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"ε": "\\varepsilon", "ζ": "\\zeta", "η": "\\eta", "θ": "\\theta",
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"ι": "\\iota", "κ": "\\kappa", "λ": "\\lambda", "μ": "\\mu",
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"ν": "\\nu", "ξ": "\\xi", "ο": "\\omicron", "π": "\\pi",
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"ρ": "\\rho", "σ": "\\sigma", "τ": "\\tau", "υ": "\\upsilon",
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"φ": "\\varphi", "χ": "\\chi", "ψ": "\\psi", "ω": "\\omega",
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"ϵ": "\\epsilon", "ϑ": "\\vartheta", "ϕ": "\\phi", "ϱ": "\\varrho",
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"ϖ": "\\varpi", "ς": "\\varsigma", "ϰ": "\\varkappa",
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# Greek letters (uppercase)
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"Α": "A", "Β": "B", "Γ": "\\Gamma", "Δ": "\\Delta",
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"Ε": "E", "Ζ": "Z", "Η": "H", "Θ": "\\Theta",
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"Ι": "I", "Κ": "K", "Λ": "\\Lambda", "Μ": "M",
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"Ν": "N", "Ξ": "\\Xi", "Ο": "O", "Π": "\\Pi",
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"Ρ": "P", "Σ": "\\Sigma", "Τ": "T", "Υ": "\\Upsilon",
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"Φ": "\\Phi", "Χ": "X", "Ψ": "\\Psi", "Ω": "\\Omega",
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# Mathematical constants and special symbols
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"∞": "\\infty", "∅": "\\emptyset", "∇": "\\nabla", "∂": "\\partial",
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"ℏ": "\\hbar", "ℓ": "\\ell", "∠": "\\angle", "∁": "\\complement",
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"℘": "\\wp", "ℵ": "\\aleph", "℧": "\\mho",
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# Geometric symbols
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"△": "\\triangle", "▲": "\\blacktriangle", "▽": "\\triangledown",
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"◁": "\\triangleleft", "▷": "\\triangleright", "◀": "\\blacktriangleleft",
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"▶": "\\blacktriangleright",
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# Square symbols (comprehensive coverage)
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"□": "\\square", # U+25A1 WHITE SQUARE
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"■": "\\blacksquare", # U+25A0 BLACK SQUARE
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"▪": "\\blacksquare", # U+25AA BLACK SMALL SQUARE
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"▫": "\\square", # U+25AB WHITE SMALL SQUARE
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"◻": "\\square", # U+25FB WHITE MEDIUM SQUARE
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"◼": "\\blacksquare", # U+25FC BLACK MEDIUM SQUARE
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"◽": "\\square", # U+25FD WHITE MEDIUM SMALL SQUARE
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"◾": "\\blacksquare", # U+25FE BLACK MEDIUM SMALL SQUARE
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# Other geometric shapes
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# NOTE: ▱ (parallelogram) is in UNICODE_PASSTHROUGH
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"◇": "\\diamond", "◆": "\\blacklozenge", "○": "\\circ", "●": "\\bullet",
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"☆": "\\star", "★": "\\bigstar", "◯": "\\bigcirc",
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# Temperature symbols
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"℃": "^\\circ\\mathrm{C}", "℉": "^\\circ\\mathrm{F}",
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# Basic operators and punctuation
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"∶": ":", # U+2236 RATIO to colon for assignment operators
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"§": "\\S", "†": "\\dagger", "‵": "\\backprime",
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"`": "\\backprime", # U+0060 GRAVE ACCENT (backtick) used as backprime in equations
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"―": "\\textemdash", # U+2015 horizontal bar
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# Multiplication and division
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"×": "\\times", "⋅": "\\cdot", "·": "\\cdot", "÷": "\\div", "∕": "/", "⁄": "/",
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"//": "/ /", # Double slash with spacing
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"⧸": "/", # U+29F8 BIG SOLIDUS (used in \not patterns but also standalone)
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# Mathematical script letters
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"ℑ": "\\Im", # Imaginary part (Fraktur I)
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"ℜ": "\\Re", # Real part (Fraktur R)
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# Arrows (basic)
