Unicode Characters in ProofPower through Lualatex Roger Bishop Jones Abstract This document serves to establish what characters render like in utf8 ProofPower documents prepared using lualatex. Created 2019 http://www.rbjones.com/rbjpub/pp/doc/t055.pdf © Roger Bishop Jones; Licenced under Gnu LGPL Contents 1 Prelude 2 2 Changes 2 2.1 Recent Changes .......................................... 2 2.2 Changes Under Consideration ................................... 2 2.3 Issues ............................................... 2 3 Introduction 3 4 Mathematical operators and symbols in Unicode 3 5 Dedicated blocks 3 5.1 Mathematical Operators block .................................. 3 5.2 Supplemental Mathematical Operators block ........................... 4 5.3 Mathematical Alphanumeric Symbols block ........................... 4 5.4 Letterlike Symbols block ..................................... 6 5.5 Miscellaneous Mathematical Symbols-A block .......................... 7 5.6 Miscellaneous Mathematical Symbols-B block .......................... 7 5.7 Miscellaneous Technical block .................................. 7 5.8 Geometric Shapes block ...................................... 8 5.9 Miscellaneous Symbols and Arrows block ............................. 9 5.10 Arrows block ........................................... 9 5.11 Supplemental Arrows-A block .................................. 10 5.12 Supplemental Arrows-B block ................................... 10 5.13 Combining Diacritical Marks for Symbols block ......................... 11 5.14 Arabic Mathematical Alphabetic Symbols block ......................... 11 5.15 Characters in other blocks ..................................... 12 6 Postscript 14 Index 15 1 Prelude 2 Changes 2.1 Recent Changes 2.2 Changes Under Consideration 2.3 Issues See also Section 6. 