# LaTeX syntax for mathematics

Abstract

Docutils supports mathematical content with a "math" directive and role. The input format is LaTeX math syntax[1] with support for literal Unicode symbols.

## 1 Inline formulas and displayed equations

The math role can be used for inline mathematical expressions: :math:`\psi(r) = \exp(-2r)` will produce ψ(r)=exp(-2 r). Inside the backtics you can write anything you would write between dollar signs in a LaTeX document. [1]

Tip

If you put .. default-role:: math at the top of your document, you can write `x^2` instead of the longer version: :math:`x^2`. You can also introduce an abbreviation like this .. role:: m(math). That will allow you to write :m:`x^2` or `x^2`:m:.

The math directive is used for displayed equations. It corresponds to an equation* or align* environment in a LaTeX document. If you write:

    .. math:: \psi(r) = e^{-2r}

you will get:

ψ(r)= e-2 r

A more complex example is the definition of the Fourier transform:

    .. math::
       :name: Fourier transform

       (\mathcal{F}f)(y)
        = \frac{1}{\sqrt{2\pi}^{\ n}}
          \int_{\mathbb{R}^n} f(x)\,
          e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.

which is rendered as:

      (\mathcal{F}f)(y)
       = \frac{1}{\sqrt{2\pi}^{\ n}}
         \int_{\mathbb{R}^n} f(x)\,
         e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 60)

TeX to MathML converter `ttm` failed:

Unknown command \mathbb in equation, Line 2.

The :name: option puts a label on the equation that can be linked to by hyperlink references.

Displayed equations can use \\ and & for line shifts and alignments:

    .. math::

     a &= (x + y)^2         &  b &= (x - y)^2 \\
       &= x^2 + 2xy + y^2   &    &= x^2 - 2xy + y^2

LaTeX output will wrap it in an align* environment. The result is:

    a & = (x + y)^2         &  b & = (x - y)^2 \\
      & = x^2 + 2xy + y^2   &    & = x^2 - 2xy + y^2

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 81)

TeX to MathML converter `ttm` failed:

Unknown or ignored environment: \begin{align*} Line 1.

The aligned environment can be used as a component in a containing expression. E.g.,

    .. math::
      \left.
        \begin{aligned}
          B' & = -\partial\times E,         \\
          E' & = \partial\times B - 4\pi j,
        \end{aligned}
      \right\}
      \qquad \text{Maxwell’s equations}

results in

    \left.
      \begin{aligned}
        B' & = -\partial\times E         \\
        E' & =  \partial\times B - 4\pi j
      \end{aligned}
    \;\right\}
    \qquad \text{Maxwell’s equations.}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 100)

'latin-1' codec can't encode character '\u2019' in position 168: ordinal not in range(256)

[1] (1,2)

The supported LaTeX commands include AMS extensions (see, e.g., the Short Math Guide). Some of the shown symbols require the "amssymb" LaTeX package (or another package providing the AMS symbol macros) when exported with the "latex" writer.

The support is limited to a subset of LaTeX math by the conversion required for many output formats. For HTML, the math_output configuration setting (or the corresponding --math-output command line option) selects between alternative output formats with different subsets of supported elements. If a writer does not support math typesetting, the content is inserted verbatim.

## 2 Mathematical symbols

The following tables are adapted from the first edition of "The LaTeX Companion" (Goossens, Mittelbach, Samarin) and the AMS Short Math Guide.

### 2.1 Accents and embellishments

The "narrow" accents are intended for a single-letter base.

\'x | \acute{x} | t · | \dot{t} | \`x | \grave{x} | x → | \vec{x}
v ‾ | \bar{v} | t ·· | \ddot{t} | x ^ | \hat{x} |  |
x ˘ | \breve{x} | \dddot{t} | \dddot{t} | \mathring{x} | \mathring{x} |  |
x ∨ | \check{x} | \ddddot{t} | \ddddot{t} | n ~ | \tilde{n} |  |

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 150)

TeX to MathML converter `ttm` failed:

Unknown command \dddot in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 150)

TeX to MathML converter `ttm` failed:

Unknown command \mathring in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 151)

TeX to MathML converter `ttm` failed:

Unknown command \ddddot in equation, Line 1.

When adding an accent to an i or j in math, dotless variants can be obtained with \imath and \jmath: ı ^ , ȷ → .

For embellishments that span multiple symbols, use:

gbi ˜ | \widetilde{gbi} | gbi ^ | \widehat{gbi}
gbi ‾ | \overline{gbi} | gbi ‾ | \underline{gbi}
gbi ⏞ | \overbrace{gbi} | gbi ⏟ | \underbrace{gbi}
gbi ← | \overleftarrow{gbi} | \underleftarrow{gbi} | \underleftarrow{gbi}
gbi → | \overrightarrow{gbi} | \underrightarrow{gbi} | \underrightarrow{gbi}
\overleftrightarrow{gbi} | \overleftrightarrow{gbi} | \underleftrightarrow{gbi} | \underleftrightarrow{gbi}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 165)

TeX to MathML converter `ttm` failed:

Unknown command \underleftarrow in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 166)

TeX to MathML converter `ttm` failed:

Unknown command \underrightarrow in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 167)

TeX to MathML converter `ttm` failed:

Unknown command \overleftrightarrow in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 167)

TeX to MathML converter `ttm` failed:

Unknown command \underleftrightarrow in equation, Line 1.