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"→": "\\rightarrow", "←": "\\leftarrow", "↔": "\\leftrightarrow",
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"⇒": "\\Longrightarrow", "⇐": "\\Longleftarrow", "⇔": "\\Longleftrightarrow",
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"⟹": "\\Longrightarrow", "⟸": "\\Longleftarrow", "⟺": "\\Longleftrightarrow",
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"⟷": "\\longleftrightarrow",
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"↑": "\\uparrow", "↓": "\\downarrow", "⇑": "\\Uparrow", "⇓": "\\Downarrow",
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"↕": "\\updownarrow", "⇕": "\\Updownarrow",
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# Arrows (diagonal)
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"↗": "\\nearrow", "↘": "\\searrow", "↙": "\\swarrow", "↖": "\\nwarrow",
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"⤴": "\\nwarrow", "⤵": "\\searrow", "⤡": "\\swarrow", "⤢": "\\nearrow",
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# Arrows (special forms)
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# NOTE: Some special arrows (↤ mapsfrom, ⟻ longmapsfrom, ⇜ leftsquigarrow, ⇝ rightsquigarrow) are in UNICODE_PASSTHROUGH
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"↦": "\\mapsto",
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"⟼": "\\longmapsto",
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"↪": "\\hookrightarrow", "↩": "\\hookleftarrow",
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"⤷": "\\hookrightarrow", "⤶": "\\hookleftarrow",
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"↬": "\\looparrowright", "↫": "\\looparrowleft",
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"⇀": "\\rightharpoonup", "↼": "\\leftharpoonup",
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"↢": "\\leftarrowtail", "↣": "\\rightarrowtail",
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"↰": "\\Lsh", "↱": "\\Rsh",
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# Arrows (negated)
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"↛": "\\nrightarrow", "↚": "\\nleftarrow", "⇏": "\\nRightarrow", "⇍": "\\nLeftarrow",
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"↮": "\\nleftrightarrow", "⇎": "\\nLeftrightarrow",
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# Set theory and logic
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# Set membership
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"∈": "\\in", "∉": "\\notin", "∋": "\\ni", "∌": "\\notni",
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"⋲": "\\in", "⋳": "\\ni", "⋴": "\\in", "⋵": "\\ni",
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"⋶": "\\in", "⋷": "\\ni", "⋸": "\\pitchfork", "⋹": "\\ltimes",
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# Subset and superset relations (basic)
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"⊂": "\\subset", "⊃": "\\supset",
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"⊆": "\\subseteq", "⊇": "\\supseteq",
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"⊄": "\\not\\subset", "⊅": "\\not\\supset",
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"⊈": "\\nsubseteq", "⊉": "\\nsupseteq",
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"⊊": "\\subsetneq", "⊋": "\\supsetneq",
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# Subset and superset relations (extended with double lines)
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"⫅": "\\subseteqq", "⫆": "\\supseteqq", # U+2AC5, U+2AC6 subset/supset with double equals
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"⫋": "\\subsetneqq", "⫌": "\\supsetneqq", # U+2ACB, U+2ACC not equal variant with double
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"⫏": "\\sqsubset", "⫐": "\\sqsupset", # U+2ACF, U+2AD0 square subset/supset
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"⫑": "\\sqsubseteq", "⫒": "\\sqsupseteq", # U+2AD1, U+2AD2 square subset/supset equal
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"⊏": "\\sqsubset", "⊐": "\\sqsupset", # U+228F, U+2290 square variants
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"⊑": "\\sqsubseteq", "⊒": "\\sqsupseteq", # U+2291, U+2292 square equal variants
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# Set operations
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# NOTE: Some symbols like ⊌ (dotcup), ⊍ (cupdot) are in UNICODE_PASSTHROUGH
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"∪": "\\cup", "∩": "\\cap", "∖": "\\setminus",
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"⊎": "\\uplus", "⊔": "\\sqcup", "⊓": "\\sqcap",
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"⨃": "\\Cup", "⨄": "\\biguplus", "⨅": "\\bigsqcap", "⨆": "\\bigsqcup",
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"⩁": "\\Cup", "⩂": "\\Cap", "⩃": "\\cupdot",
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# Logical operators
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"∧": "\\wedge", "∨": "\\vee", "¬": "\\neg", "⊕": "\\oplus",
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"⊗": "\\otimes", "⊙": "\\odot", "⊖": "\\ominus", "⊘": "\\oslash",
