Unicode mathematics with LATEX Will Robertson June 28, 2010 . Unicode mathematics with LATEX Will Robertson School of Mechanical Engineering University of Adelaide Australia June 28, 2010 . Unicode mathematics with LATEX Will Robertson LATEX3 Project June 28, 2010 . Acknowledgements — The TEX Users Group for their very generous support — Barbara Beeton for her work on the STIX fonts — Jonathan Kew, Taco Hoekwater for X TE EX, LuaTEX . Outline What is unicode mathematics? What fonts are available? Using symbols and alphabets How alphabets behave Future . Origins of unicode maths Ad hoc math font encodings: — Computer Modern Math + AMS additions — Euler — Lucida Math — MathTime Pro And of course other non-TEX fonts such as ‘Symbol’ and those used for Mathematica. Origins of unicode maths Math Font Group, http://tug.org/twg/mfg/ — Aim: as easy to switch maths fonts as text fonts — Implemented but not adopted — Designed for TEX’s constraints: 256 glyphs in 16 maths fonts — Project stalled because Unicode was the future Which future we’re now participating in . THERE EXISTS THERE DOES NOT EXIST EMPTY SET INCREMENT NABLA ELEMENT OF NOT AN ELEMENT OF SMALL ELEMENT OF CONTAINS AS MEMBER DOES NOT CONTAIN AS MEMBER existential nexist emptyset Delta gradient element notelement epsis suchthat notcontains 0x02203∃ 0x02204∄ 0x02205∅ 0x02206∆ 0x02207∇ 0x02208∈ 0x02209∉ 0x0220A∊ 0x0220B∋ 0x0220C∌ SMALL CONTAINS AS MEMBER END OF PROOF N-ARY PRODUCT N-ARY COPRODUCT N-ARY SUMMATION MINUS-OR-PLUS SIGN DOT PLUS DIVISION SLASH SET MINUS ASTERISK OPERATOR bepsi uni220E product samalg summation minusplus plusdo fraction setmn asteriskmath 0x0220D∍ 0x0220E∎ 0x0220F∏ 0x02210∐ 0x02211∑ 0x02213∓ 0x02214∔ 0x02215∕ 0x02216∖ 0x02217∗ RING OPERATOR BULLET OPERATOR SQUARE ROOT CUBE ROOT FOURTH ROOT PROPORTIONAL TO INFINITY RIGHT ANGLE ANGLE MEASURED ANGLE compfn periodcentered radical uni221B uni221C proportional infinity orthogonal angle angmsd 0x02218∘ 0x02219∙ 0x0221A√ 0x0221B∛ 0x0221C∜ 0x0221D∝ 0x0221E∞ 0x0221F∟ 0x02220∠ 0x02221∡ SPHERICAL ANGLE DIVIDES DOES NOT DIVIDE PARALLEL TO NOT PARALLEL TO LOGICAL AND LOGICAL OR INTERSECTION UNION INTEGRAL angsph divides nmid parallel notparallel logicaland logicalor intersection union integral 0x02222∢ 0x02223∣ 0x02224∤ 0x02225∥ 0x02226∦ 0x02227∧ 0x02228∨ 0x02229∩ 0x0222A∪ 0x0222B∫ DOUBLE INTEGRAL TRIPLE INTEGRAL CONTOUR INTEGRAL SURFACE INTEGRAL VOLUME INTEGRAL CLOCKWISE INTEGRAL CLOCKWISE CONTOUR INTEGRALANTICLOCKWISE CONTOUR INTEGRAL THEREFORE BECAUSE dblintegral uni222D contourintegral uni222F uni2230 uni2231 uni2232 uni2233 therefore because 0x0222C∬ 0x0222D∭ 0x0222E∮ 0x0222F∯ 0x02230∰ 0x02231∱ 0x02232∲ 0x02233∳ 0x02234∴ 0x02235∵ RATIO PROPORTION DOT MINUS EXCESS GEOMETRIC PROPORTION HOMOTHETIC TILDE OPERATOR REVERSED TILDE INVERTED LAZY S SINE WAVE ratio proportion uni2238 uni2239 uni223A uni223B similar reversedtilde uni223E uni223F From the STIX fonts documentation. 0x02236∶ 0x02237∷ 0x02238∸ 0x02239∹ 0x0223A∺ 0x0223B∻ 0x0223C∼ 0x0223D∽ 0x0223E∾ 0x0223F∿ WREATH PRODUCT NOT TILDE MINUS TILDE ASYMPTOTICALLY EQUAL TONOT ASYMPTOTICALLY EQUAL TO APPROXIMATELY EQUALAPPROXIMATELY TO BUT NOT ACTUALLYNEITHER EQUALAPPROXIMATELY TO NOR ACTUALLY EQUALALMOST TO EQUAL TO NOT ALMOST EQUAL TO wreath nsim uni2242 asymptoticallyequal nsime congruent uni2246 ncong approxequal nap . 