Another version that makes use of an ASCIIMath-like syntax would also be helpful. The ASCIIMath philosophy would be to render each symbols by at most two ascii expressions: the LaTeX name (if it is short and memorable, without leading backslash) and a short name that resembles the shape of the symbol (if possible, else no second name). The desmos.com graphing calculator is based on MathQuill and uses (a restricted form of) such input.
\mathrm: abc123@! abc123@!
\mathit: abc123@! abc123@! does it work?? cf. abc123@! abc123@!
\mathbf: abc123@! abc123@!
\mathsf: 𝖺𝖻𝖼𝟣𝟤𝟥@! abc123@!
\mathtt: 𝚊𝚋𝚌𝟷𝟸𝟹@! abc123@!
\mathcal, \mathfrak: not available in MathQuill??
\underline: x yz ⎯ ⎯ ⎯ ⎯ ⎯ xyz_, \underline{\sqrt x}: x √ ⎯ ⎯ ⎯ ⎯ ⎯ x_
\overline{xyz}: x yz ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ xyz¯, \overline{\sqrt x} x √ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ x¯
SubSup x_1^2: x 2 1 x12, x_{1}^{2}: x 2 1 x12
subscript x_11 x 1 1 x11, x_{11}: x 11 x11, x\subscript11: x \subscript11 x\subscript11
superscript x^12: x 1 2 x12, x^{12}: x 12 x12, x\superscript12: x \superscript12 x\superscript12, x\supscript12: x \supscript12 x\supscript12
\frac xy: x y xy, \dfrac xy: x y xy, \cfrac xy: x y xy, \fraction xy: \fractionx y \fractionxy
xy\over uv: x yover uv xyoveruv, x{y\over u}v: x yover uv xyoveruv only for live fractions
xy/uv: x y/uv xy/uv, x{y/u}v: x y/uv xy/uv only for live fractions
\sqrt{x^2}: x 2 ‾ ‾ √ x2, \sqrt[n]{x^n}: x n ‾ ‾ √ n xnn, root and bar have small gap in Firefox
(), [], \left\{\right\}, \langle, \rangle: (),[],(],{},l ef t l angl er ight r angl e (),[],(],{},leftlanglerightrangle, \left{\right} need to be matched, \{\},\langle,\rangle don't work??
& lang; ⟨ ⟨, & rang; ⟩ ⟩,
pipe |: |x |x works unmatched
x\text{ hi }y: x hi y x hi y
x\textnormal{ hi }y: x \textnormalhiy x\textnormalhiy
x\textrm{ hi }y: x hi y x hi y
x\textup{ hi }y: x \textuphiy x\textuphiy
x\textmd{ hi }y: x \textmdhiy x\textmdhiy
a \emph{all}b: a\emphal l b a\emphallb, a \em{all}b: a\emal l b a\emallb why do \em??
a \italic{all}b: a\italical l b a\italicallb, a \italics{all}b: a\italicsal l b a\italicsallb ??
x\textit{ hi }y: x hi y x hi y
x\textbf{ hi }y: x hi y x hi y, x\bold{ hi }y: x \boldhiy x\boldhiy, x\strong{ hi }y: x \stronghiy x\stronghiy,
x\textsf{ hi }y: x 𝗁𝗂 y x hi y, x\sf{ hi }y: x 𝗁𝗂𝗒 xhiy
x\texttt{ hi }y: x 𝚑𝚒 y x hi y, x\tt{ hi }y: x 𝚑𝚒𝚢 xhiy
x\textsc{ HIhi }y: x \textscH I hiy x\textscHIhiy
x\uppercase{ HIhi }y: x \uppercaseH I hiy x\uppercaseHIhiy
x\lowercase{ HIhi }y: x \lowercaseH I hiy x\lowercaseHIhiy
\binom nk: (n k ) (nk)
n\choose k: nchoosek nchoosek does it work?
\vector?
