Mathematics can be written in Remark using either the AsciiMath syntax, or the Latex syntax. Here we provide a brief tutorial to both syntaxes; complete list of commands for the syntaxes can be found from the above links.
Inline mathematics in AsciiMath and Latex are enclosed in ''
and $
, respectively. Display mathematics in Latex is enclosed in $$
.
Note: MathJax 2.5 — which renders the mathematics — contains a bug which makes the equation number to overlap a long equation. Since Remark refers to MathJax via CDN, this problem will be automatically fixed with the next version of MathJax.
The solution to the quadratic equation is ''x = (-b +- sqrt(b^2 - 4ac)) / (2a)''.
The solution to the quadratic equation is .
The solution to the quadratic equation is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
The solution to the quadratic equation is .
The quadratic equation is given by
$$a x^2 + b x + c = 0 \label{Quadratic}.$$
The solution to Equation $\ref{Quadratic}$ is given by
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$$
The quadratic equation is given by The solution to Equation is given by
The quadratic equation is given by
$$a x^2 + b x + c = 0 \label{Quadratic2} \tag{quadratic equation}.$$
The solution to the $\ref{Quadratic2}$ is given by
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \notag$$
The quadratic equation is given by The solution to the is given by
''R " is reflexive" <=> forall x: x R x''
$R \textrm{ is reflexive} \iff \forall x: x R x$
''R " is transitive" <=> forall x, y, z: (xRy ^^ yRz) => xRz''
$R \textrm{ is transitive} \iff \forall x, y, z: (xRy \land yRz) \implies xRz$
A function $f : \mathbb{R}^n \to \mathbb{R}^m$ is _continuous_ at $p \in \mathbb{R}^n$, if
$$\forall \varepsilon \in \mathbb{R}^{> 0}: \exists \delta \in \mathbb{R}^{> 0}: \forall x \in \mathbb{R}^n : \left\lVert x - p \right\rVert < \delta \implies \left\lVert f(x) - f(p) \right\rVert < \varepsilon.$$
A function is continuous at , if
A function ''f : RR^n -> RR^m'' is _continuous_ at ''p in RR^n'', if
''forall epsilon in RR^{> 0}: exists delta in RR^{> 0}: forall x in RR^n: ||x - p|| < delta => ||f(x) - f(p)|| < epsilon''
A function is continuous at , if
A function $f : \mathbb{R}^n \to \mathbb{R}^m$ is _differentiable_ at $p \in \mathbb{R}^n$, if
$$\frac{\left\lVert f(p + h) - \left[ f(p) + (D_p f)(h) \right] \right\rVert}{\left\lVert h \right\rVert} \xrightarrow{h \to 0} 0.$$
A function is differentiable at , if
''1 / n stackrel(n -> infty)(->) 0''
$\frac{1}{n} \xrightarrow{n \to \infty} 0$
''(x+1)/(x-1)''
$\frac{x + 1}{x - 1}$
''x^(i+j)''
$x^{i + j}$
''x_(ij)''
$x_{ij}$
''sqrt(x)''
$\sqrt{x}$
''root(n)(x)''
$\sqrt[n]{x}$
''stackrel(n -> infty)(->)''
$\overset{n \to \infty}{\to}$
$\xrightarrow{n \to \infty}$
''text(is reflexive)''
''"is reflexive"''
$\textrm{is reflexive}$
''+ - * // \\ xx -: @ o+ ox sum prod ^^ ^^^ vv vvv nn nnn uu uuu''
$+ - * / \setminus \times \div \circ \oplus \otimes \sum \prod \land \bigwedge \lor \bigvee \cap \bigcap \cup \bigcup$
''= != < <= > >= -< >- in !in sub sup sube supe -= ~= ~~ prop''
$= \neq < \leq > \geq \prec \succ \in \not\in \subset \supset \subseteq \supseteq \equiv \approxeq \approx \propto$
''and or not => iff forall exists TT |--''
$\land \lor \lnot \implies \iff \forall \exists \top \bot \vdash \vDash$
''int oint del grad +- O/ oo aleph ... cdots \ quad qquad diamond square |~ ~|''
$\int \oint \partial \nabla \pm \emptyset \infty \aleph \dots \cdots \quad \qquad \diamond \square \lceil \rceil \lfloor \rfloor$
''sin cos tan csc sec cot sinh cosh tanh log ln det dim lim mod gcd lcm''
$\sin \cos \tan \csc \sec \cot \sinh \cosh \tanh \log \ln \det \dim \lim \mod \gcd$
''(x) [x] {x} (:x:)''
$(x) [x] \{x\} \langle x \rangle$
''uarr darr -> larr harr => lArr <=>''
$\uparrow \downarrow \to \leftarrow \leftrightarrow \Uparrow \Downarrow \Rightarrow \Leftarrow \Leftrightarrow$
''hat(2 + 3 * 4)''
$\hat{x}$
$\widehat{2 + 3 * 4}$
''dot(x)''
$\dot{x}$
''ddot(x)''
$\ddot{x}$
''bar(2 + 3 * 4)''
$\overline{2 + 3 * 4}$
''ul(2 + 3 * 4)''
$\underline{2 + 3 * 4}$
''vec(2 + 3 * 4)''
$\vec{x}$
$\overrightarrow{2 + 3 * 4}$
''text(abcdefghijklmnopqrstuvwxyz)''
''text(ABCDEFGHIJKLMNOPQRSTUVWXYZ)''
$\mathrm{abcdefghijklmnopqrstuvwxyz}$
$\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''bb("abcdefghijklmnopqrstuvwxyz")''
''bb("ABCDEFGHIJKLMNOPQRSTUVWXYZ")''
$\mathbf{abcdefghijklmnopqrstuvwxyz}$
$\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''bbb("abcdefghijklmnopqrstuvwxyz")''
''bbb("ABCDEFGHIJKLMNOPQRSTUVWXYZ")''
$\mathbb{abcdefghijklmnopqrstuvwxyz}$
$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''cc("abcdefghijklmnopqrstuvwxyz")''
''cc("ABCDEFGHIJKLMNOPQRSTUVWXYZ")''
$\mathscr{abcdefghijklmnopqrstuvwxyz}$
$\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
$\mathcal{abcdefghijklmnopqrstuvwxyz}$
$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''tt("abcdefghijklmnopqrstuvwxyz")''
''tt("ABCDEFGHIJKLMNOPQRSTUVWXYZ")''
$\mathtt{abcdefghijklmnopqrstuvwxyz}$
$\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''fr("abcdefghijklmnopqrstuvwxyz")''
''fr("ABCDEFGHIJKLMNOPQRSTUVWXYZ")''
$\mathfrak{abcdefghijklmnopqrstuvwxyz}$
$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''sf("abcdefghijklmnopqrstuvwxyz")''
''sf("ABCDEFGHIJKLMNOPQRSTUVWXYZ")''
$\mathsf{abcdefghijklmnopqrstuvwxyz}$
$\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
''[[a,b],[c,d]] ((1,0),(0,1))''
$\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$
''alpha beta gamma delta epsi zeta eta theta iota kappa lambda mu nu xi o pi rho sigma tau upsilon phi chi psi omega''
''A B Gamma Delta E Z H theta I K Lambda N N Xi O Pi P Sigma T Y Phi X Psi Omega''
$\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega$
$A B \Gamma \Delta E Z H \theta I K \Lambda N N \Xi O \Pi P \Sigma T Y \Phi X \Psi \Omega$