= AsciiMath Grammar and AST

== Grammar

The AsciiMath grammar is defined as

[source]
----
v ::= [A-Za-z] | greek letters | numbers | other constant symbols
u ::= sqrt | text | bb | other unary symbols for font commands
b ::= frac | root | stackrel | other binary symbols
l ::= ( | [ | { | (: | {: | other left brackets
r ::= ) | ] | } | :) | :} | other right brackets
S ::= v | lEr | uS | bSS             Simple expression
I ::= S_S | S^S | S_S^S | S          Intermediate expression
E ::= IE | I/I                       Expression
----

syntax  in EBNF style notation is

[source]
----
asciimath = expr*
expr = intermediate fraction?
fraction = '/' intermediate
intermediate = simp sub? super?
super = '^' simp
sub =  '_' simp
simp = constant | paren_expr | unary_expr | binary_expr | text
paren_expr = lparen asciimath rparen
lparen = '(' | '[' | '{' | '(:' | '{:'
rparen = ')' | ']' | '}' | ':)' | ':}'
unary_expr = unary_op simp
unary_op = 'sqrt' | 'text'
binary_expr = binary_op simp simp
binary_op = 'frac' | 'root' | 'stackrel'
text = '"' [^"]* '"'
constant = number | symbol | identifier
number = '-'? [0-9]+ ( '.' [0-9]+ )?
symbol = /* any string in the symbol table */
identifier = [A-z]
----

== Abstract Syntax Tree

The parser returns an abstract syntax tree consisting of `AsciiMath::AST::Node` objects.
Each expression 'node' of the AST is one of the following forms:

AsciiMath::
`asciimath` is converted to a `AsciiMath::AST::Sequence`.
An empty Array is converted to nil by the parser.
A single element `AsciiMath::AST::Sequence` is unwrapped to just the element.
+
Sequences of expressions are returned as `AsciiMath::AST::Sequence`s as well.

Parentheses::
`lparen asciimath rparen` is converted to `AsciiMath::AST::Paren`.
When a `paren` expression is used to group the operands of unary or binary operators a `AsciiMath::AST::Group` is used instead.
The `group` node retains the parentheses, but these are not rendered in the final output.

Super and Sub Script::
`simp sub`, `simp super` and `simp sub super` are converted to `AsciiMath::AST::SubSup`.

Unary Expressions::
`unary_op simp` is converted to `AsciiMath::AST::UnaryOp`.

Binary Expressions::
`binary_op simp simp` is converted to `AsciiMath::AST::BinaryOp`.
+
`intermediate / intermediate` is converted to `AsciiMath::AST::InfixOp`.

Symbols::
+
`symbol` (mathematical operators, function names, arrows, accents, greek letters, etc.) is converted to `AsciiMath::AST::Symbol`.
The <<symbol_table>> below list all the symbols that are recognized by the parser.

Identifiers::
+
`identifier` is converted to `AsciiMath::AST::Identifier`.

Text::
+
`text` is converted to `AsciiMath::AST::Text`.

Numbers::
+
`number` is converted to `AsciiMath::AST::Number`.

Colors::
+
The first operand of the `color` binary operator is converted to `AsciiMath::AST::Color`.

Matrices::
Matrices in AsciiMath are a special case of nested `paren_expr`.
The matrix itself can be any `paren_expr`.
Inside this outer matrix `paren_expr` each row should be represented as a `paren_expr` using either `()` or `[]`.
Rows must be separated by commas (`,`).
The elements of each row must also be separated by commas.
Each row must contain the same number of elements.
+
When the parser detects a well-formed matrix expression it will strip away the `paren_expr` representation of the matrix and each row.
Instead it returns a `AsciiMath::AST::Matrix`.
The matrix node contains a `AsciiMath::AST::MatrixRow` for each row of the matrix.
Each `AsciiMath::AST::MatrixRow` contains a child node per column.
Empty matrix cells are represented as `AsciiMath::AST::Empty`.