2 3 Introduction 4 Mathematical operators and symbols in Unicode From Wikipedia, the free encyclopedia, transcribed into lualatex to determine which characters work. Blackboard at the Laurent Schwartz Center for Mathematics, École Polytechnique. This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols. The Unicode Standard encodes almost all standard characters used in mathematics. Unicode Technical Report #25 provides comprehensive information about the character repertoire, their prop- erties, and guidelines for implementation. Mathematical operators and symbols are in multiple Unicode blocks. Some of these blocks are dedicated to, or primarily contain, mathematical characters while others are a mix of mathematical and non-mathematical characters. This article covers all Unicode characters with a derived property of ”Math”. 5 Dedicated blocks 5.1 Mathematical Operators block Main article: Mathematical Operators (Unicode block) The Mathematical Operators block (U+2200–U+22FF) contains characters for mathematical, logical, and set notation. Mathematical Operators[1] Official Unicode Consortium code chart (PDF) 0123456789ABCDEF U+220x @ ∁ BD ∄ H ∆ r PR ∊ Q ∌ ∍ ∎ + U 221x − ¯ ∔ ∕ z ∗ ˝ ∙ ∛ ∜ 9 ∞ ∟± U+222x ∠ ∡ ∢ ∣ ∤ k ∦ ∬ ∭ ∯ ² ř ^ _ X` Y U+223x ∰ ∱ ∲ ∳ ∴ ∵ ∶ ∷ ∸ ∹ ∺³ ∻ ∼ ∽¶ ∾ ∿ U+224x o ≁ ≂ » ≄ – ≆ ≇ « ≉ ≊ ≋ ≌ — ≎ ≏ : U+225x = ≑≒≓≔≕≖≗≘≙≚≛ fl ≝ ≞ ≟ U+226x ‰” ≢ ≣ ¤ ¥ ≦ ≧ ≨ ≩ !" ≬ ≭ ≮ ≯ U+227x ≰ ≱ ≲ ≳ ≴ ≵ ≶ ≷ ≸ ≹ ă ¡ ≼ ≽ ≾ ≿ U+228x ⊀ ⊁ ĂĄ ⊄ ⊅ ĎĚ ⊈ ⊉ ⊊ ⊋ ⊌ ⊍ Z Ă U+229x ⊐ Ď ⊒ [ \ ` a b ⊘ d ⊚ ⊛ ⊜ ⊝ ⊞ ⊟ U+22Ax ⊠ ⊡ $ % J K ⊦ |ù ⊨ ⊩ ⊪ ⊫ ⊬ ⊭ ⊮ ⊯ U+22Bx ⊰ ⊱ ¡ £ ¢ ⊵⊶⊷⊸⊹⊺⊻⊼⊽⊾⊿ U+22Cx ˛ ⋅ ⋆ ⋇ ' ⋉ ⋊ ⋋ ⋌ ⋍ + U 22DxŹŽŞŤ ⋐ ⋑ ⋒ ⋓ ⋔ ⋕ ⋖ ⋗ ⋘ ⋙ ⋚ ⋛ ⋜ ⋝ ⋞ ⋟ U+22Ex ⋠ ⋡ ⋢ ⋣ ⋤ ⋥ ⋦ ⋧ ⋨ ⋩ ⋪ ⋫ ⋬ ¤ ⋮ ⋯ U+22Fx ⋰ ⋱ ⋲ ⋳ ⋴ ⋵ ⋶ ⋷ ⋸ ⋹ ⋺ ⋻ ⋼ ⋽ ⋾ ⋿ Notes 3 1. As of Unicode version 12.0 5.2 Supplemental Mathematical Operators block Main article: Supplemental Mathematical Operators (Unicode block) The Supplemental Mathematical Operators block (U+2A00–U+2AFF) contains various mathematical symbols, including N-ary operators, summations