Help:Formulas

Formulas on a wiki like Ifigenia can be represented in three ways, depending on the formula complexity and tools used:

• Unicode characters - for simple formulas, of course :-)
• Images - for formulas of any complexity, created as an image file (preferably .png or .gif) and uploaded locally.
• TeX code - for formulas of any complexity - from very simple to extremely sophisticated

Maybe, for the users of Ifigenia TeX-coded formulas may turn out to be the most natural ones. They allow relatively good integration with other TeX documents and they can be further saved as .gif images, for the sake of integration with Word documents.

Formulas in TeX

In the wiki websites, TeX-formulas are distinguished from the rest of the text by enclosing them with the tags <math> </math>. A handy way is to click the Math button and then write between the tags.

On Ifigenia, the TeX formulas are rendered using a public mimeTeX web service, so the process may be a bit slower, about 1 second per 1 <math>-call.

Rendered TeX formulas can be stored on the hard disk as .gif images.

Here is a reference list for the various TeX commands in use.

Functions, symbols, special characters

Accents/Diacritics
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}	[math]\displaystyle{ \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\! }[/math]
\check{a} \bar{a} \ddot{a} \dot{a}	[math]\displaystyle{ \check{a} \bar{a} \ddot{a} \dot{a}\,\! }[/math]
Standard functions
\sin a \cos b \tan c	[math]\displaystyle{ \sin a \cos b \tan c\,\! }[/math]
\sec d \csc e \cot f	[math]\displaystyle{ \sec d \csc e \cot f\,\! }[/math]
\arcsin h \arccos i \arctan j	[math]\displaystyle{ \arcsin h \arccos i \arctan j\,\! }[/math]
\sinh k \cosh l \tanh m \coth n	[math]\displaystyle{ \sinh k \cosh l \tanh m \coth n\,\! }[/math]
\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q	[math]\displaystyle{ \operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q\,\! }[/math]
\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t	[math]\displaystyle{ \operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t\,\! }[/math]
\lim u \limsup v \liminf w \min x \max y	[math]\displaystyle{ \lim u \limsup v \liminf w \min x \max y\,\! }[/math]
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g	[math]\displaystyle{ \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\,\! }[/math]
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n	[math]\displaystyle{ \deg h \gcd i \Pr j \det k \hom l \arg m \dim n\,\! }[/math]
Modular arithmetic
s_k \equiv 0 \pmod{m}	[math]\displaystyle{ s_k \equiv 0 \pmod{m}\,\! }[/math]
a\,\bmod\,b	[math]\displaystyle{ a\,\bmod\,b\,\! }[/math]
Derivatives
\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}	[math]\displaystyle{ \nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2} }[/math]
Sets
\forall \exists \empty \emptyset \varnothing	[math]\displaystyle{ \forall \exists \empty \emptyset \varnothing\,\! }[/math]
\in \ni \not \in \notin \subset \subseteq \supset \supseteq	[math]\displaystyle{ \in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\! }[/math]
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	[math]\displaystyle{ \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\! }[/math]
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup	[math]\displaystyle{ \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\! }[/math]
Operators
+ \oplus \bigoplus \pm \mp -	[math]\displaystyle{ + \oplus \bigoplus \pm \mp - \,\! }[/math]
\times \otimes \bigotimes \cdot \circ \bullet \bigodot	[math]\displaystyle{ \times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\! }[/math]
\star * / \div \frac{1}{2}	[math]\displaystyle{ \star * / \div \frac{1}{2}\,\! }[/math]
Logic
\land (or \and) \wedge \bigwedge \bar{q} \to p	[math]\displaystyle{ \land \wedge \bigwedge \bar{q} \to p\,\! }[/math]
\lor \vee \bigvee \lnot \neg q \And	[math]\displaystyle{ \lor \vee \bigvee \lnot \neg q \And\,\! }[/math]
Root
\sqrt{2} \sqrt[n]{x}	[math]\displaystyle{ \sqrt{2} \sqrt[n]{x}\,\! }[/math]
Relations
\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}	[math]\displaystyle{ \sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\! }[/math]
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto	[math]\displaystyle{ \le \lt \ll \gg \ge \gt \equiv \not\equiv \ne \mbox{or} \neq \propto\,\! }[/math]
Geometric
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ	[math]\displaystyle{ \Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\! }[/math]