[[symbol_table]]
== Symbol Table

|===
|AsciiMath |Symbol |MathML Value |LaTeX Value

|+ |:plus |+ (https://codepoints.net/U+002B[U+002B]) |+
|++-++ |:minus |++−++ (https://codepoints.net/U+2212[U+2212]) |++-++
|++*++ |:cdot |++⋅++ (https://codepoints.net/U+22C5[U+22C5]) |++\cdot++
|++cdot++ |:cdot |++⋅++ (https://codepoints.net/U+22C5[U+22C5]) |++\cdot++
|++**++ |:ast |++*++ (https://codepoints.net/U+002A[U+002A]) |++*++
|++ast++ |:ast |++*++ (https://codepoints.net/U+002A[U+002A]) |++*++
|++***++ |:star |++⋆++ (https://codepoints.net/U+22C6[U+22C6]) |++\star++
|++star++ |:star |++⋆++ (https://codepoints.net/U+22C6[U+22C6]) |++\star++
|++//++ |:slash |++/++ (https://codepoints.net/U+002F[U+002F]) |++/++
|++\\++ |:backslash |++\++ (https://codepoints.net/U+005C[U+005C]) |++\backslash++
|++backslash++ |:backslash |++\++ (https://codepoints.net/U+005C[U+005C]) |++\backslash++
|++setminus++ |:setminus |++\++ (https://codepoints.net/U+005C[U+005C]) |++\setminus++
|++xx++ |:times |++×++ (https://codepoints.net/U+00D7[U+00D7]) |++\times++
|++times++ |:times |++×++ (https://codepoints.net/U+00D7[U+00D7]) |++\times++
|++\|><++ |:ltimes |++⋉++ (https://codepoints.net/U+22C9[U+22C9]) |++\ltimes++
|++ltimes++ |:ltimes |++⋉++ (https://codepoints.net/U+22C9[U+22C9]) |++\ltimes++
|++><\|++ |:rtimes |++⋊++ (https://codepoints.net/U+22CA[U+22CA]) |++\rtimes++
|++rtimes++ |:rtimes |++⋊++ (https://codepoints.net/U+22CA[U+22CA]) |++\rtimes++
|++\|><\|++ |:bowtie |++⋈++ (https://codepoints.net/U+22C8[U+22C8]) |++\bowtie++
|++bowtie++ |:bowtie |++⋈++ (https://codepoints.net/U+22C8[U+22C8]) |++\bowtie++
|++-:++ |:div |++÷++ (https://codepoints.net/U+00F7[U+00F7]) |++\div++
|++div++ |:div |++÷++ (https://codepoints.net/U+00F7[U+00F7]) |++\div++
|++divide++ |:div |++÷++ (https://codepoints.net/U+00F7[U+00F7]) |++\div++
|++@++ |:circ |++⚬++ (https://codepoints.net/U+26AC[U+26AC]) |++\circ++
|++circ++ |:circ |++⚬++ (https://codepoints.net/U+26AC[U+26AC]) |++\circ++
|++o+++ |:oplus |++⊕++ (https://codepoints.net/U+2295[U+2295]) |++\oplus++
|++oplus++ |:oplus |++⊕++ (https://codepoints.net/U+2295[U+2295]) |++\oplus++
|++ox++ |:otimes |++⊗++ (https://codepoints.net/U+2297[U+2297]) |++\otimes++
|++otimes++ |:otimes |++⊗++ (https://codepoints.net/U+2297[U+2297]) |++\otimes++
|++o.++ |:odot |++⊙++ (https://codepoints.net/U+2299[U+2299]) |++\odot++
|++odot++ |:odot |++⊙++ (https://codepoints.net/U+2299[U+2299]) |++\odot++
|++sum++ |:sum |++∑++ (https://codepoints.net/U+2211[U+2211]) |++\sum++
|++prod++ |:prod |++∏++ (https://codepoints.net/U+220F[U+220F]) |++\prod++
|++^^++ |:wedge |++∧++ (https://codepoints.net/U+2227[U+2227]) |++\wedge++
|++wedge++ |:wedge |++∧++ (https://codepoints.net/U+2227[U+2227]) |++\wedge++
|++^^^++ |:bigwedge |++⋀++ (https://codepoints.net/U+22C0[U+22C0]) |++\bigwedge++
|++bigwedge++ |:bigwedge |++⋀++ (https://codepoints.net/U+22C0[U+22C0]) |++\bigwedge++
|++vv++ |:vee |++∨++ (https://codepoints.net/U+2228[U+2228]) |++\vee++
|++vee++ |:vee |++∨++ (https://codepoints.net/U+2228[U+2228]) |++\vee++
|++vvv++ |:bigvee |++⋁++ (https://codepoints.net/U+22C1[U+22C1]) |++\bigvee++
|++bigvee++ |:bigvee |++⋁++ (https://codepoints.net/U+22C1[U+22C1]) |++\bigvee++
|++nn++ |:cap |++∩++ (https://codepoints.net/U+2229[U+2229]) |++\cap++
|++cap++ |:cap |++∩++ (https://codepoints.net/U+2229[U+2229]) |++\cap++
|++nnn++ |:bigcap |++⋂++ (https://codepoints.net/U+22C2[U+22C2]) |++\bigcap++
|++bigcap++ |:bigcap |++⋂++ (https://codepoints.net/U+22C2[U+22C2]) |++\bigcap++
|++uu++ |:cup |++∪++ (https://codepoints.net/U+222A[U+222A]) |++\cup++
|++cup++ |:cup |++∪++ (https://codepoints.net/U+222A[U+222A]) |++\cup++
|++uuu++ |:bigcup |++⋃++ (https://codepoints.net/U+22C3[U+22C3]) |++\bigcup++
|++bigcup++ |:bigcup |++⋃++ (https://codepoints.net/U+22C3[U+22C3]) |++\bigcup++
|++=++ |:eq |++=++ (https://codepoints.net/U+003D[U+003D]) |++=++
|++!=++ |:ne |++≠++ (https://codepoints.net/U+2260[U+2260]) |++\neq++
|++ne++ |:ne |++≠++ (https://codepoints.net/U+2260[U+2260]) |++\neq++
|++:=++ |:assign |++≔++ (https://codepoints.net/U+2254[U+2254]) |++:=++
|++<++ |:lt |++<++ (https://codepoints.net/U+003C[U+003C]) |++<++
|++lt++ |:lt |++<++ (https://codepoints.net/U+003C[U+003C]) |++<++
|++>++ |:gt |++>++ (https://codepoints.net/U+003E[U+003E]) |++>++
|++gt++ |:gt |++>++ (https://codepoints.net/U+003E[U+003E]) |++>++