and integrals, intersections and unions, logical and relational operators, and subset/superset relations. Supplemental Mathematical Operators[1] Official Unicode Consortium code chart (PDF) 0123456789ABCDEF U+2A0x ⨃ ⨅ ⨇ ⨈ ⨉ ⨊ ⨋ ⨌ ⨍ ⨎ ⨏ + U 2A1xÄÀ ⨐ ⨑ ⨒ ⨓Ţ ⨔ ⨕ ⨖Ů ⨗ ⨘ ⨙ ⨚ ⨛ ⨜ ' ⨞ ⨟ U+2A2x ⨠ ⨡ ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨩ ⨪ ⨫ ⨬ ⨭ ⨮ ⨯ o U+2A3x ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⨹ ⨺ ⨻ PG PF 9 ⨿ U+2A4x ⩀ ⩁ ⩂ ⩃ ⩄ ⩅ ⩆ ⩇ ⩈ ⩉ ⩊ ⩋ ⩌ ⩍ ⩎ ⩏ U+2A5x ⩐ ⩑ ⩒ ⩓ ⩔ ⩕ ⩖ ⩗ ⩘ ⩙ ⩚ ⩛ ⩜ ⩝ ⩞ ⩟ U+2A6x ⩠ ⩡ ⩢ ⩣ C´ B´ ⩦ ⩧ ⩨ ⩩ ⩪ ⩫ ⩬ ⩭ ⩮ ⩯ U+2A7x ⩰ ⩱ ⩲ ⩳ ⩴ ⩵ ⩶ ⩷ ⩸ ⩹ ⩺ ⩻ ⩼ ⩽ ⩾ ⩿ U+2A8x ⪀ ⪁ ⪂ ⪃ ⪄ ⪅ ⪆ ⪇ ⪈ ⪉ ⪊ ⪋ ⪌ ⪍ ⪎ ⪏ U+2A9x ⪐ ⪑ ⪒ ⪓ ⪔ ⪕ ⪖ ⪗ ⪘ ⪙ ⪚ ⪛ ⪜ ⪝ ⪞ ⪟ U+2AAx ⪠ ⪡ ⪢ ⪣ ⪤ ⪥ ⪦ ⪧ ⪨ ⪩ ⪪ ⪫ ⪬ ⪭ ⪮ ¨ U+2ABx © ⪱⪲⪳⪴⪵⪶⪷⪸⪹⪺⪻⪼⪽⪾⪿ U+2ACx ⫀ ⫁ ⫂ ⫃ ⫄ ⫅ ⫆ ⫇ ⫈ ⫉ ⫊ ⫋ ⫌ ⫍ ⫎ ⫏ U+2ADx ⫐ ⫑ ⫒ ⫓ ⫔ ⫕ ⫖ ⫗ ⫘ ⫙ ⫚ ⫛ ⫝̸ ⫝ ⫞ ⫟ U+2AEx ⫠ ⫡ ⫢ ⫣ ⫤ ⫥ ⫦ ⫧ ⫨ ⫩ ⫪ ⫫ ⫬ ⫭ ⫮ ⫯ U+2AFx ⫰ ⫱ ⫲ ⫳ ⫴ ⫵ ⫶ ⫷ ⫸ ⫹ ⫺ ⫻ ⫼ ⫽ ⫾ ⫿ Notes 1. As of Unicode version 12.0 5.3 Mathematical Alphanumeric Symbols block Main article: Mathematical Alphanumeric Symbols (Unicode block) The Mathematical Alphanumeric Symbols block (U+1D400–U+1D7FF) contains Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The ”holes” in the alphabetic ranges are filled by previously defined characters in the Letter like Symbols block shown below. Mathematical Alphanumeric Symbols[1][2] Official Unicode Consortium code chart (PDF) 4 0123456789ABCDEF U+1D40x 퐀 퐁 퐂 퐃 퐄 퐅 퐆 퐇 퐈 퐉 퐊 퐋 퐌 퐍 퐎 퐏 U+1D41x 퐐 퐑 퐒 퐓 퐔 퐕 퐖 퐗 퐘 퐙 퐚 퐛 퐜 퐝 퐞 퐟 U+1D42x 퐠 퐡 퐢 퐣 퐤 퐥 퐦 퐧 퐨 퐩 퐪 퐫 퐬 퐭 퐮 퐯 U+1D43x 퐰 퐱 퐲 퐳 퐴 퐵 퐶 퐷 퐸 퐹 퐺 퐻 퐼 퐽 퐾 퐿 U+1D44x 푀 푁 푂 푃 푄 푅 푆 푇 푈 푉 푊 푋 푌 푍 푎 푏 U+1D45x 푐 푑 푒 푓 푔 푖 푗 푘 푙 푚 푛 표 푝 푞 푟 U+1D46x 푠 푡 푢 푣 푤 푥 푦 푧 푨 푩 푪 푫 푬 푭 푮 푯 U+1D47x 푰 푱 푲 푳 푴 푵 푶 푷 푸 푹 푺 푻 푼 푽 푾 푿 U+1D48x 풀 풁 풂 풃 풄 풅 풆 풇 품 풉 풊 풋 풌 풍 풎 풏 U+1D49x 풐 풑 풒 풓 풔 풕 풖 풗 풘 풙 풚 풛 ACD U+1D4Ax GJKNOPQST U+1D4Bx UVWXYZ 풶 풷 풸 풹 풻 풽 풾 풿 U+1D4Cx 퓀 퓁 퓂 퓃 퓅 퓆 퓇 퓈 퓉 퓊 퓋 퓌 퓍 퓎 퓏 U+1D4Dx 퓐 퓑 퓒 퓓 퓔 퓕 퓖 퓗 퓘 퓙 퓚 퓛 퓜 퓝 퓞 퓟 U+1D4Ex 퓠 퓡 퓢 퓣 