\f: \f \f ?? why?
prime x': x ′ x′, x'': x ″ x″, x''': x ‴ x‴
@: @ @, \&; & &, \%: % %, %:
\alpha: α α
\beta: β β
\gamma: γ γ
\delta: δ δ
\zeta: ζ ζ
\eta: η η
\theta: θ θ
\iota: ι ι
\kappa: κ κ
\mu: μ μ
\nu: ν ν
\xi: ξ ξ
\rho: ρ ρ
\sigma: σ σ
\tau: τ τ
\chi: χ χ
\psi: ψ ψ
\phi: ϕ ϕ //W3C or Unicode? [PJipsen: Comments from mathquill.js]
\phiv: \phiv \phiv //Elsevier and 9573-13
\varphi: φ φ //AMS and LaTeX
\epsilon: ϵ ϵ //W3C or Unicode?
\epsiv: \epsiv \epsiv //Elsevier and 9573-13
\varepsilon: ε ε //AMS and LaTeX
\piv: \piv \piv //W3C/Unicode and Elsevier and 9573-13
\varpi: ϖ ϖ //AMS and LaTeX
\sigmaf: \sigmaf \sigmaf //W3C/Unicode
\sigmav: \sigmav \sigmav //Elsevier
\varsigma: ς ς //LaTeX
\thetav: \thetav \thetav //Elsevier and 9573-13
\vartheta: ϑ ϑ //AMS and LaTeX
\thetasym: \thetasym \thetasym //W3C/Unicode
\upsilon: υ υ //AMS and LaTeX and W3C/Unicode
\upsi: \upsi \upsi //Elsevier and 9573-13
//these aren't even mentioned in the HTML character entity references
\gammad: \gammad \gammad //Elsevier
\Gammad: \Gammad \Gammad //9573-13 -- was this a typo in the reference (see above)
\digamma: ϝ ϝ //LaTeX
\kappav: \kappav \kappav //Elsevier
\varkappa: ϰ ϰ //AMS and LaTeX
\rhov: \rhov \rhov //Elsevier and 9573-13
\varrho: ϱ ϱ //AMS and LaTeX
//Greek constants, look best in un-italicised Times New Roman
\pi: π π
\lambda: λ λ
//uppercase greek letters
\Upsilon: Υ Υ //LaTeX
\Upsi: \Upsi \Upsi //Elsevier and 9573-13
\upsih: \upsih \upsih //W3C/Unicode "upsilon with hook"
\Upsih: \Upsih \Upsih //'cos it makes sense to me
//other symbols with the same LaTeX command and HTML character entity reference
\Gamma: Γ Γ
\Delta: Δ Δ
\Theta: Θ Θ
\Lambda: Λ Λ
\Xi: Ξ Ξ
\Pi: Π Π
\Sigma: Σ Σ
\Phi: Φ Φ
\Psi: Ψ Ψ
\Omega: Ω Ω
Algebra
x +y x+y
x −y x−y, unary minus −x −x
±x ±x, ∓x ∓x
x*y: x ∗y x∗y, x\cdot y: x ⋅y x⋅y, x\sdot y: x \sdoty x\sdoty
x=y: x =y x=y, x & lt; y: x <y x<y, x& gt;y: x >y x>y can't use lt, gt on keyboard
\sim: ∼ ∼
\cong: ≅ ≅
\equiv: ≡ ≡
\oplus: ⊕ ⊕
\otimes: ⊗ ⊗
\times: × ×
\div: ÷ ÷, \divide: \divide \divide, \divides: \divides \divides
\ne: ≠ ≠, \neq: ≠ ≠
\ast: ∗ ∗, \star: ⋆ ⋆, \loast: \loast \loast, \lowast: \lowast \lowast
\therefor: \therefor \therefor, \therefore: ∴ ∴
\cuz: \cuz \cuz, \because: ∵ ∵
\prop: \prop \prop, \propto: ∝ ∝
\asymp: ≍ ≍, \approx: ≈ ≈
\lt: < <
\gt: > >
\le: ≤ ≤, \leq: ≤ ≤
\ge: ≥ ≥, \geq: ≥ ≥
\isin: \isin \isin, \in: ∈ ∈
\notin: ∉ ∉
\ni: ∋ ∋, \contains: \contains \contains
\notni: \notni \notni, \niton: \niton \niton, \notcontains: \notcontains \notcontains, \doesnotcontain: \doesnotcontain \doesnotcontain