|++<=++ |:le |++≤++ (https://codepoints.net/U+2264[U+2264]) |++\le++
|++le++ |:le |++≤++ (https://codepoints.net/U+2264[U+2264]) |++\le++
|++>=++ |:ge |++≥++ (https://codepoints.net/U+2265[U+2265]) |++\ge++
|++ge++ |:ge |++≥++ (https://codepoints.net/U+2265[U+2265]) |++\ge++
|++-<++ |:prec |++≺++ (https://codepoints.net/U+227A[U+227A]) |++\prec++
|++-lt++ |:prec |++≺++ (https://codepoints.net/U+227A[U+227A]) |++\prec++
|++prec++ |:prec |++≺++ (https://codepoints.net/U+227A[U+227A]) |++\prec++
|++>-++ |:succ |++≻++ (https://codepoints.net/U+227B[U+227B]) |++\succ++
|++succ++ |:succ |++≻++ (https://codepoints.net/U+227B[U+227B]) |++\succ++
|++-<=++ |:preceq |++⪯++ (https://codepoints.net/U+2AAF[U+2AAF]) |++\preceq++
|++preceq++ |:preceq |++⪯++ (https://codepoints.net/U+2AAF[U+2AAF]) |++\preceq++
|++>-=++ |:succeq |++⪰++ (https://codepoints.net/U+2AB0[U+2AB0]) |++\succeq++
|++succeq++ |:succeq |++⪰++ (https://codepoints.net/U+2AB0[U+2AB0]) |++\succeq++
|++in++ |:in |++∈++ (https://codepoints.net/U+2208[U+2208]) |++\in++
|++!in++ |:notin |++∉++ (https://codepoints.net/U+2209[U+2209]) |++\notin++
|++notin++ |:notin |++∉++ (https://codepoints.net/U+2209[U+2209]) |++\notin++
|++sub++ |:subset |++⊂++ (https://codepoints.net/U+2282[U+2282]) |++\subset++
|++subset++ |:subset |++⊂++ (https://codepoints.net/U+2282[U+2282]) |++\subset++
|++sup++ |:supset |++⊃++ (https://codepoints.net/U+2283[U+2283]) |++\supset++
|++supset++ |:supset |++⊃++ (https://codepoints.net/U+2283[U+2283]) |++\supset++
|++sube++ |:subseteq |++⊆++ (https://codepoints.net/U+2286[U+2286]) |++\subseteq++
|++subseteq++ |:subseteq |++⊆++ (https://codepoints.net/U+2286[U+2286]) |++\subseteq++
|++supe++ |:supseteq |++⊇++ (https://codepoints.net/U+2287[U+2287]) |++\supseteq++
|++supseteq++ |:supseteq |++⊇++ (https://codepoints.net/U+2287[U+2287]) |++\supseteq++
|++-=++ |:equiv |++≡++ (https://codepoints.net/U+2261[U+2261]) |++\equiv++
|++equiv++ |:equiv |++≡++ (https://codepoints.net/U+2261[U+2261]) |++\equiv++
|++~=++ |:cong |++≅++ (https://codepoints.net/U+2245[U+2245]) |++\cong++
|++cong++ |:cong |++≅++ (https://codepoints.net/U+2245[U+2245]) |++\cong++
|++~~++ |:approx |++≈++ (https://codepoints.net/U+2248[U+2248]) |++\approx++
|++approx++ |:approx |++≈++ (https://codepoints.net/U+2248[U+2248]) |++\approx++
|++prop++ |:propto |++∝++ (https://codepoints.net/U+221D[U+221D]) |++\propto++
|++propto++ |:propto |++∝++ (https://codepoints.net/U+221D[U+221D]) |++\propto++
|++and++ |:and |++and++ (https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+006E[U+006E] https://codepoints.net/U+0064[U+0064]) |++\operatorname{and}++
|++or++ |:or |++or++ (https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0072[U+0072]) |++\operatorname{or}++
|++not++ |:not |++¬++ (https://codepoints.net/U+00AC[U+00AC]) |++\not++
|++neg++ |:not |++¬++ (https://codepoints.net/U+00AC[U+00AC]) |++\not++
|++=>++ |:implies |++⇒++ (https://codepoints.net/U+21D2[U+21D2]) |++\Rightarrow++
|++implies++ |:implies |++⇒++ (https://codepoints.net/U+21D2[U+21D2]) |++\Rightarrow++
|++if++ |:if |++if++ (https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+0066[U+0066]) |++\operatorname{if}++
|++<=>++ |:iff |++⇔++ (https://codepoints.net/U+21D4[U+21D4]) |++\Leftrightarrow++
|++iff++ |:iff |++⇔++ (https://codepoints.net/U+21D4[U+21D4]) |++\Leftrightarrow++
|++AA++ |:forall |++∀++ (https://codepoints.net/U+2200[U+2200]) |++\forall++
|++forall++ |:forall |++∀++ (https://codepoints.net/U+2200[U+2200]) |++\forall++
|++EE++ |:exists |++∃++ (https://codepoints.net/U+2203[U+2203]) |++\exists++
|++exists++ |:exists |++∃++ (https://codepoints.net/U+2203[U+2203]) |++\exists++
|++_\|_++ |:bot |++⊥++ (https://codepoints.net/U+22A5[U+22A5]) |++\bot++
|++bot++ |:bot |++⊥++ (https://codepoints.net/U+22A5[U+22A5]) |++\bot++
|++TT++ |:top |++⊤++ (https://codepoints.net/U+22A4[U+22A4]) |++\top++
|++top++ |:top |++⊤++ (https://codepoints.net/U+22A4[U+22A4]) |++\top++
|++\|--++ |:vdash |++⊢++ (https://codepoints.net/U+22A2[U+22A2]) |++\vdash++
|++vdash++ |:vdash |++⊢++ (https://codepoints.net/U+22A2[U+22A2]) |++\vdash++
|++\|==++ |:models |++⊨++ (https://codepoints.net/U+22A8[U+22A8]) |++\models++
|++models++ |:models |++⊨++ (https://codepoints.net/U+22A8[U+22A8]) |++\models++
|++(++ |:lparen |++(++ (https://codepoints.net/U+0028[U+0028]) |++(++
