-Math, Ver. 2019-08-16

Yuansheng Zhao, Xiangdong Zeng November 16, 2019

1 Introduction Garamond-Math is an open type math matching the EB Garamond (Octavio Pardo)1 and EB Garamond (Georg Mayr-Duffner)2. Many mathematical symbols are derived from other , others are made from scratch. The metric is generated with a python script. The font is mostly tested with XƎTEX, though it shoule also work with LuaTEX. Issues, bug reports, forks and other contributions are welcome. Please visit GitHub3 for development details. A minimal example with unicode-math package is as following:

%Compilewith`xelatex'command \documentclass{article} \usepackage[math-style=ISO,bold-style=ISO]{unicode-math} \setmainfont{EBGaramond}%Youshouldhaveinstalledthefont \setmathfont{Garamond-Math.otf}[StylisticSet={7,9}]%UseStylisticSetthatyoulike \begin{document} \[x^3+y^3=z^3.\] \end{document}

The result shoule be

푥3 + 푦3 = 푧3.

2 Alphabets & StylisticSets

Latin and Greek (StylisticSet 4/5 give semi/extra bold for \symbf) 훢훣퐶퐷훦퐹퐺훨훪퐽훫퐿훭훮훰훲푄푅푆훵푈푉푊훸푌훧 푎푏푐푑푒푓푔ℎ푖푗푘푙푚푛표푝푞푟푠푡푢푣푤푥푦푧 ΑΒCDΕFGΗΙJΚLΜΝΟΡQRSΤUVWΧYΖ abcdefghijklmnopqrstuvwxyz 휜휝푪푫휠푭푮휢휤푱휥푳휧휨휪휬푸푹푺휯푼푽푾휲풀휡 풂풃풄풅풆풇품풉풊풋풌풍풎풏풐풑풒풓풔풕풖풗풘풙풚풛 효횩퐂퐃횬퐅퐆횮횰퐉횱퐋횳횴횶횸퐐퐑퐒횻퐔퐕퐖횾퐘횭 퐚퐛퐜퐝퐞퐟퐠퐡퐢퐣퐤퐥퐦퐧퐨퐩퐪퐫퐬퐭퐮퐯퐰퐱퐲퐳 훢훣훤훥훦훧훨훩훳훪훫훬훭훮훯훰훱훲훴훵훶훷훸훹훺 훼훽훾훿휖휀휁휂휃휗휄휅휘휆휇휈휉휊휋휛휌휚휎휍휏휐휙휑휒휓휔 ΑΒΓΔΕΖΗΘϴΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ αβγδϵεζηθϑικϰλμνξοπϖρϱσςτυϕφχψω 휜휝휞휟휠휡휢휣휭휤휥휦휧휨휩휪휫휬휮휯휰휱휲휳휴

1https://ctan.org/pkg/ebgaramond/, and https://github.com/octaviopardo/EBGaramond12/ 2https://github.com/georgd/EB-Garamond/ 3https://github.com/YuanshengZhao/Garamond-Math/

1 휶휷휸휹흐휺휻휼휽흑휾휿흒흀흁흂흃흄흅흕흆흔흈흇흉흊흓흋흌흍흎 효횩횪횫횬횭횮횯횹횰횱횲횳횴횵횶횷횸횺횻횼횽횾횿훀 훂훃후훅훜훆훇훈훉훝훊훋훞훌훍훎훏훐훑훡훒훠훔훓훕훖훟훗훘훙훚 휜휝푪푫휠푭푮휢휤푱휥푳휧휨휪휬푸푹푺휯푼푽푾휲풀휡 풂풃풄풅풆풇품풉풊풋풌풍풎풏풐풑풒풓풔풕풖풗풘풙풚풛 휜휝푪푫휠푭푮휢휤푱휥푳휧휨휪휬푸푹푺휯푼푽푾휲풀휡 풂풃풄풅풆풇품풉풊풋풌풍풎풏풐풑풒풓풔풕풖풗풘풙풚풛