### 2.2 Binary operators

* | * | \circledast | \circledast | ⊖ | \ominus
+ | + | \circledcirc | \circledcirc | ⊕ | \oplus
- | - | \circleddash | \circleddash | ø | \oslash
: | : | ∪ | \cup | ⊗ | \otimes
\Cap | \Cap | \curlyvee | \curlyvee | ± | \pm
\Cup | \Cup | \curlywedge | \curlywedge | \rightthreetimes | \rightthreetimes
⨿ | \amalg | † | \dagger | \rtimes | \rtimes
* | \ast | ‡ | \ddagger | ∖ | \setminus
◯ | \bigcirc | ◊ | \diamond | \smallsetminus | \smallsetminus
▽ | \bigtriangledown | ÷ | \div | ⊓ | \sqcap
△ | \bigtriangleup | \divideontimes | \divideontimes | ⊔ | \sqcup
\boxdot | \boxdot | \dotplus | \dotplus | ☆ | \star
\boxminus | \boxminus | \doublebarwedge | \doublebarwedge | × | \times
\boxplus | \boxplus | \gtrdot | \gtrdot | ◃ | \triangleleft
\boxtimes | \boxtimes | \intercal | \intercal | ▹ | \triangleright
• | \bullet | \leftthreetimes | \leftthreetimes | ⊎ | \uplus
∩ | \cap | \lessdot | \lessdot | ∨ | \vee
· | \cdot | \ltimes | \ltimes | \veebar | \veebar
\centerdot | \centerdot | ∓ | \mp | ∧ | \wedge
∘ | \circ | ⊙ | \odot | ≀ | \wr

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 176)

TeX to MathML converter `ttm` failed:

Unknown command \circledast in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 177)

TeX to MathML converter `ttm` failed:

Unknown command \circledcirc in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 178)

TeX to MathML converter `ttm` failed:

Unknown command \circleddash in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 180)

TeX to MathML converter `ttm` failed:

Unknown command \Cap in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 180)

TeX to MathML converter `ttm` failed:

Unknown command \curlyvee in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 181)

TeX to MathML converter `ttm` failed:

Unknown command \Cup in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 181)

TeX to MathML converter `ttm` failed:

Unknown command \curlywedge in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 181)

TeX to MathML converter `ttm` failed:

Unknown command \rightthreetimes in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 182)

TeX to MathML converter `ttm` failed:

Unknown command \rtimes in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 184)

TeX to MathML converter `ttm` failed:

Unknown command \smallsetminus in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 186)

TeX to MathML converter `ttm` failed:

Unknown command \divideontimes in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 187)

TeX to MathML converter `ttm` failed:

Unknown command \boxdot in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 187)

TeX to MathML converter `ttm` failed:

Unknown command \dotplus in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 188)

TeX to MathML converter `ttm` failed:

Unknown command \boxminus in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 188)

TeX to MathML converter `ttm` failed:

Unknown command \doublebarwedge in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 189)

TeX to MathML converter `ttm` failed:

Unknown command \boxplus in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 189)

TeX to MathML converter `ttm` failed:

Unknown command \gtrdot in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 190)

TeX to MathML converter `ttm` failed:

Unknown command \boxtimes in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 190)

TeX to MathML converter `ttm` failed:

Unknown command \intercal in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 191)

TeX to MathML converter `ttm` failed:

Unknown command \leftthreetimes in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 192)

TeX to MathML converter `ttm` failed:

Unknown command \lessdot in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 193)

TeX to MathML converter `ttm` failed:

Unknown command \ltimes in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 193)

TeX to MathML converter `ttm` failed:

Unknown command \veebar in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 194)

TeX to MathML converter `ttm` failed:

Unknown command \centerdot in equation, Line 1.

### 2.3 Extensible delimiters

Unless you indicate otherwise, delimiters in math formulas remain at the standard size regardless of the height of the enclosed material. To get adaptable sizes, use \left and \right prefixes, for example g(A, B, Y)=f(A, B, X= h[X] (Y)) or

a n = ( 1 2 )n

Use . for "empty" delimiters:

A= 1 1-n |n=0 ∞

See also the commands for fixed delimiter sizes below.

The following symbols extend when used with \left and \right:

#### 2.3.1 Pairing delimiters

() | ( ) | ⟨⟩ | \langle \rangle
[] | [ ] | ⌈⌉ | \lceil \rceil
{} | \{ \} | ⌊⌋ | \lfloor \rfloor
\lvert \rvert | \lvert \rvert | \lgroup \rgroup | \lgroup \rgroup
\lVert \rVert | \lVert \rVert | \lmoustache \rmoustache | \lmoustache \rmoustache

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 224)

TeX to MathML converter `ttm` failed:

Unknown command \lvert in equation, Line 1. Unknown command \rvert in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 224)

TeX to MathML converter `ttm` failed:

Unknown command \lgroup in equation, Line 1. Unknown command \rgroup in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 225)

TeX to MathML converter `ttm` failed:

Unknown command \lVert in equation, Line 1. Unknown command \rVert in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 225)

TeX to MathML converter `ttm` failed:

Unknown command \lmoustache in equation, Line 1. Unknown command \rmoustache in equation, Line 1.

#### 2.3.2 Nonpairing delimiters

| | | | | | \vert | \arrowvert | \arrowvert
‖ | \| | ‖ | \Vert | \Arrowvert | \Arrowvert
/ | / | \ | \backslash | \bracevert | \bracevert

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 234)

TeX to MathML converter `ttm` failed:

Unknown command \arrowvert in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 235)

TeX to MathML converter `ttm` failed:

Unknown command \Arrowvert in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 236)

TeX to MathML converter `ttm` failed:

Unknown command \bracevert in equation, Line 1.