Arrows
\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow	[math]\displaystyle{ \leftarrow \rightarrow \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow \,\! }[/math]
\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff)	[math]\displaystyle{ \Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \,\! }[/math]
\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow	[math]\displaystyle{ \uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow \,\! }[/math]
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons	[math]\displaystyle{ \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\! }[/math]
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright	[math]\displaystyle{ \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,\! }[/math]
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft	[math]\displaystyle{ \curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\! }[/math]
\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow	[math]\displaystyle{ \mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \,\! }[/math]
Special
\And \eth \S \P \% \dagger \ddagger \ldots \cdots	[math]\displaystyle{ \And \eth \S \P \% \dagger \ddagger \ldots \cdots\,\! }[/math]
\smile \frown \wr \triangleleft \triangleright \infty \bot \top	[math]\displaystyle{ \smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\! }[/math]
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar	[math]\displaystyle{ \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\! }[/math]
\ell \mho \Finv \Re \Im \wp \complement	[math]\displaystyle{ \ell \mho \Finv \Re \Im \wp \complement\,\! }[/math]
\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp	[math]\displaystyle{ \diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\! }[/math]
Unsorted (new stuff)
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown	[math]\displaystyle{ \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown }[/math]
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge	[math]\displaystyle{ \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge }[/math]
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes	[math]\displaystyle{ \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes }[/math]
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant	[math]\displaystyle{ \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant }[/math]
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq	[math]\displaystyle{ \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq }[/math]
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft	[math]\displaystyle{ \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft }[/math]
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot	[math]\displaystyle{ \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot }[/math]
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq	[math]\displaystyle{ \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq }[/math]
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork	[math]\displaystyle{ \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork }[/math]
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq	[math]\displaystyle{ \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq }[/math]
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid	[math]\displaystyle{ \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid }[/math]
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr	[math]\displaystyle{ \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr }[/math]
\subsetneq	[math]\displaystyle{ \subsetneq }[/math]
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq	[math]\displaystyle{ \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq }[/math]
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq	[math]\displaystyle{ \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq }[/math]
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq	[math]\displaystyle{ \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq }[/math]
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus	[math]\displaystyle{ \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\! }[/math]
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq	[math]\displaystyle{ \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\! }[/math]
\dashv \asymp \doteq \parallel	[math]\displaystyle{ \dashv \asymp \doteq \parallel\,\! }[/math]
\ulcorner \urcorner \llcorner \lrcorner	[math]\displaystyle{ \ulcorner \urcorner \llcorner \lrcorner }[/math]