0x02240≀ 0x02241≁ 0x02242≂ 0x02243≃ 0x02244≄ 0x02245≅ 0x02246≆ 0x02247≇ 0x02248≈ 0x02249≉ ALMOST EQUAL OR EQUAL TO TRIPLE TILDE ALL EQUAL TO EQUIVALENT TO GEOMETRICALLY EQUIVALENT TO DIFFERENCE BETWEEN APPROACHES THE LIMIT GEOMETRICALLY EQUALAPPROXIMATELY TO EQUAL TO OR THEIMAGE IMAGE OF OF OR APPROXIMATELY EQUAL TO ape uni224B allequal uni224D bump bumpe approaches geometricallyequal approxequalorimageimageorapproximatelyequal 0x0224A≊ 0x0224B≋ 0x0224C≌ 0x0224D≍ 0x0224E≎ 0x0224F≏ 0x02250≐ 0x02251≑ 0x02252≒ 0x02253≓ COLON EQUALS EQUALS COLON RING IN EQUAL TO RING EQUAL TO CORRESPONDS TO ESTIMATES EQUIANGULAR TO STAR EQUALS DELTA EQUAL TO EQUAL TO BY DEFINITION colone ecolon ecir cire uni2258 wedgeq uni225A uni225B trie uni225D 0x02254≔ 0x02255≕ 0x02256≖ 0x02257≗ 0x02258≘ 0x02259≙ 0x0225A≚ 0x0225B≛ 0x0225C≜ 0x0225D≝ MEASURED BY QUESTIONED EQUAL TO NOT EQUAL TO IDENTICAL TO NOT IDENTICAL TO STRICTLY EQUIVALENT TO LESS-THAN OR EQUAL TO GREATER-THAN OR EQUAL TO LESS-THAN OVER EQUAL TO GREATER-THAN OVER EQUAL TO uni225E uni225F notequal equivalence notidentical uni2263 lessequal greaterequal lessoverequal greateroverequal 0x0225E≞ 0x0225F≟ 0x02260≠ 0x02261≡ 0x02262≢ 0x02263≣ 0x02264≤ 0x02265≥ 0x02266≦ 0x02267≧ LESS-THAN BUT NOT EQUAL TOGREATER-THAN BUT NOT EQUAL TO MUCH LESS-THAN MUCH GREATER-THAN BETWEEN NOT EQUIVALENT TO NOT LESS-THAN NOT GREATER-THAN NEITHER LESS-THAN NOR EQUALNEITHER TO GREATER-THAN NOR EQUAL TO lvnE gvnE muchless muchgreater twixt uni226D notless notgreater notlessnorequal notgreaternorequal 0x02268≨ 0x02269≩ 0x0226A≪ 0x0226B≫ 0x0226C≬ 0x0226D≭ 0x0226E≮ 0x0226F≯ 0x02270≰ 0x02271≱ LESS-THAN OR EQUIVALENT TOGREATER-THAN OR EQUIVALENTNEITHER TO LESS-THAN NOR EQUIVALENTNEITHER GREATER-THAN TO NOR EQUIVALENTLESS-THAN TO OR GREATER-THANGREATER-THAN OR LESS-THANNEITHER LESS-THAN NOR GREATER-THANNEITHER GREATER-THAN NOR LESS-THAN PRECEDES SUCCEEDS lessorequivalent greaterorequivalent uni2274 uni2275 lessorgreater greaterorless uni2278 notgreaternorless precedes succeeds 0x02272≲ 0x02273≳ 0x02274≴ 0x02275≵ 0x02276≶ 0x02277≷ 0x02278≸ 0x02279≹ 0x0227A≺ 0x0227B≻ PRECEDES OR EQUAL TO SUCCEEDS OR EQUAL TO PRECEDES OR EQUIVALENT TO SUCCEEDS OR EQUIVALENT TO DOES NOT PRECEDE DOES NOT SUCCEED SUBSET OF SUPERSET OF NOT A SUBSET OF NOT A SUPERSET OF cupre sccue prsim scsim notprecedes notsucceeds propersubset propersuperset notsubset notsuperset 0x0227C≼ 0x0227D≽ 0x0227E≾ 0x0227F≿ 0x02280⊀ 0x02281⊁ 0x02282⊂ 0x02283⊃ 0x02284⊄ 0x02285⊅ SUBSET OF OR EQUAL TO SUPERSET OF OR EQUAL TONEITHER A SUBSET OF NOR EQUALNEITHER TO A SUPERSET OF NOR EQUALSUBSET TO OF WITH NOT EQUAL TOSUPERSET OF WITH NOT EQUAL TO MULTISET MULTISET MULTIPLICATION MULTISET UNION SQUARE IMAGE OF reflexsubset reflexsuperset nsube nsupe subsetnotequal supersetnotequal uni228C uni228D uplus sqsub 0x02286⊆ 0x02287⊇ 0x02288⊈ 0x02289⊉ 0x0228A⊊ 0x0228B⊋ 0x0228C⊌ 0x0228D⊍ 0x0228E⊎ 0x0228F⊏ SQUARE ORIGINAL OF SQUARE IMAGE OF OR EQUAL SQUARETO ORIGINAL OF OR EQUAL TO SQUARE CAP SQUARE CUP CIRCLED PLUS CIRCLED MINUS CIRCLED TIMES CIRCLED DIVISION SLASH