The use of | and \| for pairs of vertical bars may produce incorrect spacing, e.g., |k|=|-k| produces |k|=|-k| and |\sin(x)| produces |sin(x)|. The pairing delimiters, e.g. \lvert -k\rvert and \lvert\sin(x)\rvert, prevent this problem.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 239)

TeX to MathML converter `ttm` failed:

Unknown command \lvert in equation, Line 1. Unknown command \rvert in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 239)

TeX to MathML converter `ttm` failed:

Unknown command \lvert in equation, Line 1. Unknown command \rvert in equation, Line 1.

### 2.4 Extensible vertical arrows

↑ \uparrow | ⇑ \Uparrow
↓ \downarrow | ⇓ \Downarrow
↕ \updownarrow | ⇕ \Updownarrow

### 2.5 Functions (named operators)

arccos | \arccos | gcd | \gcd | ⪻ | \Pr
arcsin | \arcsin | hom | \hom | \projlim | \projlim
arctan | \arctan | inf | \inf | sec | \sec
arg | \arg | \injlim | \injlim | sin | \sin
cos | \cos | ker | \ker | sinh | \sinh
cosh | \cosh | lg | \lg | sup | \sup
cot | \cot | lim | \lim | tan | \tan
coth | \coth | liminf | \liminf | tanh | \tanh
csc | \csc | limsup | \limsup | \varlimsup | \varlimsup
deg | \deg | ln | \ln | \varliminf | \varliminf
det | \det | log | \log | \varprojlim | \varprojlim
dim | \dim | max | \max | \varinjlim | \varinjlim
exp | \exp | min | \min |  |

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 262)

TeX to MathML converter `ttm` failed:

Unknown command \projlim in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 264)

TeX to MathML converter `ttm` failed:

Unknown command \injlim in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 269)

TeX to MathML converter `ttm` failed:

Unknown command \varlimsup in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 270)

TeX to MathML converter `ttm` failed:

Unknown command \varliminf in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 271)

TeX to MathML converter `ttm` failed:

Unknown command \varprojlim in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 272)

TeX to MathML converter `ttm` failed:

Unknown command \varinjlim in equation, Line 1.

Named operators outside the above list can be typeset with \operatorname{name}, e.g.

    \operatorname{sgn}(-3) = -1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 279)

TeX to MathML converter `ttm` failed:

Unknown command \operatorname in equation, Line 1.

The \DeclareMathOperator command can only be used in the LaTeX preamble.

### 2.6 Greek letters

Greek letters that have Latin look-alikes are rarely used in math formulas and not supported by LaTeX.

Γ | \Gamma | α | \alpha | μ | \mu | ω | \omega
Δ | \Delta | β | \beta | ν | \nu | \digamma | \digamma
Λ | \Lambda | γ | \gamma | ξ | \xi | ϵ | \varepsilon
Φ | \Phi | δ | \delta | π | \pi | \varkappa | \varkappa
Π | \Pi | ε | \epsilon | ρ | \rho | ϕ | \varphi
Ψ | \Psi | ζ | \zeta | σ | \sigma | ϖ | \varpi
Σ | \Sigma | η | \eta | τ | \tau | ϱ | \varrho
Θ | \Theta | θ | \theta | υ | \upsilon | ς | \varsigma
ϒ | \Upsilon | ι | \iota | φ | \phi | ϑ | \vartheta
Ξ | \Xi | κ | \kappa | χ | \chi |  |
Ω | \Omega | λ | \lambda | ψ | \psi |  |

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 299)

TeX to MathML converter `ttm` failed:

Unknown command \digamma in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 301)

TeX to MathML converter `ttm` failed:

Unknown command \varkappa in equation, Line 1.

In LaTeX, the default font for capital Greek letters is upright/roman. Italic capital Greek letters can be obtained by loading a package providing the "ISO" math style. They are used by default in MathML.

Individual Greek italic capitals can also be achieved preceding the letter name with var like \varPhi: \varGamma\ \varDelta\ \varLambda\ \varPhi\ \varPi\ \varPsi\ \varSigma\ \varTheta\ \varUpsilon\ \varXi\ \varOmega

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 315)

TeX to MathML converter `ttm` failed:

Unknown command \varGamma in equation, Line 1. Unknown command \varDelta in equation, Line 1. Unknown command \varLambda in equation, Line 1. Unknown command \varPhi in equation, Line 1. Unknown command \varPi in equation, Line 1. Unknown command \varPsi in equation, Line 1. Unknown command \varSigma in equation, Line 1. Unknown command \varTheta in equation, Line 2. Unknown command \varUpsilon in equation, Line 2. Unknown command \varXi in equation, Line 2. Unknown command \varOmega in equation, Line 2.

### 2.7 Letterlike symbols

∀ | \forall | ℵ | \aleph | ℏ | \hbar | ℓ | \ell
\complement | \complement | \beth | \beth | \hslash | \hslash | ℘ | \wp
∃ | \exists | \gimel | \gimel | ℑ | \Im | ℜ | \Re
\Finv | \Finv | \daleth | \daleth | ı | \imath | \circledR | \circledR
\Game | \Game | ∂ | \partial | ȷ | \jmath | \circledS | \circledS
℧ | \mho | \eth | \eth | \Bbbk | \Bbbk |  |

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 330)

TeX to MathML converter `ttm` failed:

Unknown command \complement in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 330)

TeX to MathML converter `ttm` failed:

Unknown command \beth in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 330)

TeX to MathML converter `ttm` failed:

Unknown command \hslash in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 331)

TeX to MathML converter `ttm` failed:

Unknown command \gimel in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 332)

TeX to MathML converter `ttm` failed:

Unknown command \Finv in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 332)

TeX to MathML converter `ttm` failed:

Unknown command \daleth in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 332)

TeX to MathML converter `ttm` failed:

Unknown command \circledR in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 333)

TeX to MathML converter `ttm` failed:

Unknown command \Game in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 333)

TeX to MathML converter `ttm` failed:

Unknown command \circledS in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 334)

TeX to MathML converter `ttm` failed:

Unknown command \eth in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 334)

TeX to MathML converter `ttm` failed:

Unknown command \Bbbk in equation, Line 1.