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
		HTML	PNG
Superscript	a^2	[math]\displaystyle{ a^2 }[/math]	[math]\displaystyle{ a^2 \,\! }[/math]
Subscript	a_2	[math]\displaystyle{ a_2 }[/math]	[math]\displaystyle{ a_2 \,\! }[/math]
Grouping	a^{2+2}	[math]\displaystyle{ a^{2+2} }[/math]	[math]\displaystyle{ a^{2+2}\,\! }[/math]
	a_{i,j}	[math]\displaystyle{ a_{i,j} }[/math]	[math]\displaystyle{ a_{i,j}\,\! }[/math]
Combining sub & super	x_2^3	[math]\displaystyle{ x_2^3 }[/math]
Super super	10^{10^{ \,\!{8} }	[math]\displaystyle{ 10^{10^{ \,\! 8 } } }[/math]
Super super	10^{10^{ \overset{8}{} }}	[math]\displaystyle{ 10^{10^{ \overset{8}{} }} }[/math]
Super super (wrong in HTML in some browsers)	10^{10^8}	[math]\displaystyle{ 10^{10^8} }[/math]
Preceding and/or Additional sub & super	\sideset{_1^2}{_3^4}\prod_a^b	[math]\displaystyle{ \sideset{_1^2}{_3^4}\prod_a^b }[/math]
	{}_1^2\!\Omega_3^4	[math]\displaystyle{ {}_1^2\!\Omega_3^4 }[/math]
Stacking	\overset{\alpha}{\omega}	[math]\displaystyle{ \overset{\alpha}{\omega} }[/math]
	\underset{\alpha}{\omega}	[math]\displaystyle{ \underset{\alpha}{\omega} }[/math]
	\overset{\alpha}{\underset{\gamma}{\omega}}	[math]\displaystyle{ \overset{\alpha}{\underset{\gamma}{\omega}} }[/math]
	\stackrel{\alpha}{\omega}	[math]\displaystyle{ \stackrel{\alpha}{\omega} }[/math]
Derivative (forced PNG)	x', y'', f', f''\!		[math]\displaystyle{ x', y'', f', f''\! }[/math]
Derivative (f in italics may overlap primes in HTML)	x', y'', f', f''	[math]\displaystyle{ x', y'', f', f'' }[/math]	[math]\displaystyle{ x', y'', f', f''\! }[/math]
Derivative (wrong in HTML)	x^\prime, y^{\prime\prime}	[math]\displaystyle{ x^\prime, y^{\prime\prime} }[/math]	[math]\displaystyle{ x^\prime, y^{\prime\prime}\,\! }[/math]
Derivative (wrong in PNG)	x\prime, y\prime\prime	[math]\displaystyle{ x\prime, y\prime\prime }[/math]	[math]\displaystyle{ x\prime, y\prime\prime\,\! }[/math]
Derivative dots	\dot{x}, \ddot{x}	[math]\displaystyle{ \dot{x}, \ddot{x} }[/math]
Underlines, overlines, vectors	\hat a \ \bar b \ \vec c	[math]\displaystyle{ \hat a \ \bar b \ \vec c }[/math]
	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}	[math]\displaystyle{ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} }[/math]
	\overline{g h i} \ \underline{j k l}	[math]\displaystyle{ \overline{g h i} \ \underline{j k l} }[/math]
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	[math]\displaystyle{ A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C }[/math]
Overbraces	\overbrace{ 1+2+\cdots+100 }^{5050}	[math]\displaystyle{ \overbrace{ 1+2+\cdots+100 }^{5050} }[/math]
Underbraces	\underbrace{ a+b+\cdots+z }_{26}	[math]\displaystyle{ \underbrace{ a+b+\cdots+z }_{26} }[/math]
Sum	\sum_{k=1}^N k^2	[math]\displaystyle{ \sum_{k=1}^N k^2 }[/math]
Sum (force \textstyle)	\textstyle \sum_{k=1}^N k^2	[math]\displaystyle{ \textstyle \sum_{k=1}^N k^2 }[/math]
Product	\prod_{i=1}^N x_i	[math]\displaystyle{ \prod_{i=1}^N x_i }[/math]
Product (force \textstyle)	\textstyle \prod_{i=1}^N x_i	[math]\displaystyle{ \textstyle \prod_{i=1}^N x_i }[/math]
Coproduct	\coprod_{i=1}^N x_i	[math]\displaystyle{ \coprod_{i=1}^N x_i }[/math]
Coproduct (force \textstyle)	\textstyle \coprod_{i=1}^N x_i	[math]\displaystyle{ \textstyle \coprod_{i=1}^N x_i }[/math]
Limit	\lim_{n \to \infty}x_n	[math]\displaystyle{ \lim_{n \to \infty}x_n }[/math]
Limit (force \textstyle)	\textstyle \lim_{n \to \infty}x_n	[math]\displaystyle{ \textstyle \lim_{n \to \infty}x_n }[/math]
Integral	\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx	[math]\displaystyle{ \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx }[/math]
Integral (alternate limits style)	\int_{1}^{3}\frac{e^3/x}{x^2}\, dx	[math]\displaystyle{ \int_{1}^{3}\frac{e^3/x}{x^2}\, dx }[/math]
Integral (force \textstyle)	\textstyle \int\limits_{-N}^{N} e^x\, dx	[math]\displaystyle{ \textstyle \int\limits_{-N}^{N} e^x\, dx }[/math]
Integral (force \textstyle, alternate limits style)	\textstyle \int_{-N}^{N} e^x\, dx	[math]\displaystyle{ \textstyle \int_{-N}^{N} e^x\, dx }[/math]
Double integral	\iint\limits_D \, dx\,dy	[math]\displaystyle{ \iint\limits_D \, dx\,dy }[/math]
Triple integral	\iiint\limits_E \, dx\,dy\,dz	[math]\displaystyle{ \iiint\limits_E \, dx\,dy\,dz }[/math]
Quadruple integral	\iiiint\limits_F \, dx\,dy\,dz\,dt	[math]\displaystyle{ \iiiint\limits_F \, dx\,dy\,dz\,dt }[/math]
Line or path integral	\int_C x^3\, dx + 4y^2\, dy	[math]\displaystyle{ \int_C x^3\, dx + 4y^2\, dy }[/math]
Closed line or path integral	\oint_C x^3\, dx + 4y^2\, dy	[math]\displaystyle{ \oint_C x^3\, dx + 4y^2\, dy }[/math]
Intersections	\bigcap_1^n p	[math]\displaystyle{ \bigcap_1^n p }[/math]
Unions	\bigcup_1^k p	[math]\displaystyle{ \bigcup_1^k p }[/math]