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"∀": "\\forall", "∃": "\\exists", "∄": "\\nexists",
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"⊤": "\\top", "⊥": "\\perp", "⊢": "\\vdash", "⊣": "\\dashv",
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"⊨": "\\models", "⊭": "\\not\\models",
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"∴": "\\therefore", "∵": "\\because",
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"⋏": "\\curlywedge", "⋎": "\\curlyvee",
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# Additional logical symbols
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"⊩": "\\Vdash", "⊪": "\\Vvdash", "⊫": "\\VDash", "⊬": "\\nvdash",
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"⊯": "\\nVdash", "⊮": "\\nVDash", "∎": "\\qed", "◊": "\\lozenge",
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"≐": "\\doteq", "≑": "\\doteqdot", "≒": "\\fallingdotseq", "≓": "\\risingdotseq",
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# Relations
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# Equality and equivalence
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"≈": "\\approx", "≅": "\\cong", "≡": "\\equiv", "≢": "\\not\\equiv",
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"≠": "\\neq", "≁": "\\not\\sim", "≄": "\\nsim", "≇": "\\ncong",
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"~": "\\sim", # ASCII tilde (U+007E) - similarity operator
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"∼": "\\sim", "≃": "\\simeq", "≂": "\\eqsim", "≊": "\\approxeq",
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# Inequality relations (basic)
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# NOTE: Triple relations ⋘ (lll), ⋙ (ggg) are in UNICODE_PASSTHROUGH
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"≤": "\\leqslant", "≥": "\\geqslant", "≮": "\\nless", "≯": "\\ngtr",
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"≰": "\\nleq", "≱": "\\ngeq", "≪": "\\ll", "≫": "\\gg",
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# Inequality relations (extended)
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"≦": "\\leqq", "≧": "\\geqq", "≨": "\\lneqq", "≩": "\\gneqq",
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"⩽": "\\leqslant", "⩾": "\\geqslant", "⩿": "\\gneq",
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"≶": "\\lessgtr", "≷": "\\gtrless", "≸": "\\not\\lessgtr", "≹": "\\not\\gtrless",
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# NOTE: Advanced comparison symbols (⪋ lesseqgtr, ⪌ gtreqless, ⪅ lessapprox, etc.) are in UNICODE_PASSTHROUGH
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"⪇": "\\lneq", "⪈": "\\gneq",
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# Precedence and succession
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# NOTE: Advanced precedence symbols (⋞ curlyeqprec, ⋟ curlyeqsucc, ⪷ precapprox, ⪸ succapprox) are in UNICODE_PASSTHROUGH
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"≺": "\\prec", "≻": "\\succ", "⪯": "\\preceq", "⪰": "\\succeq",
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"⪳": "\\preceqq", "⪴": "\\succeqq",
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"⪵": "\\precneqq", "⪶": "\\succneqq",
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# Similarity and comparison
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"≲": "\\lesssim", "≳": "\\gtrsim", "≴": "\\not\\lesssim", "≵": "\\not\\gtrsim",
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"∝": "\\propto", "∥": "\\parallel", "∦": "\\nparallel",
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"≍": "\\asymp", "≎": "\\Bumpeq", "≏": "\\bumpeq",
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"∽": "\\backsim", "⋍": "\\backsimeq", # U+22CD REVERSED TILDE EQUALS
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"≌": "\\cong", # U+224C ALL EQUAL TO (commonly used for congruence)
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"⊲": "\\lhd", "⊳": "\\rhd",
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"⌢": "\\frown", "⌣": "\\smile",
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# Special equality symbols
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# NOTE: Some special equality symbols (≔ coloneqq, ≕ eqqcolon, ≘ arceq, ≙ wedgeq, ≚ veeeq) are in UNICODE_PASSTHROUGH
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"≜": "\\triangleq", "≝": "\\overset{\\mathrm{def}}{=}", "≞": "\\overset{\\mathrm{m}}{=}",
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"≟": "\\overset{?}{=}", "≗": "\\circeq", "≖": "\\eqcirc",
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# Calculus and analysis
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# Integrals
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# NOTE: Many advanced integral symbols (∯, ∰, ∱, etc.) are in UNICODE_PASSTHROUGH
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# for direct MathJax rendering, so they are NOT listed here
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"∫": "\\int", "∬": "\\iint", "∭": "\\iiint", "⨌": "\\iiiint",
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"∮": "\\oint",
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# Differentials and operators