### 2.8 Math alphabets

The TeX math alphabet macros are intended for mathematical variables where style variations are important semantically. They style letters and numbers with a combination of font attributes (shape, weight, family) --- non-alphanumerical symbols, function names, and mathematical text are left unchanged.

MathML uses the mathvariant style attribute or pre-styled characters from the Mathematical Alphanumeric Symbols Unicode block.

command | example | result
--- | --- | ---
\mathrm | s_\mathrm{out} | s out
\mathbf | \mathbf{r}^2=x^2+y^2 | r 2 = x 2 + y 2
\mathit | \mathit{\sin\Gamma} | sin Γ
\mathcal | \mathcal{F}f(x) | F f(x)
\mathbb | \mathbb{R \subset C} | \mathbb{R \subset C}
\mathfrak | \mathfrak{a+b} | \mathfrak{a+b}
\mathsf | \mathsf x | x
\mathtt | \mathtt{0.12} | 0. 12

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 361)

TeX to MathML converter `ttm` failed:

Unknown command \mathbb in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 362)

TeX to MathML converter `ttm` failed:

Unknown command \mathfrak in equation, Line 1.

The set of characters in a given "math alphabet" varies. LaTeX may produce garbage for unsupported characters. Additional math alphabets are defined in LaTeX packages, e.g.,

- \mathbfit from isomath allows vector symbols in line with the International Standard [ISO-80000-2]. E.g., \mathbfit{r}^2=x^2+y^2 becomes \mathbfit{r}^2=x^2+y^2.

- Several packages, e.g. mathrsfs, define \mathscr that selects a differently shaped "script" alphabet.

The listing below shows the characters supported by Unicode and Docutils with math_output MathML. [2]

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 371)

TeX to MathML converter `ttm` failed:

Unknown command \mathbfit in equation, Line 1.

default:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz ı ȷ {ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇} 0123456789

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 382)

  'latin-1' codec can't encode character '\u03dc' in position 280: ordinal not in range(256)

mathrm:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz ı ȷ \mathrm{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇} 0123456789

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 386)

  'latin-1' codec can't encode character '\u03dc' in position 287: ordinal not in range(256)

mathbf:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz \mathbf{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖϜϝ\ \partial∇} 0123456789

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 390)

  'latin-1' codec can't encode character '\u03dc' in position 287: ordinal not in range(256)

mathit:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz ı ȷ \mathit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇} 0123456789 [2]

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 394)

  TeX to MathML converter `ttm` failed:

  Unknown command \varkappa in equation, Line 1.

mathbfit:

  \mathbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz} \mathbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 398)

  TeX to MathML converter `ttm` failed:

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  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 398)

  TeX to MathML converter `ttm` failed:

  Unknown command \mathbfit in equation, Line 1. Unknown command \varkappa in equation, Line 1.

mathcal:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz

mathscr:

  \mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 403)

  TeX to MathML converter `ttm` failed:

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mathbb:

  \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz} \mathbb{ΓΠΣ\ γπ} \mathbb{0123456789}

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 405)

  TeX to MathML converter `ttm` failed:

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  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 405)

  TeX to MathML converter `ttm` failed:

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  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 405)

  TeX to MathML converter `ttm` failed:

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mathfrak:

  \mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 409)

  TeX to MathML converter `ttm` failed:

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mathsf:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789

mathsfit:

  \mathsfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz}

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 414)

  TeX to MathML converter `ttm` failed:

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mathsfbfit:

  \mathsfbfit{ABCDEFGHIJKLMNOPQRSTUVWXYZ\ abcdefghijklmnopqrstuvwxyz} \mathsfbfit{ΓΔΘΛΞΠΣΥΦΨΩ\ αβγδεζηθικλμνξπρςστυφχψω\ ϵϑϕϰϱϖ\ \partial∇}

  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 416)

  TeX to MathML converter `ttm` failed:

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  System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 416)

  TeX to MathML converter `ttm` failed:

  Unknown command \mathsfbfit in equation, Line 1. Unknown command \varkappa in equation, Line 1.

mathtt:

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789

[2] (1,2)

Italic digits are not defined in Unicode but work in LaTeX.

In contrast to the math alphabet selectors, \boldsymbol only changes the font weight. It can be used to get a bold version of any mathematical symbol:

    V_i x \pm \cos(\alpha) \approx 3\Gamma \quad \forall x\in\mathbb{R}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 429)

TeX to MathML converter `ttm` failed:

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    \boldsymbol{V_i x \pm \cos(\alpha) \approx 3\Gamma \quad \forall x\in\mathbb{R}}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 429)

TeX to MathML converter `ttm` failed:

Unknown command \mathbb in equation, Line 1.

It is usually ill-advised to apply \boldsymbol to more than one symbol at a time.