|++left(++ |:lparen |++(++ (https://codepoints.net/U+0028[U+0028]) |++(++
|++)++ |:rparen |++)++ (https://codepoints.net/U+0029[U+0029]) |++)++
|++right)++ |:rparen |++)++ (https://codepoints.net/U+0029[U+0029]) |++)++
|++[++ |:lbracket |++[++ (https://codepoints.net/U+005B[U+005B]) |++[++
|++left[++ |:lbracket |++[++ (https://codepoints.net/U+005B[U+005B]) |++[++
|++]++ |:rbracket |++]++ (https://codepoints.net/U+005D[U+005D]) |++]++
|++right]++ |:rbracket |++]++ (https://codepoints.net/U+005D[U+005D]) |++]++
|++{++ |:lbrace |++{++ (https://codepoints.net/U+007B[U+007B]) |++\{++
|++}++ |:rbrace |++}++ (https://codepoints.net/U+007D[U+007D]) |++\}++
|++\|++ |:vbar |++\|++ (https://codepoints.net/U+007C[U+007C]) |++\|++
|++:\|:++ |:vbar |++\|++ (https://codepoints.net/U+007C[U+007C]) |++\|++
|++\|:++ |:vbar |++\|++ (https://codepoints.net/U+007C[U+007C]) |++\|++
|++:\|++ |:vbar |++\|++ (https://codepoints.net/U+007C[U+007C]) |++\|++
|++(:++ |:langle |++〈++ (https://codepoints.net/U+2329[U+2329]) |++\langle++
|++<<++ |:langle |++〈++ (https://codepoints.net/U+2329[U+2329]) |++\langle++
|++langle++ |:langle |++〈++ (https://codepoints.net/U+2329[U+2329]) |++\langle++
|++:)++ |:rangle |++〉++ (https://codepoints.net/U+232A[U+232A]) |++\rangle++
|++>>++ |:rangle |++〉++ (https://codepoints.net/U+232A[U+232A]) |++\rangle++
|++rangle++ |:rangle |++〉++ (https://codepoints.net/U+232A[U+232A]) |++\rangle++
|++int++ |:integral |++∫++ (https://codepoints.net/U+222B[U+222B]) |++\int++
|++dx++ |:dx |++dx++ (https://codepoints.net/U+0064[U+0064] https://codepoints.net/U+0078[U+0078]) |++dx++
|++dy++ |:dy |++dy++ (https://codepoints.net/U+0064[U+0064] https://codepoints.net/U+0079[U+0079]) |++dy++
|++dz++ |:dz |++dz++ (https://codepoints.net/U+0064[U+0064] https://codepoints.net/U+007A[U+007A]) |++dz++
|++dt++ |:dt |++dt++ (https://codepoints.net/U+0064[U+0064] https://codepoints.net/U+0074[U+0074]) |++dt++
|++oint++ |:contourintegral |++∮++ (https://codepoints.net/U+222E[U+222E]) |++\oint++
|++del++ |:partial |++∂++ (https://codepoints.net/U+2202[U+2202]) |++\del++
|++partial++ |:partial |++∂++ (https://codepoints.net/U+2202[U+2202]) |++\del++
|++grad++ |:nabla |++∇++ (https://codepoints.net/U+2207[U+2207]) |++\nabla++
|++nabla++ |:nabla |++∇++ (https://codepoints.net/U+2207[U+2207]) |++\nabla++
|+++-++ |:pm |++±++ (https://codepoints.net/U+00B1[U+00B1]) |++\pm++
|++pm++ |:pm |++±++ (https://codepoints.net/U+00B1[U+00B1]) |++\pm++
|++O/++ |:emptyset |++∅++ (https://codepoints.net/U+2205[U+2205]) |++\emptyset++
|++emptyset++ |:emptyset |++∅++ (https://codepoints.net/U+2205[U+2205]) |++\emptyset++
|++oo++ |:infty |++∞++ (https://codepoints.net/U+221E[U+221E]) |++\infty++
|++infty++ |:infty |++∞++ (https://codepoints.net/U+221E[U+221E]) |++\infty++
|++aleph++ |:aleph |++ℵ++ (https://codepoints.net/U+2135[U+2135]) |++\aleph++
|++...++ |:ellipsis |++…++ (https://codepoints.net/U+2026[U+2026]) |++\ldots++
|++ldots++ |:ellipsis |++…++ (https://codepoints.net/U+2026[U+2026]) |++\ldots++
|++:.++ |:therefore |++∴++ (https://codepoints.net/U+2234[U+2234]) |++\therefore++
|++therefore++ |:therefore |++∴++ (https://codepoints.net/U+2234[U+2234]) |++\therefore++
|++:'++ |:because |++∵++ (https://codepoints.net/U+2235[U+2235]) |++\because++
|++because++ |:because |++∵++ (https://codepoints.net/U+2235[U+2235]) |++\because++
|++/_++ |:angle |++∠++ (https://codepoints.net/U+2220[U+2220]) |++\angle++
|++angle++ |:angle |++∠++ (https://codepoints.net/U+2220[U+2220]) |++\angle++
|++/_\++ |:triangle |++△++ (https://codepoints.net/U+25B3[U+25B3]) |++\triangle++
|++triangle++ |:triangle |++△++ (https://codepoints.net/U+25B3[U+25B3]) |++\triangle++
|++'++ |:prime |++′++ (https://codepoints.net/U+2032[U+2032]) |++'++
|++prime++ |:prime |++′++ (https://codepoints.net/U+2032[U+2032]) |++'++
|++tilde++ |:tilde |++~++ (https://codepoints.net/U+007E[U+007E]) |++\~++
|++\ ++ |:nbsp |++ ++ (https://codepoints.net/U+00A0[U+00A0]) |++\;++
|++frown++ |:frown |++⌢++ (https://codepoints.net/U+2322[U+2322]) |++\frown++
|++quad++ |:quad |++  ++ (https://codepoints.net/U+00A0[U+00A0] https://codepoints.net/U+00A0[U+00A0]) |++\quad++
|++qquad++ |:qquad |++    ++ (https://codepoints.net/U+00A0[U+00A0] https://codepoints.net/U+00A0[U+00A0] https://codepoints.net/U+00A0[U+00A0] https://codepoints.net/U+00A0[U+00A0]) |++\qquad++