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"∆": "\\Delta", "∂": "\\partial", "∇": "\\nabla",
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"∝": "\\propto", "∞": "\\infty",
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# Cardinality symbols
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# NOTE: Hebrew letters ℶ (beth), ℷ (gimel), ℸ (daleth) are in UNICODE_PASSTHROUGH
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"ℵ": "\\aleph",
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# Number sets (use \mathbb for blackboard bold notation)
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"ℕ": "\\mathbb{N}", "ℤ": "\\mathbb{Z}", "ℚ": "\\mathbb{Q}",
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"ℝ": "\\mathbb{R}", "ℂ": "\\mathbb{C}", "ℍ": "\\mathbb{H}",
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"ℙ": "\\mathbb{P}", "𝔽": "\\mathbb{F}", "𝔾": "\\mathbb{G}",
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# Special operators
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# Basic arithmetic operators
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"±": "\\pm", "∓": "\\mp", "−": "-", "∔": "\\dotplus",
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# Binary operators (algebraic)
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"⋆": "\\star", "∗": "\\ast", "∘": "\\circ", "∙": "\\bullet",
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"⋄": "\\diamond", "⋅": "\\cdot", "•": "\\bullet",
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# Binary operators (lattice and semilattice)
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# NOTE: ⊌ (dotcup), ⊍ (cupdot) are in UNICODE_PASSTHROUGH
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"⊔": "\\sqcup", "⊓": "\\sqcap", "⊎": "\\uplus",
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# Binary operators (group theory)
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# NOTE: Some group theory operators (⋋ leftthreetimes, ⋌ rightthreetimes, ⋇ divideontimes) are in UNICODE_PASSTHROUGH
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"⋉": "\\ltimes", "⋊": "\\rtimes",
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"⨿": "\\amalg", "⋈": "\\bowtie",
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# Binary operators (wreath and semidirect products)
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"≀": "\\wr", "⊺": "\\intercal", "⊻": "\\veebar",
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# Binary operators (extended)
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# NOTE: Advanced box operators (⧄ boxbox, ⧅ boxast, ⧆ boxcirc, ⧇ boxbslash, ⧈ boxslash) are in UNICODE_PASSTHROUGH
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"⊝": "\\ominus", "⊞": "\\boxplus", "⊟": "\\boxminus", "⊠": "\\boxtimes",
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"⊡": "\\boxdot",
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# Big operators
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"∑": "\\sum", "∏": "\\prod", "∐": "\\coprod", "⋃": "\\bigcup",
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"⋂": "\\bigcap", "⋁": "\\bigvee", "⋀": "\\bigwedge", "⨁": "\\bigoplus",
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"⨂": "\\bigotimes", "⨄": "\\biguplus", "⨅": "\\bigsqcap", "⨆": "\\bigsqcup",
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# Delimiters and brackets
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# Angle brackets
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"⟨": "\\langle", "⟩": "\\rangle", "⟪": "\\langle\\langle", "⟫": "\\rangle\\rangle",
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"〈": "\\langle", "〉": "\\rangle", # CJK angle brackets
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# Floor and ceiling
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"⌊": "\\lfloor", "⌋": "\\rfloor", "⌈": "\\lceil", "⌉": "\\rceil",
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# Special brackets
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# NOTE: Some special brackets (⦅ llparenthesis, ⦆ rrparenthesis, 〚 llbracket, 〛 rrbracket, ⦉ Langle, ⦊ Rangle) are in UNICODE_PASSTHROUGH
|
||||
"⦃": "\\{", "⦄": "\\}",
|
||||
"⟦": "[\\![", "⟧": "]\\!]", "⟬": "\\llbracket", "⟭": "\\rrbracket",
|
||||
"⦇": "\\llparenthesis", "⦈": "\\rrparenthesis",
|
||||
|
||||
# Absolute value and norm
|
||||
"|": "|", "‖": "\\|", "∥": "\\parallel", # ‖ (U+2016) is double vertical line for norms → \|
|
||||
|
||||
# Miscellaneous symbols
|
||||
# NOTE: Radical symbols must include {} braces for valid LaTeX
|
||||
# Users may type these directly as text (malformed input), so we ensure valid output
|
||||
"√": "\\sqrt{}", "∛": "\\sqrt[3]{}", "∜": "\\sqrt[4]{}",
|
||||
"∡": "\\measuredangle", "∢": "\\sphericalangle", "°": "^\\circ",
|
||||
# Prime notation - both Unicode primes and ASCII apostrophe (commonly used in Word)
|
||||
"'": "\\prime", # ASCII apostrophe (U+0027) - commonly typed instead of Unicode prime
|
||||
"′": "\\prime", "″": "\\prime\\prime", "‴": "\\prime\\prime\\prime", "⁗": "\\prime\\prime\\prime\\prime",
|
||||
"℮": "e", "ℯ": "e", "ⅈ": "i", "ⅉ": "j",
|