Sans and Typerwriter: From Libertinus Math4 혈혉혊혋혌혍혎혏혐협혒혓혔형혖혗혘혙혚혛혜혝혞혟혠혡 혢혣혤혥혦혧혨혩혪혫혬혭혮혯혰혱혲혳혴혵혶혷호혹혺혻 햠햡햢햣햤향햦햧햨햩햪햫햬햭햮햯햰햱햲햳햴햵햶햷햸햹 햺햻햼햽햾햿헀헁헂헃헄헅헆헇허헉헊헋헌헍헎헏헐헑헒헓 혼혽혾혿홀홁홂홃홄홅홆홇홈홉홊홋홌홍홎홏홐홑홒홓화확 홖홗환홙홚홛활홝홞홟홠홡홢홣홤홥홦홧홨황홪홫홬홭홮홯 흖흗헖헗흚헙헚흜헜헝흟헟흡흢흤흦헤헥헦흩헨헩헪희헬흛 헮헯헰헱헲헳헴헵헶헷헸헹헺헻헼헽헾헿혀혁혂혃현혅혆혇 홰홱홲홳홴홵홶홷홸홹홺홻홼홽홾홿횀횁횂횃횄횅횆횇횈횉 횊횋회획횎횏횐횑횒횓횔횕횖횗횘횙횚횛횜횝횞횟횠횡횢횣

Blackboard (StylisticSet 1 → rounded XITS Math5) 픸픹ℂ픻피픽픾ℍ핀핁핂핃필ℕ핆ℙℚℝ핊핋핌핍핎핏핐ℤ 핒핓핔핕핖핗하학핚핛한핝핞핟할핡핢핣핤핥핦핧함합핪핫 픸픹ℂ픻피픽픾ℍ핀핁핂핃필ℕ핆ℙℚℝ핊핋핌핍핎핏핐ℤ 핒핓핔핕핖핗하학핚핛한핝핞핟할핡핢핣핤핥핦핧함합핪핫

Script: Rounded XITS Math [StylisticSet 3 → scaled CM; 8 → Garamond-compatible ones (experimental)] 풜ℬ풞풟ℰℱ풢ℋℐ풥풦ℒℳ풩풪풫풬ℛ풮풯풰풱풲풳풴풵 풶풷풸풹ℯ풻ℊ풽풾풿퓀퓁퓂퓃ℴ퓅퓆퓇퓈퓉퓊퓋퓌퓍퓎퓏 퓐퓑퓒퓓퓔퓕퓖퓗퓘퓙퓚퓛퓜퓝퓞퓟퓠퓡퓢퓣퓤퓥퓦퓧퓨퓩 퓪퓫퓬퓭퓮퓯퓰퓱퓲퓳퓴퓵퓶퓷퓸퓹퓺퓻퓼퓽퓾퓿픀픁픂픃 풜ℬ풞풟ℰℱ풢ℋℐ풥풦ℒℳ풩풪풫풬ℛ풮풯풰풱풲풳풴풵 퓐퓑퓒퓓퓔퓕퓖퓗퓘퓙퓚퓛퓜퓝퓞퓟퓠퓡퓢퓣퓤퓥퓦퓧퓨퓩 풜ℬ풞풟ℰℱ풢ℋℐ풥풦ℒℳ풩풪풫풬ℛ풮풯풰풱풲풳풴풵 풶풷풸풹ℯ풻ℊ풽풾풿퓀퓁퓂퓃ℴ퓅퓆퓇퓈퓉퓊퓋퓌퓍퓎퓏

Fraktur: From Noto Sans Math6 프픅ℭ픇픈픉픊ℌℑ픍픎픏픐픑픒픓픔ℜ픖픗픘픙픚픛픜ℨ 픞픟픠픡픢픣픤픥픦픧픨픩픪픫픬픭픮픯픰픱픲픳픴픵픶픷 핬항핮핯핰핱핲핳해핵핶핷핸핹핺핻핼핽핾핿햀햁햂햃햄햅 햆햇했행햊햋햌햍햎햏햐햑햒햓햔햕햖햗햘햙햚햛햜햝햞햟

4https://github.com/khaledhosny/libertinus/ 5https://github.com/khaledhosny/xits/ 6https://github.com/googlefonts/noto-fonts/

2 Digits: Same width between weight and /sans 3.141592653589793238462643383279502884197169399375105820974944592307816406286 ퟥ.ퟣퟦퟣퟧퟫퟤퟨퟧퟥퟧퟪퟫퟩퟫퟥퟤퟥퟪퟦퟨퟤퟨퟦퟥퟥퟪퟥퟤퟩퟫퟧퟢퟤퟪퟪퟦퟣퟫퟩퟣퟨퟫퟥퟫퟫퟥퟩퟧퟣퟢퟧퟪퟤퟢퟫퟩퟦퟫퟦퟦퟧퟫퟤퟥퟢퟩퟪퟣퟨퟦퟢퟨퟤퟪퟨ ퟑ.ퟏퟒퟏퟓퟗퟐퟔퟓퟑퟓퟖퟗퟕퟗퟑퟐퟑퟖퟒퟔퟐퟔퟒퟑퟑퟖퟑퟐퟕퟗퟓퟎퟐퟖퟖퟒퟏퟗퟕퟏퟔퟗퟑퟗퟗퟑퟕퟓퟏퟎퟓퟖퟐퟎퟗퟕퟒퟗퟒퟒퟓퟗퟐퟑퟎퟕퟖퟏퟔퟒퟎퟔퟐퟖퟔ