|++cdots++ |:cdots |++⋯++ (https://codepoints.net/U+22EF[U+22EF]) |++\cdots++
|++vdots++ |:vdots |++⋮++ (https://codepoints.net/U+22EE[U+22EE]) |++\vdots++
|++ddots++ |:ddots |++⋱++ (https://codepoints.net/U+22F1[U+22F1]) |++\ddots++
|++diamond++ |:diamond |++⋄++ (https://codepoints.net/U+22C4[U+22C4]) |++\diamond++
|++square++ |:square |++□++ (https://codepoints.net/U+25A1[U+25A1]) |++\square++
|++\|__++ |:lfloor |++⌊++ (https://codepoints.net/U+230A[U+230A]) |++\lfloor++
|++lfloor++ |:lfloor |++⌊++ (https://codepoints.net/U+230A[U+230A]) |++\lfloor++
|++__\|++ |:rfloor |++⌋++ (https://codepoints.net/U+230B[U+230B]) |++\rfloor++
|++rfloor++ |:rfloor |++⌋++ (https://codepoints.net/U+230B[U+230B]) |++\rfloor++
|++\|~++ |:lceiling |++⌈++ (https://codepoints.net/U+2308[U+2308]) |++\lceil++
|++lceiling++ |:lceiling |++⌈++ (https://codepoints.net/U+2308[U+2308]) |++\lceil++
|++~\|++ |:rceiling |++⌉++ (https://codepoints.net/U+2309[U+2309]) |++\rceil++
|++rceiling++ |:rceiling |++⌉++ (https://codepoints.net/U+2309[U+2309]) |++\rceil++
|++CC++ |:dstruck_captial_c |++ℂ++ (https://codepoints.net/U+2102[U+2102]) |++\mathbb{C}++
|++NN++ |:dstruck_captial_n |++ℕ++ (https://codepoints.net/U+2115[U+2115]) |++\mathbb{N}++
|++QQ++ |:dstruck_captial_q |++ℚ++ (https://codepoints.net/U+211A[U+211A]) |++\mathbb{Q}++
|++RR++ |:dstruck_captial_r |++ℝ++ (https://codepoints.net/U+211D[U+211D]) |++\mathbb{R}++
|++ZZ++ |:dstruck_captial_z |++ℤ++ (https://codepoints.net/U+2124[U+2124]) |++\mathbb{Z}++
|++f++ |:f |++f++ (https://codepoints.net/U+0066[U+0066]) |++f++
|++g++ |:g |++g++ (https://codepoints.net/U+0067[U+0067]) |++g++
|++lim++ |:lim |++lim++ (https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006D[U+006D]) |++\lim++
|++Lim++ |:Lim |++Lim++ (https://codepoints.net/U+004C[U+004C] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006D[U+006D]) |++\operatorname{Lim}++
|++min++ |:min |++min++ (https://codepoints.net/U+006D[U+006D] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006E[U+006E]) |++\min++
|++max++ |:max |++max++ (https://codepoints.net/U+006D[U+006D] https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+0078[U+0078]) |++\max++
|++sin++ |:sin |++sin++ (https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006E[U+006E]) |++\sin++
|++Sin++ |:Sin |++Sin++ (https://codepoints.net/U+0053[U+0053] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006E[U+006E]) |++\operatorname{Sin}++
|++cos++ |:cos |++cos++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0073[U+0073]) |++\cos++
|++Cos++ |:Cos |++Cos++ (https://codepoints.net/U+0043[U+0043] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0073[U+0073]) |++\operatorname{Cos}++
|++tan++ |:tan |++tan++ (https://codepoints.net/U+0074[U+0074] https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+006E[U+006E]) |++\tan++
|++Tan++ |:Tan |++Tan++ (https://codepoints.net/U+0054[U+0054] https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+006E[U+006E]) |++\operatorname{Tan}++
|++sinh++ |:sinh |++sinh++ (https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006E[U+006E] https://codepoints.net/U+0068[U+0068]) |++\sinh++
|++Sinh++ |:Sinh |++Sinh++ (https://codepoints.net/U+0053[U+0053] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006E[U+006E] https://codepoints.net/U+0068[U+0068]) |++\operatorname{Sinh}++
|++cosh++ |:cosh |++cosh++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0068[U+0068]) |++\cosh++
|++Cosh++ |:Cosh |++Cosh++ (https://codepoints.net/U+0043[U+0043] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0068[U+0068]) |++\operatorname{Cosh}++
|++tanh++ |:tanh |++tanh++ (https://codepoints.net/U+0074[U+0074] https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+006E[U+006E] https://codepoints.net/U+0068[U+0068]) |++\tanh++
|++Tanh++ |:Tanh |++Tanh++ (https://codepoints.net/U+0054[U+0054] https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+006E[U+006E] https://codepoints.net/U+0068[U+0068]) |++\operatorname{Tanh}++
|++cot++ |:cot |++cot++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0074[U+0074]) |++\cot++
|++Cot++ |:Cot |++Cot++ (https://codepoints.net/U+0043[U+0043] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0074[U+0074]) |++\operatorname{Cot}++