||||
# NOTE: ⋰ (iddots) is in UNICODE_PASSTHROUGH
|
||||
"…": "\\ldots", "⋯": "\\cdots", "⋮": "\\vdots", "⋱": "\\ddots",
|
||||
"♭": "\\flat", "♮": "\\natural", "♯": "\\sharp",
|
||||
|
||||
# Fullwidth punctuation (CJK)
|
||||
"，": ", ", # U+FF0C fullwidth comma (Chinese comma) → regular comma with space
|
||||
|
||||
# Accent marks (for detection in mover elements)
|
||||
"¨": "__DDOT__", # U+00A8 diaeresis (standalone) - placeholder for ddot detection
|
||||
"⃛": "__DDDOT__", # U+20DB combining three dots above - placeholder for dddot detection
|
||||
"̈": "__DDOT__", # U+0308 combining diaeresis - placeholder for ddot detection
|
||||
"⃛": "__DDDOT__", # U+20DB combining triple dot above - placeholder for dddot detection
|
||||
|
||||
# Chemistry arrows and symbols (harpoons)
|
||||
"⇌": "\\rightleftharpoons", # U+21CC rightleftharpoons (equilibrium)
|
||||
"⇋": "\\leftrightharpoons", # U+21CB leftrightharpoons (equilibrium reversed)
|
||||
"⇀": "\\rightharpoonup", # U+21C0 rightharpoonup
|
||||
"⇁": "\\rightharpoondown", # U+21C1 rightharpoondown
|
||||
"↼": "\\leftharpoonup", # U+21BC leftharpoonup
|
||||
"↽": "\\leftharpoondown", # U+21BD leftharpoondown
|
||||
"⥂": "\\rightleftharpoons", # U+2942 alternate form
|
||||
"⥃": "\\leftrightharpoons", # U+2943 alternate form
|
||||
"⥄": "\\rightleftarrows", # U+2944 right over left arrows
|
||||
"⥅": "\\leftrightarrows", # U+2945 left over right arrows
|
||||
"⥆": "\\rightleftarrows", # U+2946 right over left arrows
|
||||
"⥇": "\\leftrightarrows", # U+2947 left over right arrows
|
||||
"⇄": "\\rightleftarrows", # U+21C4 right over left (already in extended arrows)
|
||||
"⇆": "\\leftrightarrows", # U+21C6 left over right (already in extended arrows)
|
||||
"⇉": "\\rightrightarrows", # U+21C9 double right (already in extended arrows)
|
||||
"⇇": "\\leftleftarrows", # U+21C7 double left (already in extended arrows)
|
||||
|
||||
# Overbrace and underbrace characters
|
||||
"⏞": "\\overbrace", "⏟": "\\underbrace",
|
||||
|
||||
# Extended mathematical operators (remaining unique ones)
|
||||
# NOTE: ⊚ (ocirc), ⊛ (oast) are in UNICODE_PASSTHROUGH
|
||||
|
||||
# Extended relation symbols (remaining unique ones)
|
||||
# NOTE: Several special equality symbols (≔ coloneqq, ≕ eqqcolon, ≘ arceq, ≙ wedgeq, ≚ veeeq) are in UNICODE_PASSTHROUGH
|
||||
"≆": "\\approxeq", "≛": "\\triangleq",
|
||||
|
||||
# Extended arrows (remaining unique ones)
|
||||
"⇈": "\\upuparrows", "⇊": "\\downdownarrows",
|
||||
"⇅": "\\updownarrows", "⇵": "\\downuparrows", "↶": "\\curvearrowleft",
|
||||
"↷": "\\curvearrowright", "↺": "\\circlearrowleft", "↻": "\\circlearrowright",
|
||||
|
||||
# Extended logical symbols
|
||||
# NOTE: ⟀ (lozengeminus) is in UNICODE_PASSTHROUGH
|
||||
"⟁": "\\lozengepls", "⟂": "\\perp", "⟃": "\\between",
|
||||
"⟄": "\\pitchfork", "⟅": "\\varpropto", "⟆": "\\backprime", "⟇": "\\caretinsert",
|
||||
|
||||
# Extended geometric symbols
|
||||
"⟐": "\\angle", "⟑": "\\measuredangle", "⟒": "\\sphericalangle", "⟓": "\\rightangle",
|
||||
"⟔": "\\angle", "⟕": "\\measuredangle", "⟖": "\\sphericalangle", "⟗": "\\rightangle",
|
||||
|
||||
# Extended miscellaneous symbols
|
||||
"⟘": "\\perp", "⟙": "\\diamondsuit", "⟚": "\\heartsuit", "⟛": "\\clubsuit",
|
||||
"⟜": "\\spadesuit", "⟝": "\\varnothing", "⟞": "\\diameter", "⟟": "\\house",
|
||||
}
|
||||
|
||||
# Additional Symbol Replacements (Consolidated from scattered code)
|
||||
# ========================================================================
|
||||
|
||||
# These symbols are used in specific contexts (e.g., function subscripts)
|
||||
# and should be applied consistently across the codebase
|
||||
ADDITIONAL_SYMBOL_REPLACEMENTS = {
|
||||
# Arrows used in function subscripts (line 1828)
|
||||
'→': '\\to ',
|
||||
|
||||
# These are handled in UNICODE_TO_LATEX but kept for reference in subscript context
|
||||
# '∞': '\\infty', # Already in UNICODE_TO_LATEX
|
||||
# '≤': '\\leqslant ', # Already in UNICODE_TO_LATEX
|
||||
# '≥': '\\geqslant ', # Already in UNICODE_TO_LATEX
|
||||
# '≠': '\\ne ', # Already in UNICODE_TO_LATEX as \\neq
|
||||
# '±': '\\pm ', # Already in UNICODE_TO_LATEX
|
||||
}
|
||||
|
||||
# LaTeX command normalization (converting between command variants)
|
||||
LATEX_COMMAND_REPLACEMENTS = {
|
||||
# Logical equivalence (line 5545)
|
||||
'\\Longleftrightarrow': '\\iff ',
|
||||
|
||||
# Arrow shorthand (line 5548)
|
||||
'\\lra': '\\leftrightarrow',
|
||||
|
||||
}
|
||||
|
||||
# Summation symbols for OMML fallback parser
|
||||
SUMMATION_SYMBOLS = {
|
||||
'∑': 'sum',
|
||||
'∏': 'prod',
|
||||
'∫': 'integral',
|
||||
'Σ': 'sum',
|
||||
'Π': 'prod'
|
||||
}
|
||||
|
||||
# LaTeX commands not supported by MathJax - use Unicode fallback
|
||||
# Maps LaTeX command (without backslash) to Unicode character
|
||||
# This comprehensive list ensures proper rendering in MathJax environments
|
||||
MATHJAX_UNSUPPORTED_TO_UNICODE = {
|
||||
# =========================================================================
|
||||
# INTEGRAL OPERATORS - Many not in standard MathJax
|
||||
# =========================================================================
|
||||