### 2.9 Miscellaneous symbols

# | \# | ♣ | \clubsuit | ¬ | \neg
& | \& | ♦ | \diamondsuit | \nexists | \nexists
∠ | \angle | ∅ | \emptyset | ' | \prime
\backprime | \backprime | ∃ | \exists | ♯ | \sharp
\bigstar | \bigstar | ♭ | \flat | ♠ | \spadesuit
\blacklozenge | \blacklozenge | ∀ | \forall | \sphericalangle | \sphericalangle
\blacksquare | \blacksquare | ♥ | \heartsuit | \square | \square
\blacktriangle | \blacktriangle | ∞ | \infty | √ | \surd
\blacktriangledown | \blacktriangledown | \lozenge | \lozenge | ⊤ | \top
⊥ | \bot | \measuredangle | \measuredangle | ▵ | \triangle
\diagdown | \diagdown | ∇ | \nabla | \triangledown | \triangledown
\diagup | \diagup | ♮ | \natural | \varnothing | \varnothing

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 452)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 454)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 455)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 456)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 456)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 457)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 457)

TeX to MathML converter `ttm` failed:

Unknown command \square in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 458)

TeX to MathML converter `ttm` failed:

Unknown command \blacktriangle in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 459)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 459)

TeX to MathML converter `ttm` failed:

Unknown command \lozenge in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 460)

TeX to MathML converter `ttm` failed:

Unknown command \measuredangle in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 461)

TeX to MathML converter `ttm` failed:

Unknown command \diagdown in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 461)

TeX to MathML converter `ttm` failed:

Unknown command \triangledown in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 462)

TeX to MathML converter `ttm` failed:

Unknown command \diagup in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 462)

TeX to MathML converter `ttm` failed:

Unknown command \varnothing in equation, Line 1.

### 2.10 Punctuation

. | . | ! | ! | : | \vdots
/ | / | ? | ? | … | \dotsb
| | | | : | \colon [3] | … | \dotsc
' | ' | … | \cdots | … | \dotsi
; | ; | ⋱ | \ddots | \dotsm | \dotsm
: | : | … | \ldots | \dotso | \dotso

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 475)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 476)

TeX to MathML converter `ttm` failed:

Unknown command \dotso in equation, Line 1.

[3]

Punctuation (not ratio): Compare spacing in a: b→c to a: b=c.

### 2.11 Relation symbols

#### 2.11.1 Arrows

\circlearrowleft | \circlearrowleft | \circlearrowright | \circlearrowright
\curvearrowleft | \curvearrowleft | \curvearrowright | \curvearrowright
↩ | \hookleftarrow | ↪ | \hookrightarrow
← | \leftarrow | → | \rightarrow
⇐ | \Leftarrow | ⇒ | \Rightarrow
\leftarrowtail | \leftarrowtail | \rightarrowtail | \rightarrowtail
↽ | \leftharpoondown | ⇁ | \rightharpoondown
↼ | \leftharpoonup | ⇀ | \rightharpoonup
\leftleftarrows | \leftleftarrows | \rightrightarrows | \rightrightarrows
↔ | \leftrightarrow | ⇔ | \Leftrightarrow
\leftrightarrows | \leftrightarrows | \rightleftarrows | \rightleftarrows
\leftrightharpoons | \leftrightharpoons | ⇌ | \rightleftharpoons
\leftrightsquigarrow | \leftrightsquigarrow | \rightsquigarrow | \rightsquigarrow
\Lleftarrow | \Lleftarrow | \Rrightarrow | \Rrightarrow
← | \longleftarrow | → | \longrightarrow
⇐ | \Longleftarrow | ⇒ | \Longrightarrow
↔ | \longleftrightarrow | ⟺ | \Longleftrightarrow
\looparrowleft | \looparrowleft | \looparrowright | \looparrowright
\Lsh | \Lsh | \Rsh | \Rsh
→ | \mapsto | ⟼ | \longmapsto
\multimap | \multimap |  |
\nleftarrow | \nleftarrow | \nrightarrow | \nrightarrow
\nLeftarrow | \nLeftarrow | \nRightarrow | \nRightarrow
\nleftrightarrow | \nleftrightarrow | \nLeftrightarrow | \nLeftrightarrow
↖ | \nwarrow | ↗ | \nearrow
↙ | \swarrow | ↘ | \searrow
\twoheadleftarrow | \twoheadleftarrow | \twoheadrightarrow | \twoheadrightarrow
\upharpoonleft | \upharpoonleft | \upharpoonright | \upharpoonright
\downharpoonleft | \downharpoonleft | \downharpoonright | \downharpoonright
\upuparrows | \upuparrows | \downdownarrows | \downdownarrows

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 491)

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TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 492)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 492)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 496)

TeX to MathML converter `ttm` failed:

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TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 499)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 499)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 501)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 501)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 502)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 503)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 503)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 504)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 504)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 508)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 508)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 509)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 509)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 511)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 512)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 512)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 513)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 513)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 514)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 514)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 517)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 517)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 518)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 518)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 519)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 519)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 520)

TeX to MathML converter `ttm` failed:

Unknown command \upuparrows in equation, Line 1.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 520)

TeX to MathML converter `ttm` failed:

Unknown command \downdownarrows in equation, Line 1.

Synonyms: \gets \gets, → \to, \restriction \restriction.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 523)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 523)

TeX to MathML converter `ttm` failed:

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#### 2.11.2 Comparison

< | < | ≥ | \geq | << | \ll | ≺ | \prec
= | = | \geqq | \geqq | \lll | \lll | \precapprox | \precapprox
> | > | \geqslant | \geqslant | \lnapprox | \lnapprox | \preccurlyeq | \preccurlyeq
≈ | \approx | >> | \gg | \lneq | \lneq | ⪯ | \preceq
\approxeq | \approxeq | \ggg | \ggg | \lneqq | \lneqq | \precnapprox | \precnapprox
≈ | \asymp | \gnapprox | \gnapprox | \lnsim | \lnsim | \precneqq | \precneqq
\backsim | \backsim | \gneq | \gneq | \ncong | \ncong | \precnsim | \precnsim
\backsimeq | \backsimeq | \gneqq | \gneqq | ≠ | \neq | \precsim | \precsim
\bumpeq | \bumpeq | \gnsim | \gnsim | \ngeq | \ngeq | \risingdotseq | \risingdotseq
\Bumpeq | \Bumpeq | \gtrapprox | \gtrapprox | \ngeqq | \ngeqq | ~ | \sim
\circeq | \circeq | \gtreqless | \gtreqless | \ngeqslant | \ngeqslant | ≈ | \simeq
≅ | \cong | \gtreqqless | \gtreqqless | \ngtr | \ngtr | ≻ | \succ
\curlyeqprec | \curlyeqprec | \gtrless | \gtrless | \nleq | \nleq | \succapprox | \succapprox
\curlyeqsucc | \curlyeqsucc | >~ | \gtrsim | \nleqq | \nleqq | \succcurlyeq | \succcurlyeq
≐ | \doteq | ≤ | \leq | \nleqslant | \nleqslant | ⪰ | \succeq
\doteqdot | \doteqdot | \leqq | \leqq | \nless | \nless | \succnapprox | \succnapprox
\eqcirc | \eqcirc | \leqslant | \leqslant | \nprec | \nprec | \succneqq | \succneqq
\eqsim | \eqsim | \lessapprox | \lessapprox | \npreceq | \npreceq | \succnsim | \succnsim
\eqslantgtr | \eqslantgtr | \lesseqgtr | \lesseqgtr | \nsim | \nsim | \succsim | \succsim
\eqslantless | \eqslantless | \lesseqqgtr | \lesseqqgtr | \nsucc | \nsucc | \thickapprox | \thickapprox
≡ | \equiv | \lessgtr | \lessgtr | \nsucceq | \nsucceq | \thicksim | \thicksim
\fallingdotseq | \fallingdotseq | <~ | \lesssim |  |  | \triangleq | \triangleq

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 533)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 533)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 533)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 534)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 535)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 535)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 535)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 535)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 536)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 536)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 536)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 537)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 537)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 537)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 537)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 538)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 538)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 538)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 539)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 539)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 539)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 539)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 540)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 540)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 540)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 541)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 541)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 541)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 542)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 542)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 543)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 543)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 543)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 543)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 544)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 544)

TeX to MathML converter `ttm` failed:

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 544)

TeX to MathML converter `ttm` failed:

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The commands \lvertneqq and \gvertneqq are not supported with MathML output, as there is no corresponding Unicode character.

Synonyms: ≠ \ne, ≤ \le, ≥ \ge, \Doteq \Doteq, \llless \llless, \gggtr \gggtr.

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Symbols can be negated prepending \not, e.g. ≠ \not=, \not\equiv \not\equiv, \not\gtrless \not\gtrless, \not\lessgtr \not\lessgtr.

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#### 2.11.3 Miscellaneous relations

\backepsilon | \backepsilon | \ntrianglelefteq | \ntrianglelefteq | ⊆ | \subseteq
\because | \because | \ntriangleright | \ntriangleright | \subseteqq | \subseteqq
\between | \between | \ntrianglerighteq | \ntrianglerighteq | \subsetneq | \subsetneq
\blacktriangleleft | \blacktriangleleft | \nvdash | \nvdash | \subsetneqq | \subsetneqq
\blacktriangleright | \blacktriangleright | \nVdash | \nVdash | ⊃ | \supset
⋈ | \bowtie | \nvDash | \nvDash | \Supset | \Supset
⊣ | \dashv | \nVDash | \nVDash | ⊇ | \supseteq
⌢ | \frown | ∥ | \parallel | \supseteqq | \supseteqq
∈ | \in | ⊥ | \perp | \supsetneq | \supsetneq
∣ | \mid | \pitchfork | \pitchfork | \supsetneqq | \supsetneqq
⊧ | \models | ∝ | \propto | \therefore | \therefore
∋ | \ni | \shortmid | \shortmid | \trianglelefteq | \trianglelefteq
\nmid | \nmid | \shortparallel | \shortparallel | \trianglerighteq | \trianglerighteq
∉ | \notin | \smallfrown | \smallfrown | \varpropto | \varpropto
\nparallel | \nparallel | \smallsmile | \smallsmile | \vartriangle | \vartriangle
\nshortmid | \nshortmid | ⌣ | \smile | \vartriangleleft | \vartriangleleft
\nshortparallel | \nshortparallel | ⊏ | \sqsubset | \vartriangleright | \vartriangleright
\nsubseteq | \nsubseteq | ⊑ | \sqsubseteq | ⊢ | \vdash
\nsubseteqq | \nsubseteqq | ⊐ | \sqsupset | \Vdash | \Vdash
\nsupseteq | \nsupseteq | ⊒ | \sqsupseteq | \vDash | \vDash
\nsupseteqq | \nsupseteqq | ⊂ | \subset | \Vvdash | \Vvdash
\ntriangleleft | \ntriangleleft | \Subset | \Subset |  |

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Synonyms: ⊃ \owns.

Symbols can be negated prepending \not, e.g. \not\in \not\in, \not\ni \not\ni.

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The commands \varsubsetneq, \varsubsetneqq, \varsupsetneq, and \varsupsetneqq are not supported with MathML output as there is no corresponding Unicode character.

### 2.12 Variable-sized operators

∑ \sum | Π \prod | ⋂ \bigcap | ⨀ \bigodot
∫ \int | ∐ \coprod | ⋃ \bigcup | ⨁ \bigoplus
∮ \oint | ⋀ \bigwedge | ⨄ \biguplus | ⨂ \bigotimes
\smallint \smallint | ⋁ \bigvee | ⨆ \bigsqcup |

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Larger symbols are used in displayed formulas, sum-like symbols have indices above/below the symbol:

∑n=1 N a n ∫0 1 f(x) dx Π i=1 10 b i …

## 3 Notations

### 3.1 Top and bottom embellishments

See Accents and embellishments.