\sub: \sub \sub, \subset: ⊂ ⊂
\sup: sup sup, \supset: ⊃ ⊃, \superset: \superset \superset
\nsub: \nsub \nsub, \notsub: \notsub \notsub, \nsubset: \nsubset \nsubset, \notsubset: \notsubset \notsubset
\nsup: \nsup \nsup, \notsup: \notsup \notsup, \nsupset: \nsupset \nsupset, \notsupset: \notsupset \notsupset, \nsuperset: \nsuperset \nsuperset, \notsuperset: \notsuperset \notsuperset
\sube: \sube \sube, \subeq: \subeq \subeq, \subsete: \subsete \subsete, \subseteq: ⊆ ⊆
\supe: \supe \supe, \supeq: \supeq \supeq, \supsete: \supsete \supsete, \supseteq: ⊇ ⊇, \supersete: \supersete \supersete, \superseteq: \superseteq \superseteq
\nsube: \nsube \nsube, \nsubeq: \nsubeq \nsubeq, \notsube: \notsube \notsube, \notsubeq: \notsubeq \notsubeq, \nsubsete: \nsubsete \nsubsete, \nsubseteq: ⊈ ⊈, \notsubsete: \notsubsete \notsubsete, \notsubseteq: \notsubseteq \notsubseteq
\nsupe: \nsupe \nsupe, \nsupeq: \nsupeq \nsupeq, \notsupe: \notsupe \notsupe, \notsupeq: \notsupeq \notsupeq, \nsupsete: \nsupsete \nsupsete, \nsupseteq: ⊉ ⊉, \notsupsete: \notsupsete \notsupsete, \notsupseteq: \notsupseteq \notsupseteq, \nsupersete: \nsupersete \nsupersete, \nsuperseteq: \nsuperseteq \nsuperseteq, \notsupersete: \notsupersete \notsupersete, \notsuperseteq: \notsuperseteq \notsuperseteq
//sum, product, coproduct, integral
\sum: ∑ ∑, \summation: \summation \summation
\prod: ∏ ∏, \product: \product \product
\coprod: ∐ ∐, \coproduct: \coproduct \coproduct
\int: ∫ ∫, \integral: \integral \integral
//the canonical sets of numbers
\N: \N \N, \naturals: \naturals \naturals, \Naturals: \Naturals \Naturals
\P: \P \P, \primes: \primes \primes, \Primes: \Primes \Primes, \projective: \projective \projective, \Projective: \Projective \Projective, \probability: \probability \probability, \Probability: \Probability \Probability
\Z: \Z \Z, \integers: \integers \integers, \Integers: \Integers \Integers
\Q: \Q \Q, \rationals: \rationals \rationals, \Rationals: \Rationals \Rationals
\R: \R \R, \reals: \reals \reals, \Reals: \Reals \Reals
\C: \C \C, \complex: \complex \complex, \Complex: \Complex \Complex, \complexes: \complexes \complexes, \Complexes: \Complexes \Complexes, \complexplane: \complexplane \complexplane, \Complexplane: \Complexplane \Complexplane, \ComplexPlane: \ComplexPlane \ComplexPlane
\H: \H \H, \Hamiltonian: \Hamiltonian \Hamiltonian, \quaternions: \quaternions \quaternions, \Quaternions: \Quaternions \Quaternions
//spacing
\quad: | | ||, \emsp: |\emsp| |\emsp|, \qquad: | | ||
\, \,, \: \:, \; \;, \! \! //these cause mathquill-textbox errors??