\partial: (StylisticSet 2 → curved ones) 휇 흀흁흂 휕휇(∂ 휙) − 흐 흏흁(휜흀훛흂풇) 휇 흀흁흂 휕휇(∂ 휙) − 흐 흏흁(휜흀훛흂풇)

\hbar: (StylisticSet 6 → horizontal bars) ℏ ℏ

Italic 풉: (StylisticSet 10 → out-bending ones) 풉 풉 ℏ = ℏ = 2π 2π

\tilde: (StylisticSet 9 → “normal” ones) 퐹̃ 퐹̃

\int: (StylisticSet 7 → a variant with inversion symmetry) 1 d ∮ 훦⃗ ⋅ d푙⃗ = − ∬ 훣⃗ ⋅ d푆⃗ 휕훴 푐 d푡 훴 1 d ∮ 훦⃗ ⋅ d푙⃗ = − ∬ 훣⃗ ⋅ d푆⃗ 휕훴 푐 d푡 훴

Binany Operators: (StylisticSet 11 → larger ones) 푠 = 훢 + 푏 × 1 ÷ 푥3 푠 = 훢 + 푏 × 1 ÷ 푥3

Extensible Arrow Hack The font contains the math table for constructing extensible arrow. However unicode-math does not privode an inter- 7 face to that. In LuaTEX one can use \Uhextensible . A more general solution is to add the following code in preamble. \usepackage{extarrow} %or mathtools \makeatletter \renewcommand{\relbar}{\symbol{"E010}\mkern-.2mu\symbol{"E010}\mkern1.8mu} \renewcommand{\Relbar}{\symbol{"E011}\mkern-.2mu\symbol{"E011}\mkern1.8mu} \makeatother Then \xleftarrow and other commands will work:

H SO CH COOH + C H OH →2 4 CH COOC H + H O. 3 2 5 △ 3 2 5 2 3 Known Issue • Various spacing problems. Though math fonts technically should not be kerned, some pairs looks very ugly (Ex. 푉훢); sometimes sub/superscript may also have same problem. However, do note that due to the mechanism in math mode, making all spacing look perfect is amlost impossible (as far as I can do, and low x-height and large italic angle only make things even worse), in many cases, adjusting manually (i.e. using \, or \!) is required. • Fake optical size. EB Garamond does not contain a complete set of glyphs (normal + bold + optical size of both weights). The “optical size ssty” is made by interpolating different weights at the present (without this, the double script is too thin to be readable). 7https://tex.stackexchange.com/questions/423893/

3 4 Equation Samples 1 + 2 − 3 × 4 ÷ 5 ± 6 ∓ 7 ∔ 8 = −푎 ⊕ 푏 ⊗ 푐 − {푧} ∀휖, ∃훿 ∶ 푥 ∈ 훢 ∪ 훣 ⊂ 푆 ∩ 훵 ⋭ 푈 휇 휇 휇 휇 휎 휇 휎 푅휈휅휆 = 휕휅훤휆휈 − 휕휆훤휅휈 + 훤휅휎훤휆휈 − 훤휆휎훤휅휈 휕푥푖1 휕푥푖푘 휕푥′훽1 휕푥′훽푙 훵′훽1⋯훽푙 = 훵푗1⋯푗푙 ⋯ ⋯ 훼1⋯훼푘 푖 ⋯푖 ′훼 ′훼 1 푘 휕푥 1 휕푥 푘 휕푥푗1 휕푥푗푙

훸푝 ̂ ̃ ∫ 2 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 √ 1−푚푢+푚훥/푘 2푚푢/푘 푥←푦↔푤⇒푏⇔푐↑푦↕푤⇓푏⇕푐⇘푝⇙푝푥↼푥↿훸↤푌↦훧↥푓⇄푓⇅푓ℎ⇶ℎ⬱푝 1 ln(푥 + 1) 1 ∞ (−푥)푖−1 ∞ 1 (−푥)푖−1 ∞ (−1)푖+1 π2 ∫ d푥 = ∫ ∑ d푥 = ∑ ∫ d푥 = ∑ 2 = 0 푥 0 푖=1 푖 푖=1 0 푖 푖=1 푖 12