|++sec++ |:sec |++sec++ (https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0065[U+0065] https://codepoints.net/U+0063[U+0063]) |++\sec++
|++Sec++ |:Sec |++Sec++ (https://codepoints.net/U+0053[U+0053] https://codepoints.net/U+0065[U+0065] https://codepoints.net/U+0063[U+0063]) |++\operatorname{Sec}++
|++csc++ |:csc |++csc++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0063[U+0063]) |++\csc++
|++Csc++ |:Csc |++Csc++ (https://codepoints.net/U+0043[U+0043] https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0063[U+0063]) |++\operatorname{Csc}++
|++arcsin++ |:arcsin |++arcsin++ (https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+0072[U+0072] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006E[U+006E]) |++\arcsin++
|++arccos++ |:arccos |++arccos++ (https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+0072[U+0072] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0073[U+0073]) |++\arccos++
|++arctan++ |:arctan |++arctan++ (https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+0072[U+0072] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0074[U+0074] https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+006E[U+006E]) |++\arctan++
|++coth++ |:coth |++coth++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0074[U+0074] https://codepoints.net/U+0068[U+0068]) |++\coth++
|++sech++ |:sech |++sech++ (https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0065[U+0065] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0068[U+0068]) |++\operatorname{sech}++
|++csch++ |:csch |++csch++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0073[U+0073] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0068[U+0068]) |++\operatorname{csch}++
|++exp++ |:exp |++exp++ (https://codepoints.net/U+0065[U+0065] https://codepoints.net/U+0078[U+0078] https://codepoints.net/U+0070[U+0070]) |++\exp++
|++abs++ |:abs |++abs++ (https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+0062[U+0062] https://codepoints.net/U+0073[U+0073]) |++\abs++
|++Abs++ |:abs |++abs++ (https://codepoints.net/U+0061[U+0061] https://codepoints.net/U+0062[U+0062] https://codepoints.net/U+0073[U+0073]) |++\abs++
|++norm++ |:norm |++norm++ (https://codepoints.net/U+006E[U+006E] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0072[U+0072] https://codepoints.net/U+006D[U+006D]) |++\norm++
|++floor++ |:floor |++floor++ (https://codepoints.net/U+0066[U+0066] https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0072[U+0072]) |++\floor++
|++ceil++ |:ceil |++ceil++ (https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0065[U+0065] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006C[U+006C]) |++\ceil++
|++log++ |:log |++log++ (https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0067[U+0067]) |++\log++
|++Log++ |:Log |++Log++ (https://codepoints.net/U+004C[U+004C] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0067[U+0067]) |++\operatorname{Log}++
|++ln++ |:ln |++ln++ (https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+006E[U+006E]) |++\ln++
|++Ln++ |:Ln |++Ln++ (https://codepoints.net/U+004C[U+004C] https://codepoints.net/U+006E[U+006E]) |++\operatorname{Ln}++
|++det++ |:det |++det++ (https://codepoints.net/U+0064[U+0064] https://codepoints.net/U+0065[U+0065] https://codepoints.net/U+0074[U+0074]) |++\det++
|++dim++ |:dim |++dim++ (https://codepoints.net/U+0064[U+0064] https://codepoints.net/U+0069[U+0069] https://codepoints.net/U+006D[U+006D]) |++\dim++
|++mod++ |:mod |++mod++ (https://codepoints.net/U+006D[U+006D] https://codepoints.net/U+006F[U+006F] https://codepoints.net/U+0064[U+0064]) |++\mod++
|++gcd++ |:gcd |++gcd++ (https://codepoints.net/U+0067[U+0067] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+0064[U+0064]) |++\gcd++
|++lcm++ |:lcm |++lcm++ (https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+0063[U+0063] https://codepoints.net/U+006D[U+006D]) |++\operatorname{lcm}++
|++lub++ |:lub |++lub++ (https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+0075[U+0075] https://codepoints.net/U+0062[U+0062]) |++\operatorname{lub}++
|++glb++ |:glb |++glb++ (https://codepoints.net/U+0067[U+0067] https://codepoints.net/U+006C[U+006C] https://codepoints.net/U+0062[U+0062]) |++\operatorname{glb}++
|++uarr++ |:uparrow |++↑++ (https://codepoints.net/U+2191[U+2191]) |++\uparrow++
|++uparrow++ |:uparrow |++↑++ (https://codepoints.net/U+2191[U+2191]) |++\uparrow++