//binary operators
\diamond: ⋄ ⋄
\bigtriangleup: △ △
\ominus: ⊖ ⊖
\uplus: ⊎ ⊎
\bigtriangledown: ▽ ▽
\sqcap: ⊓ ⊓
\triangleleft: ◃ ◃
\sqcup: ⊔ ⊔
\triangleright: ▹ ▹
\odot: ⊙ ⊙
\bigcirc: ◯ ◯
\dagger: † †
\ddagger: ‡ ‡
\wr: ≀ ≀
\amalg: ⨿ ⨿
//relationship symbols
\models: ⊨ ⊨
\prec: ≺ ≺
\succ: ≻ ≻
\preceq: ⪯ ⪯
\succeq: ⪰ ⪰
\simeq: ≃ ≃
\mid: ∣ ∣
\ll: ≪ ≪
\gg: ≫ ≫
\parallel: ∥ ∥
\bowtie: ⋈ ⋈
\sqsubset: ⊏ ⊏
\sqsupset: ⊐ ⊐
\smile: ⌣ ⌣
\sqsubseteq: ⊑ ⊑
\sqsupseteq: ⊒ ⊒
\doteq: ≐ ≐
\frown: ⌢ ⌢
\vdash: ⊢ ⊢
\dashv: ⊣ ⊣
//arrows
\longleftarrow: ⟵ ⟵
\longrightarrow: ⟶ ⟶
\Longleftarrow: ⟸ ⟸
\Longrightarrow: ⟹ ⟹
\longleftrightarrow: ⟷ ⟷
\updownarrow: ↕ ↕
\Longleftrightarrow: ⟺ ⟺
\Updownarrow: ⇕ ⇕
\mapsto: ↦ ↦
\nearrow: ↗ ↗
\hookleftarrow: ↩ ↩
\hookrightarrow: ↪ ↪
\searrow: ↘ ↘
\leftharpoonup: ↼ ↼
\rightharpoonup: ⇀ ⇀
\swarrow: ↙ ↙
\leftharpoondown: ↽ ↽
\rightharpoondown: ⇁ ⇁
\nwarrow: ↖ ↖
//Misc
\ldots: … …
\cdots: ⋯ ⋯
\vdots: ⋮ ⋮
\ddots: ⋱ ⋱
\surd: √ √
\triangle: △ △
\ell: ℓ ℓ
\top: ⊤ ⊤
\flat: ♭ ♭
\natural: ♮ ♮
\sharp: ♯ ♯
\wp: ℘ ℘
\bot: ⊥ ⊥
\clubsuit: ♣ ♣
\diamondsuit: ♢ ♢
\heartsuit: ♡ ♡
\spadesuit: ♠ ♠
//variable-sized
\oint: ∮ ∮
\bigcap: ⋂ ⋂
\bigcup: ⋃ ⋃
\bigsqcup: ⨆ ⨆
\bigvee: ⋁ ⋁
\bigwedge: ⋀ ⋀
\bigodot: ⨀ ⨀
\bigotimes: ⨂ ⨂
\bigoplus: ⨁ ⨁
\biguplus: ⨄ ⨄
//delimiters
\lfloor: ⌊ ⌊
\rfloor: ⌋ ⌋
\lceil: ⌈ ⌈
\rceil: ⌉ ⌉
\slash: \slash \slash
\opencurlybrace: \opencurlybrace \opencurlybrace
\closecurlybrace: \closecurlybrace \closecurlybrace
//various symbols
\caret: \caret \caret
\underscore: \underscore \underscore
\backslash: ∖ ∖
\vert: | |
\perp: ⊥ ⊥, \perpendicular: \perpendicular \perpendicular
\nabla: ∇ ∇, \del: \del \del
\hbar: ℏ ℏ
\AA: \AA \AA, \Angstrom: \Angstrom \Angstrom, \angstrom: \angstrom \angstrom
\ring: \ring \ring, \circ: ∘ ∘, \circle: \circle \circle
\bull: \bull \bull, \bullet: ∙ ∙
\setminus: ∖ ∖, \smallsetminus: ∖ ∖
\not: ⧸ ⧸, \neg: ¬ ¬
\dots: … …, \ellip: \ellip \ellip, \hellip: \hellip \hellip, \ellipsis: \ellipsis \ellipsis, \hellipsis: \hellipsis \hellipsis
\converges: \converges \converges, \darr: \darr \darr, \dnarr: \dnarr \dnarr, \dnarrow: \dnarrow \dnarrow, \downarrow: ↓ ↓
\dArr: \dArr \dArr, \dnArr: \dnArr \dnArr, \dnArrow: \dnArrow \dnArrow, \Downarrow: ⇓ ⇓
\diverges: \diverges \diverges, \uarr: \uarr \uarr, \uparrow: ↑ ↑
\uArr: \uArr \uArr, \Uparrow: ⇑ ⇑
\to: → →, \rarr: \rarr \rarr, \rightarrow: → →
\implies: ⟹ ⟹, \rArr: \rArr \rArr, \Rightarrow: ⇒ ⇒
\gets: ← ←, \larr: \larr \larr, \leftarrow: ← ←