CIRCLED DOT OPERATOR sqsup sqsube sqsupe sqcap sqcup circleplus minuscircle circlemultiply osol circleot 0x02290⊐ 0x02291⊑ 0x02292⊒ 0x02293⊓ 0x02294⊔ 0x02295⊕ 0x02296⊖ 0x02297⊗ 0x02298⊘ 0x02299⊙ OpenType mathematics The unicode maths encoding saw the inception of the STIX fonts — Which have now been released! (Good timing.) — We now had the means to typeset any known maths glyph — But maths needs more than glyphs for proper typesetting . Bogusław Jackowski Figure 3: Assembling an accented formula, wy wx ; symbols are explained in the text ≤ Bogusław Jackowski.Figure “Appendix G illuminated”. 2: Assembling a radical; symbols explained In: TUGboat in the text 27.1 (2006), pp. 83{90 kern, δ, is inserted between the boxes, where δ = − min(x-height, hx ). The x-height is defined by the fifth dimen parameter (\fontdimen5. ) of. the accenter. font.. The horizontal shift of the accenter, s, is equal to the implicit kern between the accentee and the special character, skewchar (defined by the command \skewchar); in the plain format, it is the character of code 127 (tie after) for family 1, and the character of code 48 (prime) for family 2. The kern has nothing to do with the shape of the \skewchar, but is intended to provide an appropriate correction due to the skew- ness of the accentee. If the accentee is already a boxed formula, TEX assumes that s = 0. The width of the resulting formula is always equal to the width of the accentee, wx ; the baseline of the resulting formula coincides with the baseline of the Figure 4: Assembling an accented formula, wy > wx ; accentee. symbols have the same meaning as in Figure 3 86 TUGboat, Volume 27 (2006), No. 1 — Proceedings of EuroTEX 2006 Microsoft Word 2007 Murray Sargeant and others: — from the unicode maths encoding, — extended OpenType, — implemented a unicode maths typesetting engine for Microsoft Word (and now Office). OpenType fonts can now contain the necessary information for typesetting maths. The package \usepackage{unicode-math} — Requires a 32-bit unicode-aware TEX variant — Written for X LE ATEX — LuaLATEX support imminent . OpenType Maths Fonts Cambria Math Microsoft ∞ 퐹(푠) = ℒ{푓(푡)} = e−푠푡푓(푡) d푡 0 \setmathfont{Cambria Math} . OpenType Maths Fonts Asana Math Apostolos Syropoulos ∞ 퐹(푠) = ℒ{푓(푡)} = ﾙ e−푠푡푓(푡) d푡 \setmathfont{Asana Math} . OpenType Maths Fonts XITS Math Khaled Hosny ∞ 퐹(푠) = ℒ {푓(푡)} = e−푠푡푓(푡) d푡 0 \setmathfont{XITS Math} . OpenType Maths Fonts STIX ∞ −푠푡 퐹(푠) = ℒ {푓(푡)} = ∫0 e 푓(푡) d푡 \setmathfont{STIXGeneral} . OpenType Maths Fonts Neo Euler Khaled Hosny F(s) = ℒ {f(t)} = ef(t) dt \setmathfont[math-style=upright]{Neo Euler} . Symbols in the source — Backwards compatibility is paramount — Existing maths document should work (modulo edge cases) — Inputing symbols and characters: . Symbols in the source — Backwards compatibility is paramount — Existing maths document should work (modulo edge cases) — Inputing symbols and characters: ascii w unicode 푤 (U+1D464) . Symbols in the source — Backwards compatibility is paramount — Existing maths document should work (modulo edge cases) — Inputing symbols and characters: name \circledast char ⊛ (U+229B) . Symbols in the source — Backwards