|++darr++ |:downarrow |++↓++ (https://codepoints.net/U+2193[U+2193]) |++\downarrow++
|++downarrow++ |:downarrow |++↓++ (https://codepoints.net/U+2193[U+2193]) |++\downarrow++
|++rarr++ |:rightarrow |++→++ (https://codepoints.net/U+2192[U+2192]) |++\rightarrow++
|++rightarrow++ |:rightarrow |++→++ (https://codepoints.net/U+2192[U+2192]) |++\rightarrow++
|++->++ |:to |++→++ (https://codepoints.net/U+2192[U+2192]) |++\rightarrow++
|++to++ |:to |++→++ (https://codepoints.net/U+2192[U+2192]) |++\rightarrow++
|++>->++ |:rightarrowtail |++↣++ (https://codepoints.net/U+21A3[U+21A3]) |++\rightarrowtail++
|++rightarrowtail++ |:rightarrowtail |++↣++ (https://codepoints.net/U+21A3[U+21A3]) |++\rightarrowtail++
|++->>++ |:twoheadrightarrow |++↠++ (https://codepoints.net/U+21A0[U+21A0]) |++\twoheadrightarrow++
|++twoheadrightarrow++ |:twoheadrightarrow |++↠++ (https://codepoints.net/U+21A0[U+21A0]) |++\twoheadrightarrow++
|++>->>++ |:twoheadrightarrowtail |++⤖++ (https://codepoints.net/U+2916[U+2916]) |++\twoheadrightarrowtail++
|++twoheadrightarrowtail++ |:twoheadrightarrowtail |++⤖++ (https://codepoints.net/U+2916[U+2916]) |++\twoheadrightarrowtail++
|++\|->++ |:mapsto |++↦++ (https://codepoints.net/U+21A6[U+21A6]) |++\mapsto++
|++mapsto++ |:mapsto |++↦++ (https://codepoints.net/U+21A6[U+21A6]) |++\mapsto++
|++larr++ |:leftarrow |++←++ (https://codepoints.net/U+2190[U+2190]) |++\leftarrow++
|++leftarrow++ |:leftarrow |++←++ (https://codepoints.net/U+2190[U+2190]) |++\leftarrow++
|++harr++ |:leftrightarrow |++↔++ (https://codepoints.net/U+2194[U+2194]) |++\leftrightarrow++
|++leftrightarrow++ |:leftrightarrow |++↔++ (https://codepoints.net/U+2194[U+2194]) |++\leftrightarrow++
|++rArr++ |:Rightarrow |++⇒++ (https://codepoints.net/U+21D2[U+21D2]) |++\Rightarrow++
|++Rightarrow++ |:Rightarrow |++⇒++ (https://codepoints.net/U+21D2[U+21D2]) |++\Rightarrow++
|++lArr++ |:Leftarrow |++⇐++ (https://codepoints.net/U+21D0[U+21D0]) |++\Leftarrow++
|++Leftarrow++ |:Leftarrow |++⇐++ (https://codepoints.net/U+21D0[U+21D0]) |++\Leftarrow++
|++hArr++ |:Leftrightarrow |++⇔++ (https://codepoints.net/U+21D4[U+21D4]) |++\Leftrightarrow++
|++Leftrightarrow++ |:Leftrightarrow |++⇔++ (https://codepoints.net/U+21D4[U+21D4]) |++\Leftrightarrow++
|++sqrt++ |:sqrt |++sqrt++ () |++\sqrt++
|++root++ |:root |++root++ () |++\root++
|++frac++ |:frac |++frac++ () |++\frac++
|++/++ |:frac |++frac++ () |++\frac++
|++stackrel++ |:stackrel |++stackrel++ () |++\stackrel++
|++overset++ |:overset |++overset++ () |++\overset++
|++underset++ |:underset |++underset++ () |++\underset++
|++color++ |:color |++color++ () |++\color++
|++_++ |:sub |++_++ (https://codepoints.net/U+005F[U+005F]) |++\text{–}++
|++^++ |:sup |++^++ (https://codepoints.net/U+005E[U+005E]) |++\text{^}++
|++hat++ |:hat |++^++ (https://codepoints.net/U+005E[U+005E]) |++\hat++
|++bar++ |:overline |++¯++ (https://codepoints.net/U+00AF[U+00AF]) |++\overline++
|++vec++ |:vec |++→++ (https://codepoints.net/U+2192[U+2192]) |++\vec++
|++dot++ |:dot |++.++ (https://codepoints.net/U+002E[U+002E]) |++\dot++
|++ddot++ |:ddot |++..++ (https://codepoints.net/U+002E[U+002E] https://codepoints.net/U+002E[U+002E]) |++\ddot++
|++overarc++ |:overarc |++⏜++ (https://codepoints.net/U+23DC[U+23DC]) |++\overarc++
|++overparen++ |:overarc |++⏜++ (https://codepoints.net/U+23DC[U+23DC]) |++\overarc++
|++ul++ |:underline |++_++ (https://codepoints.net/U+005F[U+005F]) |++\underline++
|++underline++ |:underline |++_++ (https://codepoints.net/U+005F[U+005F]) |++\underline++
|++ubrace++ |:underbrace |++⏟++ (https://codepoints.net/U+23DF[U+23DF]) |++\underbrace++
|++underbrace++ |:underbrace |++⏟++ (https://codepoints.net/U+23DF[U+23DF]) |++\underbrace++
|++obrace++ |:overbrace |++⏞++ (https://codepoints.net/U+23DE[U+23DE]) |++\overbrace++
|++overbrace++ |:overbrace |++⏞++ (https://codepoints.net/U+23DE[U+23DE]) |++\overbrace++
|++cancel++ |:cancel |++cancel++ () |++\cancel++
|++bb++ |:bold |++bold++ () |++\mathbf++
|++bbb++ |:double_struck |++double_struck++ () |++\mathbb++
|++ii++ |:italic |++italic++ () |++\mathit++
|++bii++ |:bold_italic |++bold_italic++ () |++\mathbf++
|++cc++ |:script |++script++ () |++\mathscr++
|++bcc++ |:bold_script |++bold_script++ () |++\mathscr++
|++tt++ |:monospace |++monospace++ () |++\mathtt++