# Surface and volume integrals
|
||||
'oiint': '∯', # U+222F SURFACE INTEGRAL
|
||||
'oiiint': '∰', # U+2230 VOLUME INTEGRAL
|
||||
# Clockwise/counterclockwise integrals - NOT in MathJax
|
||||
'intclockwise': '∱', # U+2231 CLOCKWISE INTEGRAL
|
||||
'varointclockwise': '∲', # U+2232 CLOCKWISE CONTOUR INTEGRAL
|
||||
'varointctrclockwise': '∳', # U+2233 ANTICLOCKWISE CONTOUR INTEGRAL
|
||||
# Extended integrals - limited MathJax support
|
||||
'fint': '⨍', # U+2A0D FINITE PART INTEGRAL
|
||||
'pointint': '⨎', # U+2A0E PATH INTEGRAL (line integral)
|
||||
'sqint': '⨏', # U+2A0F INTEGRAL WITH SQUARED OPERATOR
|
||||
'intlarhk': '⨐', # U+2A10 CIRCULATION FUNCTION
|
||||
'intbar': '⨑', # U+2A11 INTEGRAL WITH OVERBAR
|
||||
'intBar': '⨒', # U+2A12 INTEGRAL WITH DOUBLE OVERBAR
|
||||
'fintbar': '⨓', # U+2A13 FINITE PART INTEGRAL WITH OVERBAR
|
||||
'ointbar': '⨔', # U+2A14 CONTOUR INTEGRAL WITH OVERBAR
|
||||
'ointBar': '⨕', # U+2A15 CONTOUR INTEGRAL WITH DOUBLE OVERBAR
|
||||
'oiintbar': '⨖', # U+2A16 SURFACE INTEGRAL WITH OVERBAR
|
||||
'oiintBar': '⨗', # U+2A17 SURFACE INTEGRAL WITH DOUBLE OVERBAR
|
||||
|
||||
# =========================================================================
|
||||
# BINARY OPERATORS - Non-standard or limited support
|
||||
# =========================================================================
|
||||
# Division operator
|
||||
'divideontimes': '⋇', # U+22C7 DIVISION TIMES
|
||||
# Circle operators - non-standard names
|
||||
'oast': '⊛', # U+229B CIRCLED ASTERISK OPERATOR
|
||||
'ocirc': '⊚', # U+229A CIRCLED RING OPERATOR
|
||||
# Box operators - extended (standard ones like boxplus ARE supported)
|
||||
'boxbox': '⧄', # U+29C4 SQUARED SQUARE
|
||||
'boxast': '⧅', # U+29C5 SQUARED ASTERISK
|
||||
'boxcirc': '⧆', # U+29C6 SQUARED SMALL CIRCLE
|
||||
'boxbslash': '⧇', # U+29C7 SQUARED BACKSLASH
|
||||
'boxslash': '⧈', # U+29C8 SQUARED SLASH
|
||||
# Semidirect products
|
||||
'leftthreetimes': '⋋', # U+22CB LEFT SEMIDIRECT PRODUCT
|
||||
'rightthreetimes': '⋌', # U+22CC RIGHT SEMIDIRECT PRODUCT
|
||||
# Set operations with dot
|
||||
'dotcup': '⊌', # U+228C MULTISET
|
||||
'cupdot': '⊍', # U+228D MULTISET MULTIPLICATION
|
||||
|
||||
# =========================================================================
|
||||
# ARROWS - Extended arrows with limited MathJax support
|
||||
# =========================================================================
|
||||
'mapsfrom': '↤', # U+21A4 LEFTWARDS ARROW FROM BAR
|
||||
'longmapsfrom': '⟻', # U+27FB LONG LEFTWARDS ARROW FROM BAR
|
||||
'leftsquigarrow': '⇜', # U+21DC LEFTWARDS SQUIGGLE ARROW
|
||||
'rightsquigarrow': '⇝', # U+21DD RIGHTWARDS SQUIGGLE ARROW
|
||||
# 'looparrowleft': '↫', # U+21AB LEFTWARDS ARROW WITH LOOP
|
||||
# 'looparrowright': '↬', # U+21AC RIGHTWARDS ARROW WITH LOOP
|
||||
# 'leftarrowtail': '↢', # U+21A2 LEFTWARDS ARROW WITH TAIL
|
||||
# 'rightarrowtail': '↣', # U+21A3 RIGHTWARDS ARROW WITH TAIL
|
||||
# 'Lsh': '↰', # U+21B0 UPWARDS ARROW WITH TIP LEFTWARDS
|
||||
# 'Rsh': '↱', # U+21B1 UPWARDS ARROW WITH TIP RIGHTWARDS
|
||||
# 'curvearrowleft': '↶', # U+21B6 ANTICLOCKWISE TOP SEMICIRCLE ARROW
|
||||
# 'curvearrowright': '↷', # U+21B7 CLOCKWISE TOP SEMICIRCLE ARROW
|
||||
# 'circlearrowleft': '↺', # U+21BA ANTICLOCKWISE OPEN CIRCLE ARROW
|
||||
# 'circlearrowright': '↻', # U+21BB CLOCKWISE OPEN CIRCLE ARROW
|
||||
# 'upuparrows': '⇈', # U+21C8 UPWARDS PAIRED ARROWS
|
||||
# 'downdownarrows': '⇊', # U+21CA DOWNWARDS PAIRED ARROWS
|
||||
# 'updownarrows': '⇅', # U+21C5 UPWARDS ARROW LEFTWARDS OF DOWNWARDS
|
||||
# 'downuparrows': '⇵', # U+21F5 DOWNWARDS ARROW LEFTWARDS OF UPWARDS
|
||||
|
||||
# =========================================================================
|
||||
# RELATION SYMBOLS - Extended relations
|
||||
# =========================================================================
|
||||
# Triple comparisons
|
||||
'lll': '⋘', # U+22D8 VERY MUCH LESS-THAN
|
||||
'ggg': '⋙', # U+22D9 VERY MUCH GREATER-THAN
|
||||
# Combined relations
|
||||
'lesseqgtr': '⪋', # U+2A8B LESS-THAN EQUAL TO OR GREATER-THAN
|
||||
'gtreqless': '⪌', # U+2A8C GREATER-THAN EQUAL TO OR LESS-THAN
|
||||
'lessapprox': '⪅', # U+2A85 LESS-THAN OR APPROXIMATE
|
||||
'gtrapprox': '⪆', # U+2A86 GREATER-THAN OR APPROXIMATE
|
||||
'lnapprox': '⪉', # U+2A89 LESS-THAN AND NOT APPROXIMATE
|
||||
'gnapprox': '⪊', # U+2A8A GREATER-THAN AND NOT APPROXIMATE
|
||||
# Precedence relations
|
||||
'precapprox': '⪷', # U+2AB7 PRECEDES ABOVE ALMOST EQUAL TO
|
||||
'succapprox': '⪸', # U+2AB8 SUCCEEDS ABOVE ALMOST EQUAL TO
|
||||
'curlyeqprec': '⋞', # U+22DE EQUAL TO OR PRECEDES
|
||||
'curlyeqsucc': '⋟', # U+22DF EQUAL TO OR SUCCEEDS
|
||||
# Similarity relations
|
||||
# 'backsim': '∽', # U+223D REVERSED TILDE
|
||||
# 'backsimeq': '⋍', # U+22CD REVERSED TILDE EQUALS
|
||||
# Special equality symbols
|
||||
'wedgeq': '≙', # U+2259 ESTIMATES (wedge equals)
|
||||
'veeeq': '≚', # U+225A EQUIANGULAR TO
|
||||
'arceq': '≘', # U+2258 CORRESPONDS TO
|
||||
'coloneqq': '≔', # U+2254 COLON EQUALS
|
||||
'eqqcolon': '≕', # U+2255 EQUALS COLON
|
||||
'Coloneqq': '⩴', # U+2A74 DOUBLE COLON EQUAL
|
||||
'eqcolon': '∹', # U+2239 EXCESS (-:)