### 3.2 Extensible arrows

xleftarrow and xrightarrow produce arrows that extend automatically to accommodate unusually wide subscripts or superscripts. These commands take one optional argument (the subscript) and one mandatory argument (the superscript, possibly empty):

    A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C

results in

    A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C

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### 3.3 Affixing symbols to other symbols

In addition to the standard accents and embellishments, other symbols can be placed above or below a base symbol with the \overset and \underset commands. The symbol is set in "scriptstyle" (smaller font size). For example, writing \overset{*}{X} becomes \overset{*}{X} and \underset{+}{M} becomes \underset{+}{M}.

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### 3.4 Matrices

The matrix and cases environments can also contain \\ and &:

    .. math::
       \left ( \begin{matrix} a & b \\ c & d \end{matrix}\right)

Result:

    \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right)

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The environments pmatrix, bmatrix, Bmatrix, vmatrix, and Vmatrix have (respectively) ( ), [ ], { }, | |, and ‖ ‖ delimiters built in, e.g.

    \begin{pmatrix} a & b \\ c & d \end{pmatrix} \qquad
    \begin{bmatrix} a & b \\ c & d \end{bmatrix} \qquad
    \begin{Vmatrix} a & b \\ c & d \end{Vmatrix}

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Unknown or ignored environment: \begin{pmatrix} Line 1. Improper \\ or \cr outside array environment ignored, Line ~1.. Unknown or ignored environment: \begin{bmatrix} Line 1. Improper \\ or \cr outside array environment ignored, Line ~1.. Unknown or ignored environment: \begin{Vmatrix} Line 1. Improper \\ or \cr outside array environment ignored, Line ~1.. Error: Fatal Abnormal eqdepth 2 on display equation exit, line 2.

To produce a small matrix suitable for use in text, there is a smallmatrix environment \bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\bigr) that comes closer to fitting within a single text line than a normal matrix.

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For piecewise function definitions there is a cases environment:

    \mathrm{sgn}(x) = \begin{cases}
                -1 & x<0\\
      \phantom{-}1 & x>0
    \end{cases}

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### 3.5 Spacing commands

Horizontal spacing of elements can be controlled with the following commands:

3 4 |  | 3\qquad 4 | = 2em
3 4 |  | 3\quad 4 | = 1em
3 4 | 3~4 | 3\nobreakspace 4 |
3 4 | 3\ 4 |  | escaped space
3 4 | 3\;4 | 3\thickspace 4 |
3 4 | 3\:4 | 3\medspace 4 |
3 4 | 3\,4 | 3\thinspace 4 |
3 4 | 3 4 |  | regular space [4]
3 4 | 3\!4 | 3\negthinspace 4 | negative space [5]
3\negmedspace 4 |  | 3\negmedspace 4 |
3\negthickspace 4 |  | 3\negthickspace 4 |
3 4 |  | 3\hspace{1ex}4 | custom length
3\mspace{20mu}4 |  | 3\mspace{20mu}4 | custom length [6]

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[4]

Whitespace characters are ignored in LaTeX math mode.

[5]

Negative spacing does not work with MathML (last tested in Firefox 115).

[6]

In LaTeX, the unit must be 'mu' (1 mu = 1/18em).

There are also three commands that leave a space equal to the height and width of its argument. For example \phantom{XXX} results in space as wide and high as three X’s:

+1 XXX-1

The commands \hphantom and \vphantom insert space with the width or height of the argument. They are not supported with math_output MathML.

### 3.6 Modular arithmetic and modulo operation

The commands \bmod, \pmod, \mod, and \pod deal with the special spacing conventions of the “mod” notation. [7]

command | example | result
--- | --- | ---
\bmod | \gcd(n,m \bmod n) | gcd(n, m mod n)
\pmod | x\equiv y \pmod b | x≡y mod b
\mod | x\equiv y \mod c | x\equiv y \mod c
\pod | x\equiv y \pod d | x\equiv y \pod d
| \operatorname{mod}(m,n) | \operatorname{mod}(m,n)

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[7]

Currently not supported by the "HTML" math_output option of the HTML writer.

### 3.7 Roots

command | example | result
--- | --- | ---
\sqrt | \sqrt{x^2-1} | x 2 -1
| \sqrt[3n]{x^2-1} | x 2 -1 3 n
| \sqrt\frac{1}{2} | 1 2

### 3.8 Boxed formulas

The command \boxed puts a box around its argument:

    \boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}

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## 4 Fractions and related constructions

The \frac command takes two ar guments, numerator and denominator, and typesets them in normal fraction form. For example, U = \frac{R}{I} produces U= R I . Use \dfrac or \tfrac to force text style and display style respectively.

    \frac{x+1}{x-1}  \quad
    \dfrac{x+1}{x-1} \quad
    \tfrac{x+1}{x-1}

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and in text: x+1 x-1 , \dfrac{x+1}{x-1}, \tfrac{x+1}{x-1}.

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For binomial expressions such as \binom{n}{k}, there are \binom, \dbinom and \tbinom commands:

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    2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}

prints

    2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}

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The \cfrac command for continued fractions uses displaystyle and padding for sub-fractions:

    \frac{\pi}{4} = 1 + \cfrac{1^2}{
                        2 + \cfrac{3^2}{
                            2 + \cfrac{5^2}{
                                2 + \cfrac{7^2}{2 + \cdots}
                        }}}
    \qquad \text{vs.}\qquad
    \frac{\pi}{4} = 1 + \frac{1^2}{
                        2 + \frac{3^2}{
                            2 + \frac{5^2}{
                                2 + \frac{7^2}{2 + \cdots}
                        }}}

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Unknown command \cfrac in equation, Line 1. Unknown command \cfrac in equation, Line 1. Unknown command \cfrac in equation, Line 1. Unknown command \cfrac in equation, Line 1.