퓤 퓥 퓦 퓧 퓨 퓩 퓪 퓫 퓬 퓭 퓮 퓯 U+1D4Fx 퓰 퓱 퓲 퓳 퓴 퓵 퓶 퓷 퓸 퓹 퓺 퓻 퓼 퓽 퓾 퓿 U+1D50x 픀 픁 픂 픃 프 픅 픇 픈 픉 픊 픍 픎 픏 U+1D51x 픐 픑 픒 픓 픔 픖 픗 픘 픙 픚 픛 픜 픞 픟 U+1D52x 픠 픡 픢 픣 픤 픥 픦 픧 픨 픩 픪 픫 픬 픭 픮 픯 U+1D53x 픰 픱 픲 픳 픴 픵 픶 픷 ABDEFG U+1D54x IJKLMOSTUVWX U+1D55x Y 핒핓핔핕핖핗하학핚핛한핝핞핟 U+1D56x 할 핡 핢 핣 핤 핥 핦 핧 함 합 핪 핫 핬 항 핮 핯 U+1D57x 핰 핱 핲 핳 해 핵 핶 핷 핸 핹 핺 핻 핼 핽 핾 핿 U+1D58x 햀 햁 햂 햃 햄 햅 햆 햇 했 행 햊 햋 햌 햍 햎 햏 U+1D59x 햐 햑 햒 햓 햔 햕 햖 햗 햘 햙 햚 햛 햜 햝 햞 햟 U+1D5Ax 햠 햡 햢 햣 햤 향 햦 햧 햨 햩 햪 햫 햬 햭 햮 햯 U+1D5Bx 햰 햱 햲 햳 햴 햵 햶 햷 햸 햹 햺 햻 햼 햽 햾 햿 U+1D5Cx 헀 헁 헂 헃 헄 헅 헆 헇 허 헉 헊 헋 헌 헍 헎 헏 U+1D5Dx 헐 헑 헒 헓 헔 헕 헖 헗 험 헙 헚 헛 헜 헝 헞 헟 U+1D5Ex 헠 헡 헢 헣 헤 헥 헦 헧 헨 헩 헪 헫 헬 헭 헮 헯 U+1D5Fx 헰 헱 헲 헳 헴 헵 헶 헷 헸 헹 헺 헻 헼 헽 헾 헿 U+1D60x 혀 혁 혂 혃 현 혅 혆 혇 혈 혉 혊 혋 혌 혍 혎 혏 U+1D61x 혐 협 혒 혓 혔 형 혖 혗 혘 혙 혚 혛 혜 혝 혞 혟 U+1D62x 혠 혡 혢 혣 혤 혥 혦 혧 혨 혩 혪 혫 혬 혭 혮 혯 U+1D63x 혰 혱 혲 혳 혴 혵 혶 혷 호 혹 혺 혻 혼 혽 혾 혿 U+1D64x 홀 홁 홂 홃 홄 홅 홆 홇 홈 홉 홊 홋 홌 홍 홎 홏 U+1D65x 홐 홑 홒 홓 화 확 홖 홗 환 홙 홚 홛 활 홝 홞 홟 U+1D66x 홠 홡 홢 홣 홤 홥 홦 홧 홨 황 홪 홫 홬 홭 홮 홯 U+1D67x 홰 홱 홲 홳 홴 홵 홶 홷 홸 홹 홺 홻 홼 홽 홾 홿 U+1D68x 횀 횁 횂 횃 횄 횅 횆 횇 횈 횉 횊 횋 회 획 횎 횏 U+1D69x 횐 횑 횒 횓 횔 횕 횖 횗 횘 횙 횚 횛 횜 횝 횞 횟 U+1D6Ax 횠 횡 횢 횣 횤 횥 효 횩 횪 횫 횬 횭 횮 횯 U+1D6Bx 횰 횱 횲 횳 횴 횵 횶 횷 횸 횹 횺 횻 횼 횽 횾 횿 5 U+1D6Cx 훀 훁 훂 훃 후 훅 훆 훇 훈 훉 훊 훋 훌 훍 훎 훏 U+1D6Dx 훐 훑 훒 훓 훔 훕 훖 훗 훘 훙 훚 훛 훜 훝 훞 훟 U+1D6Ex 훠 훡 훢 훣 훤 훥 훦 훧 훨 훩 훪 훫 훬 훭 훮 훯 U+1D6Fx 훰 훱 훲 훳 훴 훵 훶 훷 훸 훹 훺 훻 훼 훽 훾 훿 U+1D70x 휀 휁 휂 휃 휄 휅 휆 휇 휈 휉 휊 휋 휌 휍 휎 휏 U+1D71x 휐 휑 휒 휓 휔 휕 휖 휗 휘 휙 휚 휛 휜 휝 휞 휟 U+1D72x 휠 휡 휢 휣 휤 휥 휦 휧 휨 휩 휪 휫 휬 휭 휮 휯 U+1D73x 휰 휱 휲 휳 휴 휵 휶 휷 휸 휹 휺 휻 휼 휽 휾 휿 U+1D74x 흀 흁 흂 흃 흄 흅 흆 흇 흈 흉 흊 흋 흌 흍 흎 흏 U+1D75x 흐 흑 흒 흓 흔 흕 흖 흗 흘 흙 흚 흛 흜 흝 흞 흟 U+1D76x 흠 흡 흢 흣 흤 흥 흦 흧 흨 흩 흪 흫 희 흭 흮 흯 U+1D77x 흰 흱 흲 흳 흴 흵 흶 흷 흸 흹 흺 흻 흼 흽 흾 흿 U+1D78x 힀 힁 힂 힃 힄 힅 힆 힇 히 힉 힊 힋 힌 힍 힎 힏 U+1D79x 힐 힑 힒 힓 힔 힕 힖 힗 힘 힙 힚 힛 힜 힝 힞 힟 U+1D7Ax 힠 힡 힢 힣 힤 힥 힦 힧 힨 힩 힪 힫 힬 힭 힮 힯 U+1D7Bx ힰ ힱ ힲ ힳ ힴ ힵ ힶ ힷ ힸ ힹ ힺ ힻ ힼ ힽ ힾ ힿ U+1D7Cx ퟀ ퟁ ퟂ ퟃ ퟄ ퟅ ퟆ ퟇ ퟈ ퟉ ퟊ ퟋ ퟎ ퟏ U+1D7Dx ퟐ ퟑ ퟒ ퟓ ퟔ ퟕ ퟖ ퟗ ퟘ ퟙ ퟚ ퟛ ퟜ ퟝ ퟞ ퟟ U+1D7Ex ퟠ ퟡ ퟢ ퟣ ퟤ ퟥ ퟦ ퟧ ퟨ ퟩ ퟪ ퟫ ퟬ ퟭ ퟮ ퟯ U+1D7Fx ퟰ ퟱ ퟲ ퟳ ퟴ ퟵ ퟶ ퟷ ퟸ ퟹ ퟺ ퟻ ퟼ ퟽ ퟾ ퟿ Notes 1.