|
||||
|
||||
# =========================================================================
|
||||
# BRACKET/DELIMITER SYMBOLS
|
||||
# =========================================================================
|
||||
'llbracket': '〚', # U+301A LEFT WHITE SQUARE BRACKET
|
||||
'rrbracket': '〛', # U+301B RIGHT WHITE SQUARE BRACKET
|
||||
'llparenthesis': '⦅', # U+2985 LEFT WHITE PARENTHESIS
|
||||
'rrparenthesis': '⦆', # U+2986 RIGHT WHITE PARENTHESIS
|
||||
'Langle': '⦉', # U+2989 Z NOTATION LEFT BINDING BRACKET
|
||||
'Rangle': '⦊', # U+298A Z NOTATION RIGHT BINDING BRACKET
|
||||
|
||||
# =========================================================================
|
||||
# GEOMETRIC AND MISCELLANEOUS SYMBOLS
|
||||
# =========================================================================
|
||||
'parallelogram': '▱', # U+25B1 WHITE PARALLELOGRAM
|
||||
'iddots': '⋰', # U+22F0 UP RIGHT DIAGONAL ELLIPSIS
|
||||
# 'mho': '℧', # U+2127 INVERTED OHM SIGN
|
||||
# 'complement': '∁', # U+2201 COMPLEMENT
|
||||
# Hebrew letters (beyond aleph)
|
||||
'beth': 'ℶ', # U+2136 BET SYMBOL
|
||||
'gimel': 'ℷ', # U+2137 GIMEL SYMBOL
|
||||
'daleth': 'ℸ', # U+2138 DALET SYMBOL
|
||||
|
||||
# =========================================================================
|
||||
# LOGICAL AND SET OPERATORS
|
||||
# =========================================================================
|
||||
# Extended subset/superset relations
|
||||
# 'subseteqq': '⫅', # U+2AC5 SUBSET OF ABOVE EQUALS SIGN
|
||||
# 'supseteqq': '⫆', # U+2AC6 SUPERSET OF ABOVE EQUALS SIGN
|
||||
# 'subsetneqq': '⫋', # U+2ACB SUBSET OF ABOVE NOT EQUAL TO
|
||||
# 'supsetneqq': '⫌', # U+2ACC SUPERSET OF ABOVE NOT EQUAL TO
|
||||
# Logic symbols
|
||||
'lozengeminus': '⟀', # U+27C0 THREE DIMENSIONAL ANGLE
|
||||
'between': '≬', # U+226C BETWEEN
|
||||
}
|
||||
|
||||
# Regional symbol preferences (e.g., Chinese region prefers varnothing over emptyset)
|
||||
# Maps standard LaTeX command to regional alternative
|
||||
REGIONAL_SYMBOL_PREFERENCES = {
|
||||
# Chinese region: prefer varnothing (⌀) over emptyset (∅)
|
||||
# varnothing has a diagonal line which is clearer in Chinese typography
|
||||
'emptyset': 'varnothing', # ∅ → ⌀
|
||||
}
|
||||
|
||||
# Unicode symbols that should be kept as-is (NOT converted to LaTeX)
|
||||
# These are symbols whose LaTeX commands are not supported or render poorly in MathJax.
|
||||
# By keeping them as Unicode, they render correctly using system fonts.
|
||||
# This set is the "inverse" of MATHJAX_UNSUPPORTED_TO_UNICODE - same symbols, different direction.
|
||||
UNICODE_PASSTHROUGH = {
|
||||
# =========================================================================
|
||||
# INTEGRAL OPERATORS - Keep as Unicode for MathJax compatibility
|
||||
# =========================================================================
|
||||
'∯', # U+222F SURFACE INTEGRAL (oiint)
|
||||
'∰', # U+2230 VOLUME INTEGRAL (oiiint)
|
||||
'∱', # U+2231 CLOCKWISE INTEGRAL (intclockwise)
|
||||
'∲', # U+2232 CLOCKWISE CONTOUR INTEGRAL (varointclockwise)
|
||||
'∳', # U+2233 ANTICLOCKWISE CONTOUR INTEGRAL (varointctrclockwise)
|
||||
'⨍', # U+2A0D FINITE PART INTEGRAL (fint)
|
||||
'⨎', # U+2A0E PATH INTEGRAL (pointint)
|
||||
'⨏', # U+2A0F INTEGRAL WITH SQUARED OPERATOR (sqint)
|
||||
'⨐', # U+2A10 CIRCULATION FUNCTION (intlarhk)
|
||||
'⨑', # U+2A11 INTEGRAL WITH OVERBAR (intbar)
|
||||
'⨒', # U+2A12 INTEGRAL WITH DOUBLE OVERBAR (intBar)
|
||||
'⨓', # U+2A13 FINITE PART INTEGRAL WITH OVERBAR (fintbar)
|
||||
'⨔', # U+2A14 CONTOUR INTEGRAL WITH OVERBAR (ointbar)
|
||||
'⨕', # U+2A15 CONTOUR INTEGRAL WITH DOUBLE OVERBAR (ointBar)
|
||||
'⨖', # U+2A16 SURFACE INTEGRAL WITH OVERBAR (oiintbar)
|
||||
'⨗', # U+2A17 SURFACE INTEGRAL WITH DOUBLE OVERBAR (oiintBar)
|
||||
|
||||
# =========================================================================
|
||||
# BINARY OPERATORS - Keep as Unicode
|
||||
# =========================================================================
|
||||
'⋇', # U+22C7 DIVISION TIMES (divideontimes)
|
||||
'⊛', # U+229B CIRCLED ASTERISK OPERATOR (oast)
|
||||
'⊚', # U+229A CIRCLED RING OPERATOR (ocirc)
|
||||
'⧄', # U+29C4 SQUARED SQUARE (boxbox)
|
||||
'⧅', # U+29C5 SQUARED ASTERISK (boxast)
|
||||
'⧆', # U+29C6 SQUARED SMALL CIRCLE (boxcirc)
|
||||
'⧇', # U+29C7 SQUARED BACKSLASH (boxbslash)
|
||||
'⧈', # U+29C8 SQUARED SLASH (boxslash)
|
||||
'⋋', # U+22CB LEFT SEMIDIRECT PRODUCT (leftthreetimes)
|
||||
'⋌', # U+22CC RIGHT SEMIDIRECT PRODUCT (rightthreetimes)
|
||||
'⊌', # U+228C MULTISET (dotcup)
|
||||
'⊍', # U+228D MULTISET MULTIPLICATION (cupdot)