\impliedby: ⟸ ⟸, \lArr: \lArr \lArr, \Leftarrow: ⇐ ⇐
\harr: \harr \harr, \lrarr: \lrarr \lrarr, \leftrightarrow: ↔ ↔
\iff: ⟺ ⟺, \hArr: \hArr \hArr, \lrArr: \lrArr \lrArr, \Leftrightarrow: ⇔ ⇔
\Re: ℜ ℜ, \Real: \Real \Real, \real: \real \real
\Im: ℑ ℑ, \imag: \imag \imag, \image: \image \image, \imagin: \imagin \imagin, \imaginary: \imaginary \imaginary, \Imaginary: \Imaginary \Imaginary
\part: \part \part, \partial: ∂ ∂
\inf: inf inf, \infin: \infin \infin, \infty: ∞ ∞, \infinity: \infinity \infinity
\alef: \alef \alef, \alefsym: \alefsym \alefsym, \aleph: ℵ ℵ, \alephsym: \alephsym \alephsym
\forall: ∀ ∀ thankfully mathquill has only one version of forall [PJ]
\xist: \xist \xist, \xists: \xists \xists, \exist: \exist \exist, \exists: ∃ ∃
\and: \and \and, \land: ∧ ∧, \wedge: ∧ ∧
\or: \or \or, \lor: ∨ ∨, \vee: ∨ ∨
\o: \o \o, \O: \O \O, \empty: \empty \empty, \emptyset: ∅ ∅, \oslash: ⊘ ⊘, \Oslash: \Oslash \Oslash, \nothing: \nothing \nothing, \varnothing: ∅ ∅
\cup: ∪ ∪, \union: \union \union
\cap: ∩ ∩, \intersect: \intersect \intersect, \intersection: \intersection \intersection
\deg: deg deg, \degree: \degree \degree
\ang: \ang \ang, \angle: ∠ ∠
\ln: ln ln
\lg: lg lg
\log: log log
\span: \span \span
\proj: \proj \proj
\det: det det
\dim: dim dim
\min: min min
\max: max max
\mod: \mod\mod
\lcm: \lcm \lcm
\gcd: gcd gcd, \gcf: \gcf \gcf, \hcf: \hcf \hcf
\lim: lim lim
\sin: sin sin
\cos: cos cos
\tan: tan tan
\sec: sec sec
\cosec: \cosec \cosec, \csc: csc csc
\cotan: \cotan \cotan, \cot: cot cot
\sinh: sinh sinh
\cosh: cosh cosh
\tanh: tanh tanh
\sech: \sech \sech
\cosech: \cosech \cosech, \csch: \csch \csch
\cotanh: \cotanh \cotanh, \coth: coth coth
\asin: \asin \asin
\acos: \acos \acos
\atan: \atan \atan
\asec: \asec \asec
\acosec: \acosec \acosec, \acsc: \acsc \acsc
\acotan: \acotan \acotan, \acot: \acot \acot
\asinh: \asinh \asinh
\acosh: \acosh \acosh
\atanh: \atanh \atanh
\asech: \asech \asech
\acosech: \acosech \acosech, \acsch: \acsch \acsch
\acotanh: \acotanh \acotanh, \acoth: \acoth \acoth
\arcsin: arcsin arcsin
\arccos: arccos arccos
\arctan: arctan arctan
\arcsec: \arcsec \arcsec
\arccosec: \arccosec \arccosec, \arccsc: \arccsc \arccsc
\arccotan: \arccotan \arccotan, \arccot: \arccot \arccot
\arcsinh: \arcsinh \arcsinh
\arccosh: \arccosh \arccosh
\arctanh: \arctanh \arctanh
\arcsech: \arcsech \arcsech
\arccosech: \arccosech \arccosech, \arccsch: \arccsch \arccsch
\arccotanh: \arccotanh \arccotanh, \arccoth: \arccoth \arccoth