Alphabets and typefaces

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta	[math]\displaystyle{ \Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\! }[/math]
\Eta \Theta \Iota \Kappa \Lambda \Mu	[math]\displaystyle{ \Eta \Theta \Iota \Kappa \Lambda \Mu \,\! }[/math]
\Nu \Xi \Pi \Rho \Sigma \Tau	[math]\displaystyle{ \Nu \Xi \Pi \Rho \Sigma \Tau\,\! }[/math]
\Upsilon \Phi \Chi \Psi \Omega	[math]\displaystyle{ \Upsilon \Phi \Chi \Psi \Omega \,\! }[/math]
\alpha \beta \gamma \delta \epsilon \zeta	[math]\displaystyle{ \alpha \beta \gamma \delta \epsilon \zeta \,\! }[/math]
\eta \theta \iota \kappa \lambda \mu	[math]\displaystyle{ \eta \theta \iota \kappa \lambda \mu \,\! }[/math]
\nu \xi \pi \rho \sigma \tau	[math]\displaystyle{ \nu \xi \pi \rho \sigma \tau \,\! }[/math]
\upsilon \phi \chi \psi \omega	[math]\displaystyle{ \upsilon \phi \chi \psi \omega \,\! }[/math]
\varepsilon \digamma \vartheta \varkappa	[math]\displaystyle{ \varepsilon \digamma \vartheta \varkappa \,\! }[/math]
\varpi \varrho \varsigma \varphi	[math]\displaystyle{ \varpi \varrho \varsigma \varphi\,\! }[/math]
Blackboard Bold/Scripts
\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G}	[math]\displaystyle{ \mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} \,\! }[/math]
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M}	[math]\displaystyle{ \mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} \,\! }[/math]
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T}	[math]\displaystyle{ \mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} \,\! }[/math]
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}	[math]\displaystyle{ \mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}\,\! }[/math]
boldface (vectors)
\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G}	[math]\displaystyle{ \mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} \,\! }[/math]
\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M}	[math]\displaystyle{ \mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} \,\! }[/math]
\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T}	[math]\displaystyle{ \mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} \,\! }[/math]
\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z}	[math]\displaystyle{ \mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} \,\! }[/math]
\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g}	[math]\displaystyle{ \mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} \,\! }[/math]
\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m}	[math]\displaystyle{ \mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} \,\! }[/math]
\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t}	[math]\displaystyle{ \mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} \,\! }[/math]
\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z}	[math]\displaystyle{ \mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} \,\! }[/math]
\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4}	[math]\displaystyle{ \mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} \,\! }[/math]
\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}	[math]\displaystyle{ \mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}\,\! }[/math]
Boldface (greek)
\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}	[math]\displaystyle{ \boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} \,\! }[/math]
\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}	[math]\displaystyle{ \boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}\,\! }[/math]
\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}	[math]\displaystyle{ \boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}\,\! }[/math]
\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}	[math]\displaystyle{ \boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}\,\! }[/math]
\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}	[math]\displaystyle{ \boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}\,\! }[/math]
\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}	[math]\displaystyle{ \boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}\,\! }[/math]
\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}	[math]\displaystyle{ \boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}\,\! }[/math]
\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}	[math]\displaystyle{ \boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}\,\! }[/math]
\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}	[math]\displaystyle{ \boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} \,\! }[/math]
\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}	[math]\displaystyle{ \boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}\,\! }[/math]
Italics
\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G}	[math]\displaystyle{ \mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} \,\! }[/math]
\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M}	[math]\displaystyle{ \mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} \,\! }[/math]
\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T}	[math]\displaystyle{ \mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} \,\! }[/math]
\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z}	[math]\displaystyle{ \mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} \,\! }[/math]
\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g}	[math]\displaystyle{ \mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} \,\! }[/math]
\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m}	[math]\displaystyle{ \mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} \,\! }[/math]
\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t}	[math]\displaystyle{ \mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} \,\! }[/math]
\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z}	[math]\displaystyle{ \mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} \,\! }[/math]
\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4}	[math]\displaystyle{ \mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} \,\! }[/math]
\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}	[math]\displaystyle{ \mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}\,\! }[/math]
Roman typeface
\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G}	[math]\displaystyle{ \mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} \,\! }[/math]
\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M}	[math]\displaystyle{ \mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} \,\! }[/math]
\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T}	[math]\displaystyle{ \mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} \,\! }[/math]
\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z}	[math]\displaystyle{ \mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} \,\! }[/math]
\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}	[math]\displaystyle{ \mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}\,\! }[/math]
\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m}	[math]\displaystyle{ \mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} \,\! }[/math]
\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t}	[math]\displaystyle{ \mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} \,\! }[/math]
\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z}	[math]\displaystyle{ \mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} \,\! }[/math]
\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4}	[math]\displaystyle{ \mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} \,\! }[/math]
\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}	[math]\displaystyle{ \mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}\,\! }[/math]
Fraktur typeface
\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G}	[math]\displaystyle{ \mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} \,\! }[/math]
\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M}	[math]\displaystyle{ \mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} \,\! }[/math]
\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T}	[math]\displaystyle{ \mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} \,\! }[/math]
\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z}	[math]\displaystyle{ \mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} \,\! }[/math]
\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g}	[math]\displaystyle{ \mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} \,\! }[/math]
\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m}	[math]\displaystyle{ \mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} \,\! }[/math]
\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t}	[math]\displaystyle{ \mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} \,\! }[/math]
\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z}	[math]\displaystyle{ \mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} \,\! }[/math]
\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4}	[math]\displaystyle{ \mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} \,\! }[/math]
\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}	[math]\displaystyle{ \mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}\,\! }[/math]
Calligraphy/Script
\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G}	[math]\displaystyle{ \mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} \,\! }[/math]
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M}	[math]\displaystyle{ \mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} \,\! }[/math]
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T}	[math]\displaystyle{ \mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} \,\! }[/math]
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}	[math]\displaystyle{ \mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}\,\! }[/math]
Hebrew
\aleph \beth \gimel \daleth	[math]\displaystyle{ \aleph \beth \gimel \daleth\,\! }[/math]