The optional argument [l] or [r] for left or right placement of the numerator is not supported by MathML Core:

    \cfrac[l]{x}{x-1} \quad
    \cfrac{x}{x-1}    \quad
    \cfrac[r]{x}{x-1}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 820)

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Unknown command \cfrac in equation, Line 1. Unknown command \cfrac in equation, Line 1. Unknown command \cfrac in equation, Line 1.

## 5 Delimiter sizes

Besides the automatic scaling of extensible delimiters with \left and \right, there are four commands to manually select delimiters of fixed size:

Sizing | no | \left | \bigl | \Bigl | \biggl | \Biggl
command |  | \right | \bigr | \Bigr | \biggr | \Biggr
Result | (b)( c d ) | (b)( c d ) | (b ) ( c d ) | (b ) ( c d ) | (b ) ( c d ) | (b ) ( c d )

There are two or three situations where the delimiter size is commonly adjusted using these commands:

The first kind of adjustment is done for cumulative operators with limits, such as summation signs. With \left and \right the delimiters usually turn out larger than necessary, and using the Big or bigg sizes instead gives better results:

    \left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p}
    \text{ versus }
    \biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 854)

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Unknown command \lvert in equation, Line 1. Unknown command \rvert in equation, Line 1. Unknown command \lvert in equation, Line 1. Unknown command \rvert in equation, Line 1.

The second kind of situation is clustered pairs of delimiters, where left and right make them all the same size (because that is adequate to cover the encompassed material), but what you really want is to make some of the delimiters slightly larger to make the nesting easier to see.

(( a 1 b 1 )-( a 2 b 2 ))(( a 2 b 1 )+( a 1 b 2 )) versus (( a 1 b 1 )-( a 2 b 2 ) ) (( a 2 b 1 )+( a 1 b 2 ) )

The third kind of situation is a slightly oversize object in running text, such as | b' d' | where the delimiters produced by \left and \right cause too much line spreading. [8] In that case \bigl and \bigr can be used to produce delimiters that are larger than the base size but still able to fit within the normal line spacing: | b' d' |.

[8]

With MathML, an example would be parentheses around a smallmatrix environment \left(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right) vs. \Bigl(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\Bigr).

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 877)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 877)

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## 6 Text

The main use of the command \text is for words or phrases in a display. It is similar to \mbox in its effects but, unlike \mbox, automatically produces subscript-size text if used in a subscript, k_{\text{B}}T becomes k B T.

Whitespace is kept inside the argument:

f[ x i-1 , x i ] is monotonic for i=1, …, c+1

The text may contain math commands wrapped in $ signs, e.g.

    (-1)^{n_i} = \begin{cases} -1 \quad \text{if $n_i$ is odd,} \\
                  +1 \quad \text{if $n_i$ is even.}
    \end{cases}

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 898)

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Unknown or ignored environment: \begin{cases} Line 1. Improper \\ or \cr outside array environment ignored, Line ~1..

## 7 Integrals and sums

The limits on integrals, sums, and similar symbols are placed either to the side of or above and below the base symbol, depending on convention and context. In inline formulas and fractions, the limits on sums, and similar symbols like

lim n→∞ ∑1 n 1 n

move to index positions: lim n→∞ ∑1 n 1 n .

### 7.1 Altering the placement of limits

The commands \intop and \ointop produce integral signs with limits as in sums and similar: \intop_0^1, \ointop_c and

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 921)

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System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 921)

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Unknown command \ointop in equation, Line 1.

    \intop_0^1 \quad \ointop_c
       \quad \text{vs.} \quad
    \int^1_0   \quad \oint_c

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Unknown command \intop in equation, Line 1. Unknown command \ointop in equation, Line 1.

The commands \limits and \nolimits override the default placement of the limits for any operator; \displaylimits forces standard positioning as for the sum command. They should follow immediately after the operator to which they apply.

Compare the same term with default positions, \limits, and \nolimits in inline and display mode: lim x→0 f(x), lim x→0 f(x), \lim\nolimits_{x\to0}f(x), vs.

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 933)

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Unknown command \nolimits in equation, Line 1.

    \lim_{x\to0}f(x), \quad
    \lim\limits_{x\to0}f(x) \quad
    \lim\nolimits_{x\to0}f(x).

System Message: WARNING/2 (../../../docs/ref/rst/mathematics.rst, line 937)

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Unknown command \nolimits in equation, Line 1.

## 8 Changing the size of elements in a formula

The declarations [9] \displaystyle, \textstyle, \scriptstyle, and \scriptscriptstyle, select a symbol size and spacing that would be applied in display math, inline math, first-order subscript, or second-order subscript, respectively even when the current context would normally yield some other size.

For example :math:`\displaystyle \sum_{n=0}^\infty \frac{1}{n}` is printed as ∑n=0 ∞ 1 n rather than ∑n=0 ∞ 1 n and

    \frac{\scriptstyle\sum_{n > 0} z^n}
    {\displaystyle\prod_{1\leq k\leq n} (1-q^k)}

yields

∑n>0 z n Π 1≤k≤n (1- q k ) instead of the default ∑n>0 z n Π 1≤k≤n (1- q k ) .
[9]

"Declarations" are commands that affect processing of the current "group". In particular, notice where the braces fall that delimit the effect of the command: Right: {\displaystyle ...} Wrong: \displaystyle{...}.

With math_output MathML, the declaration must be the first element after the opening bracket.

[ISO-80000-2]

Quantities and units – Part 2: Mathematical signs and symbols to be used in the natural sciences and technology: http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=31887.