|
||||
|
||||
# =========================================================================
|
||||
# ARROWS - Keep as Unicode for consistency
|
||||
# =========================================================================
|
||||
'↤', # U+21A4 LEFTWARDS ARROW FROM BAR (mapsfrom)
|
||||
'⟻', # U+27FB LONG LEFTWARDS ARROW FROM BAR (longmapsfrom)
|
||||
'⇜', # U+21DC LEFTWARDS SQUIGGLE ARROW (leftsquigarrow)
|
||||
'⇝', # U+21DD RIGHTWARDS SQUIGGLE ARROW (rightsquigarrow)
|
||||
# '↫', # U+21AB LEFTWARDS ARROW WITH LOOP (looparrowleft)
|
||||
# '↬', # U+21AC RIGHTWARDS ARROW WITH LOOP (looparrowright)
|
||||
# '↢', # U+21A2 LEFTWARDS ARROW WITH TAIL (leftarrowtail)
|
||||
# '↣', # U+21A3 RIGHTWARDS ARROW WITH TAIL (rightarrowtail)
|
||||
# '↰', # U+21B0 UPWARDS ARROW WITH TIP LEFTWARDS (Lsh)
|
||||
# '↱', # U+21B1 UPWARDS ARROW WITH TIP RIGHTWARDS (Rsh)
|
||||
# '↶', # U+21B6 ANTICLOCKWISE TOP SEMICIRCLE ARROW (curvearrowleft)
|
||||
# '↷', # U+21B7 CLOCKWISE TOP SEMICIRCLE ARROW (curvearrowright)
|
||||
# '↺', # U+21BA ANTICLOCKWISE OPEN CIRCLE ARROW (circlearrowleft)
|
||||
# '↻', # U+21BB CLOCKWISE OPEN CIRCLE ARROW (circlearrowright)
|
||||
# '⇈', # U+21C8 UPWARDS PAIRED ARROWS (upuparrows)
|
||||
# '⇊', # U+21CA DOWNWARDS PAIRED ARROWS (downdownarrows)
|
||||
# '⇅', # U+21C5 UPWARDS ARROW LEFTWARDS OF DOWNWARDS (updownarrows)
|
||||
# '⇵', # U+21F5 DOWNWARDS ARROW LEFTWARDS OF UPWARDS (downuparrows)
|
||||
|
||||
# =========================================================================
|
||||
# RELATION SYMBOLS - Keep as Unicode
|
||||
# =========================================================================
|
||||
'⋘', # U+22D8 VERY MUCH LESS-THAN (lll)
|
||||
'⋙', # U+22D9 VERY MUCH GREATER-THAN (ggg)
|
||||
'⪋', # U+2A8B LESS-THAN EQUAL TO OR GREATER-THAN (lesseqgtr)
|
||||
'⪌', # U+2A8C GREATER-THAN EQUAL TO OR LESS-THAN (gtreqless)
|
||||
'⪅', # U+2A85 LESS-THAN OR APPROXIMATE (lessapprox)
|
||||
'⪆', # U+2A86 GREATER-THAN OR APPROXIMATE (gtrapprox)
|
||||
'⪉', # U+2A89 LESS-THAN AND NOT APPROXIMATE (lnapprox)
|
||||
'⪊', # U+2A8A GREATER-THAN AND NOT APPROXIMATE (gnapprox)
|
||||
'⪷', # U+2AB7 PRECEDES ABOVE ALMOST EQUAL TO (precapprox)
|
||||
'⪸', # U+2AB8 SUCCEEDS ABOVE ALMOST EQUAL TO (succapprox)
|
||||
'⋞', # U+22DE EQUAL TO OR PRECEDES (curlyeqprec)
|
||||
'⋟', # U+22DF EQUAL TO OR SUCCEEDS (curlyeqsucc)
|
||||
# '∽', # U+223D REVERSED TILDE (backsim)
|
||||
# '⋍', # U+22CD REVERSED TILDE EQUALS (backsimeq)
|
||||
'≙', # U+2259 ESTIMATES (wedgeq)
|
||||
'≚', # U+225A EQUIANGULAR TO (veeeq)
|
||||
'≘', # U+2258 CORRESPONDS TO (arceq)
|
||||
'≔', # U+2254 COLON EQUALS (coloneqq)
|
||||
'≕', # U+2255 EQUALS COLON (eqqcolon)
|
||||
'⩴', # U+2A74 DOUBLE COLON EQUAL (Coloneqq)
|
||||
'∹', # U+2239 EXCESS (eqcolon)
|
||||
'≬', # U+226C BETWEEN (between)
|
||||
|
||||
# =========================================================================
|
||||
# BRACKET/DELIMITER SYMBOLS - Keep as Unicode
|
||||
# =========================================================================
|
||||
'〚', # U+301A LEFT WHITE SQUARE BRACKET (llbracket)
|
||||
'〛', # U+301B RIGHT WHITE SQUARE BRACKET (rrbracket)
|
||||
'⦅', # U+2985 LEFT WHITE PARENTHESIS (llparenthesis)
|
||||
'⦆', # U+2986 RIGHT WHITE PARENTHESIS (rrparenthesis)
|
||||
'⦉', # U+2989 Z NOTATION LEFT BINDING BRACKET (Langle)
|
||||
'⦊', # U+298A Z NOTATION RIGHT BINDING BRACKET (Rangle)
|
||||
|
||||
# =========================================================================
|
||||
# GEOMETRIC AND MISCELLANEOUS SYMBOLS - Keep as Unicode
|
||||
# =========================================================================
|
||||
'▱', # U+25B1 WHITE PARALLELOGRAM (parallelogram)
|
||||
'⋰', # U+22F0 UP RIGHT DIAGONAL ELLIPSIS (iddots)
|
||||
# '℧', # U+2127 INVERTED OHM SIGN (mho)
|
||||
# '∁', # U+2201 COMPLEMENT (complement)
|
||||
'ℶ', # U+2136 BET SYMBOL (beth)
|
||||
'ℷ', # U+2137 GIMEL SYMBOL (gimel)
|
||||
'ℸ', # U+2138 DALET SYMBOL (daleth)
|
||||
'⟀', # U+27C0 THREE DIMENSIONAL ANGLE (lozengeminus)
|
||||
|
||||
# =========================================================================
|
||||
# LOGICAL AND SET OPERATORS - Keep as Unicode
|
||||
# =========================================================================
|
||||
# '⫅', # U+2AC5 SUBSET OF ABOVE EQUALS SIGN (subseteqq)
|
||||
# '⫆', # U+2AC6 SUPERSET OF ABOVE EQUALS SIGN (supseteqq)
|
||||
# '⫋', # U+2ACB SUBSET OF ABOVE NOT EQUAL TO (subsetneqq)
|
||||
# '⫌', # U+2ACC SUPERSET OF ABOVE NOT EQUAL TO (supsetneqq)
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user