∞ ∞ ∞ ∞ ∞ ∫ ∫ ∑ ∏ ∐ ∰ ∲ ∳ ⨑ ∱ 0 0 푖=1 푗=푖 푘=푖

(((((푥))))) [[[[[푥]]]]] {{{{{푥}}}}} ∣∣∣∣|푥|∣∣∣∣ ∥∥∥∥‖푥‖∥∥∥∥ ⟨⟨⟨⟨⟨푥⟩⟩⟩⟩⟩

⟮⟮⟮⟮⟮푥⟯⟯⟯⟯⟯ ⌊⌊⌊⌊⌊푥⌋⌋⌋⌋⌋ ⌈⌈⌈⌈⌈푥⌉⌉⌉⌉⌉

2 1 1 1 1 1 1 푎2 e푥 ⟨푥| + |푥⟩ + ⟨훼∣훽⟩ + ∣훼⟩⟨훽∣ + ⟨ ∣ + ∣ ⟩ + ⟨ ∣ ⟩ + ∣ ⟩⟨ ∣ + ⟨ ∣ + ∣ ⟩ 2 2 2 2 2 2 푏2 e푦2 ⓿❶❷❸❹❺❻❼❽❾❿ + 훢훣퐶⓪①②③④⑤⑥⑦⑧⑨⑩

푢0 1 0 푢 cos 푘푎 sin 푘푎 ( 1 ) = ∑ [( ) 퐶 cos(휔 푡 + 휑 ) + ( ) 퐶 cos(휔 푡 + 휑 )] ⋮ ⋮ ⏟⏟⏟⏟⏟푘+ 푘 푘+ ⋮ ⏟⏟⏟⏟⏟푘− 푘 푘− 푘>0 2 2 푞푘+ 푞푘− 푢훮−1 cos 푘 (훮 − 1) 푎 √훮 sin 푘 (훮 − 1) 푎 √훮

푛 1 2 −1 푗푘 ℱ−1(|푗⟩) = ∑ exp (−2πi ) |푘⟩. 푛 2푛 √2 푘=0 1 1 푛−1 푙 1 2 푘푙 = ∑ ⋯ ∑ exp (−2πi푗 ∑ ) |푘푛−1 ⋯ 푘0⟩ √2푛 2푛 푘푛−1=0 푘0=0 푙=0 1 1 1 푛 푘 = ∑ ⋯ ∑ ⨂ [exp (−2πi푗 푛−푙 ) |푘 ⟩] 푛 푙 푛−푙 √2 푙=1 2 푘푛−1=0 푘0=0 1 푛 1 푘 = ⨂ [ ∑ exp (−2πi푗 푛−푙 ) |푘 ⟩] 푛 푙 푛−푙 √2 푙=1 2 푘푛−푙=0 푛 1 푙 = ⨂ [|0⟩ + e−2πi푗/2 |1⟩ ] 푛 푛−푙 푛−푙 √2 푙=1 1 푛 = ⨂ [|0⟩ + e−2πi(0.푗푙−1…푗0)|1⟩ ] . 푛 푛−푙 푛−푙 √2 푙=1

4 2 2 푡f ∞ 푚 푥f − 푥i cos 휔푡f 푎푛푛π 2 푛π푡 푆 = ∫ [(−휔푥i sin 휔푡 + 휔 cos 휔푡) + ∑ ( ) cos ] d푡 2 0 sin 휔푡f 푛=1 푡f 푡f 2 2 푡f ∞ 푚휔 푥f − 푥i cos 휔푡f 2 2 푛π푡 − ∫ [(푥i cos 휔푡 + sin 휔푡) + ∑ 푎푛 sin ] d푡 2 0 sin 휔푡f 푛=1 푡f 2 ∞ 푡f 2 푚 푎푛푛π 2 푛π푡 푚휔 2 2 푛π푡 = ∑ ∫ [ ( ) cos − 푎푛 sin ] d푡 푛=1 0 2 푡f 푡f 2 푡f 2 2 푡f 푚휔 2 푥f − 푥i cos 휔푡f 2 2 + ∫ [푥i − ( ) ] (sin 휔푡 − cos 휔푡) d푡 2 0 sin 휔푡f

2 푡f 푚휔 푥f − 푥i cos 휔푡f − ∫ 4푥i ( )(sin 휔푡 cos 휔푡) d푡. 2 0 sin 휔푡f 푚휔 푈 (푥f, 푡f; 푥i, 푡i) =√ 2πiℏ sin [휔 (푡f − 푡i)]

i푚휔 2 2 × exp { [(푥i + 푥f ) cos [휔 (푡f − 푡i)] − 2푥i푥f]} . 2ℏ sin [휔 (푡f − 푡i)]

5