|++fr++ |:fraktur |++fraktur++ () |++\mathfrak++
|++bfr++ |:bold_fraktur |++bold_fraktur++ () |++\mathfrak++
|++sf++ |:sans_serif |++sans_serif++ () |++\mathsf++
|++bsf++ |:bold_sans_serif |++bold_sans_serif++ () |++\mathsf++
|++sfi++ |:sans_serif_italic |++sans_serif_italic++ () |++\mathsf++
|++sfbi++ |:sans_serif_bold_italic |++sans_serif_bold_italic++ () |++\mathsf++
|++alpha++ |:alpha |++α++ (https://codepoints.net/U+03B1[U+03B1]) |++\alpha++
|++Alpha++ |:Alpha |++Α++ (https://codepoints.net/U+0391[U+0391]) |++\Alpha++
|++beta++ |:beta |++β++ (https://codepoints.net/U+03B2[U+03B2]) |++\beta++
|++Beta++ |:Beta |++Β++ (https://codepoints.net/U+0392[U+0392]) |++\Beta++
|++gamma++ |:gamma |++γ++ (https://codepoints.net/U+03B3[U+03B3]) |++\gamma++
|++Gamma++ |:Gamma |++Γ++ (https://codepoints.net/U+0393[U+0393]) |++\Gamma++
|++delta++ |:delta |++δ++ (https://codepoints.net/U+03B4[U+03B4]) |++\delta++
|++Delta++ |:Delta |++Δ++ (https://codepoints.net/U+0394[U+0394]) |++\Delta++
|++epsi++ |:epsilon |++ε++ (https://codepoints.net/U+03B5[U+03B5]) |++\epsilon++
|++epsilon++ |:epsilon |++ε++ (https://codepoints.net/U+03B5[U+03B5]) |++\epsilon++
|++Epsilon++ |:Epsilon |++Ε++ (https://codepoints.net/U+0395[U+0395]) |++\Epsilon++
|++varepsilon++ |:varepsilon |++ɛ++ (https://codepoints.net/U+025B[U+025B]) |++\varepsilon++
|++zeta++ |:zeta |++ζ++ (https://codepoints.net/U+03B6[U+03B6]) |++\zeta++
|++Zeta++ |:Zeta |++Ζ++ (https://codepoints.net/U+0396[U+0396]) |++\Zeta++
|++eta++ |:eta |++η++ (https://codepoints.net/U+03B7[U+03B7]) |++\eta++
|++Eta++ |:Eta |++Η++ (https://codepoints.net/U+0397[U+0397]) |++\Eta++
|++theta++ |:theta |++θ++ (https://codepoints.net/U+03B8[U+03B8]) |++\theta++
|++Theta++ |:Theta |++Θ++ (https://codepoints.net/U+0398[U+0398]) |++\Theta++
|++vartheta++ |:vartheta |++ϑ++ (https://codepoints.net/U+03D1[U+03D1]) |++\vartheta++
|++iota++ |:iota |++ι++ (https://codepoints.net/U+03B9[U+03B9]) |++\iota++
|++Iota++ |:Iota |++Ι++ (https://codepoints.net/U+0399[U+0399]) |++\Iota++
|++kappa++ |:kappa |++κ++ (https://codepoints.net/U+03BA[U+03BA]) |++\kappa++
|++Kappa++ |:Kappa |++Κ++ (https://codepoints.net/U+039A[U+039A]) |++\Kappa++
|++lambda++ |:lambda |++λ++ (https://codepoints.net/U+03BB[U+03BB]) |++\lambda++
|++Lambda++ |:Lambda |++Λ++ (https://codepoints.net/U+039B[U+039B]) |++\Lambda++
|++mu++ |:mu |++μ++ (https://codepoints.net/U+03BC[U+03BC]) |++\mu++
|++Mu++ |:Mu |++Μ++ (https://codepoints.net/U+039C[U+039C]) |++\Mu++
|++nu++ |:nu |++ν++ (https://codepoints.net/U+03BD[U+03BD]) |++\nu++
|++Nu++ |:Nu |++Ν++ (https://codepoints.net/U+039D[U+039D]) |++\Nu++
|++xi++ |:xi |++ξ++ (https://codepoints.net/U+03BE[U+03BE]) |++\xi++
|++Xi++ |:Xi |++Ξ++ (https://codepoints.net/U+039E[U+039E]) |++\Xi++
|++omicron++ |:omicron |++ο++ (https://codepoints.net/U+03BF[U+03BF]) |++\omicron++
|++Omicron++ |:Omicron |++Ο++ (https://codepoints.net/U+039F[U+039F]) |++\Omicron++
|++pi++ |:pi |++π++ (https://codepoints.net/U+03C0[U+03C0]) |++\pi++
|++Pi++ |:Pi |++Π++ (https://codepoints.net/U+03A0[U+03A0]) |++\Pi++
|++rho++ |:rho |++ρ++ (https://codepoints.net/U+03C1[U+03C1]) |++\rho++
|++Rho++ |:Rho |++Ρ++ (https://codepoints.net/U+03A1[U+03A1]) |++\Rho++
|++sigma++ |:sigma |++σ++ (https://codepoints.net/U+03C3[U+03C3]) |++\sigma++
|++Sigma++ |:Sigma |++Σ++ (https://codepoints.net/U+03A3[U+03A3]) |++\Sigma++
|++tau++ |:tau |++τ++ (https://codepoints.net/U+03C4[U+03C4]) |++\tau++
|++Tau++ |:Tau |++Τ++ (https://codepoints.net/U+03A4[U+03A4]) |++\Tau++
|++upsilon++ |:upsilon |++υ++ (https://codepoints.net/U+03C5[U+03C5]) |++\upsilon++
|++Upsilon++ |:Upsilon |++Υ++ (https://codepoints.net/U+03A5[U+03A5]) |++\Upsilon++
|++phi++ |:phi |++φ++ (https://codepoints.net/U+03C6[U+03C6]) |++\phi++
|++Phi++ |:Phi |++Φ++ (https://codepoints.net/U+03A6[U+03A6]) |++\Phi++
|++varphi++ |:varphi |++ϕ++ (https://codepoints.net/U+03D5[U+03D5]) |++\varphi++
|++chi++ |:chi |++χ++ (https://codepoints.net/U+03C7[U+03C7]) |++\chi++
|++Chi++ |:Chi |++Χ++ (https://codepoints.net/U+03A7[U+03A7]) |++\Chi++
|++psi++ |:psi |++ψ++ (https://codepoints.net/U+03C8[U+03C8]) |++\psi++
|++Psi++ |:Psi |++Ψ++ (https://codepoints.net/U+03A8[U+03A8]) |++\Psi++
|++omega++ |:omega |++ω++ (https://codepoints.net/U+03C9[U+03C9]) |++\omega++
|++Omega++ |:Omega |++Ω++ (https://codepoints.net/U+03A9[U+03A9]) |++\Omega++
|===