Feature	Syntax	How it looks rendered
non-italicised characters	\mbox{abc}	[math]\displaystyle{ \mbox{abc} }[/math]	[math]\displaystyle{ \mbox{abc} \,\! }[/math]
mixed italics (bad)	\mbox{if} n \mbox{is even}	[math]\displaystyle{ \mbox{if} n \mbox{is even} }[/math]	[math]\displaystyle{ \mbox{if} n \mbox{is even} \,\! }[/math]
mixed italics (good)	\mbox{if }n\mbox{ is even}	[math]\displaystyle{ \mbox{if }n\mbox{ is even} }[/math]	[math]\displaystyle{ \mbox{if }n\mbox{ is even} \,\! }[/math]
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space)	\mbox{if}~n\ \mbox{is even}	[math]\displaystyle{ \mbox{if}~n\ \mbox{is even} }[/math]	[math]\displaystyle{ \mbox{if}~n\ \mbox{is even} \,\! }[/math]

Alternatives

Formulas in simple text

These can be produced with:

• the keyboard symbols,
• the symbols from the virtual keyboard (available by clicking on the button in edit mode)
• any other Unicode symbols
• formatting commands like <sub> </sub> (subscript), <sup> </sup> (superscript), '' '' (italic)

The major drawback is that in this way only one-line simple formulas can be produced; multiline formula, fractions, matrices, etc cannot be created using simple text. However, it can prove handy for really small formula or variables/constants/functions definitions, and for people who do not master TeX.

Examples

Source code (in edit mode)	Result (in read mode)
x<sup>2</sup> + y<sup>2</sup> = z<sup>2</sup>	x2 + y2 = z2
''π<sub>A</sub>(x) = 1 - (μ<sub>A</sub>(x) + ν<sub>A</sub>(x))''	πA(x) = 1 - (μA(x) + νA(x))
A = ∑<sub>i=1</sub><sup>n</sup> a<sub>i</sub>	A = ∑i=1n ai

Formulas in uploaded images

You may first want to read Help:Upload and Help:Images and files.

The major drawbacks of this approach are:

• Images are difficult to edit, and need external graphic editor for this sake.
• Images may scale down, but may not scale up well (unless in vector graphic format).
• Images files may be unnecessary large.
• Files can only be uploaded by registered users.

See also

• Help:Formulas in MS Word
• Help:Displaying a formula on Meta-Wikipedia
• Manual of Style (mathematics) on English Wikipedia
• Help:Contents for other help pages