Introducing Latex - Bruce E. Shapiro

Introducing Latex - Bruce E. Shapiro Introducing Latex - Bruce E. Shapiro

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A Symbol Tables A.1 Math Fonts \mathbb \mathcal \mathfrak \mathbf A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z A, B, C, D, E, F, G, H, I, J , K, L, M, N , O, P, Q, R, S, T , U, V, W, X , Y, Z A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z A.2 Math Accents ∑ ∑ ⋂ ⋂ ⊙ ⊙ |= \models ⊥ \perp ‖ \| \sum \bigcap \bigodot ∏ ∏ ⋃ ⋃ ⊗ ⊗ ≍ \asymp ⊲⊳ \bowtie | \mid \prod \bigcup \bigotimes ≻ \succ ≽ \succeq ⌢ \frown ∐ ∐ ⊔ ⊔ ⊕ ⊕ ≺ \prec ≼ \preceq ⌣ \smile \coprod \bigsqcup \bigoplus ∫ ∫ ∮ ∮ ⊎ ⊎ \int \oint \biguplus ∨ ∨ ∧ ∧ \bigvee \bigwedge A.5 Named Math Functions â \hat{a} á \acute{a} ā \bar{a} \arccos \cos \csc \exp \ker \limsup ȧ \dot{a} ă \breve{a} ǎ \check{a} \arcsin \cosh \deg \gcd \lg \ln à \grave{a} ⃗a \vec{a} ä \ddot{a} \arctan \cot \det \hom \lim \log ã \tilde{a} \arg \coth \dim \inf \liminf \max \min \Pr \sec \sin \sinh \sup \tan \tanh A.6 Brackets α \alpha κ \kappa σ \sigma The \left and \right commands may be applied to each of these β \beta λ \lambda ς \varsigma symbols. γ \gamma µ \mu τ \tau ( ( / / ↑ \uparrow | | δ \delta ν \nu υ \upsilon ) ) \ \backslash ↓ \downarrow ‖ \| ɛ \epsilon ξ \xi φ \phi [ [ ⌊ \lfloor ↕ \updownarrow 〈 \langle ε \varepsilon o o ϕ \varphi ] ] ⌋ \rfloor ⇑ \Uparrow 〉 \rangle ζ \zeta π \pi χ \chi { \{ ⌈ \lceil ⇓ \Downarrow η \eta ϖ \varpi ψ \psi } \} ⌉ \rceil ⇕ \Updownarrow θ \theta ϖ \varpi ω \omega ϑ \vartheta ρ \rho γ \gamma ϱ \varrho A.7 Relational Symbols Γ \Gamma Ξ \Xi Φ \Phi ≤ \le ≥ \ge ≠ \neq ∆ \Delta Π \Pi Ψ \Psi . ≤ \leq ≥ \geq = \doteq Θ \Theta Σ \Sigma Ω \Omega ≪ \ll ≫ \gg ≈ \approx Λ \Lambda Υ \Upsilon ⊂ \subset ⊃ \supset ∼ = \cong ⊆ \subseteq ⊇ \supseteq ≡ \equiv ⊏ \sqsubset ⊐ \sqsupset ∝ \propto ⊑ \sqsubseteq ⊒ \sqsupseteq ∼ \sim ∈ \in ∋ \ni ≃ \simeq ⊢ \vdash ⊣ \dashv ‖ \parallel A.3 Greek Letters A.4 Variable Size Symbols Introducing L A TEX (rev. 2012.1) Page 20

A.8 AMS Relational Symbols A.11 Standard Arrows Requires \usepackage{amssymb} ≦ \leqq ⊃ \supset ⊜ \circeq \leqslant \supseteqq \triangleq \eqslantless \precapprox ∼ \thicksim \lesssim \vDash ≈ \thickapprox \lessapprox \Vvdash ⊳ \vartriangleleft ≅ \approxeq ⌣ \smallsmile \trianglelefteq ⋖ \lessdot ⌢ \smallfrown ⊐ \sqsupset ≪ \lll ≏ \bumpeq \succcurlyeq ≶ \lessgtr ≎ \Bumpeq \curlyeqsucc \doteqdot ≧ \geqq \succsim ≬ \between \geqslant \succapprox ⋔ \pitchfork \eqslantgtr ⊲ \vartriangleright ∽ \backsim \gtrsim \trianglerighteq ⋍ \backsimeq \gtrapprox \preccurlyeq \subseteqq ⋗ \gtrdot \curlyeqprec ⋐ \Subset ≫ \ggg \shortparallel ⊏ \sqsubset ≷ \gtrless \risingdotseq ⊩ \Vdash \gtreqless \fallingdotseq \shortmid \gtreqqless ∝ \varpropto \precsim ≖ \eqcirc ◭ \blacktriangleleft ∴ \therefore ∵ \because \backepsilon ← \leftarrow ←− \longleftarrow ⇐ \Leftarrow ⇐= \Longleftarrow → \rightarrow −→ \longrightarrow ⇒ \Rightarrow =⇒ \Longrightarrow ↔ \leftrightarrow ←→ \longleftrightarrow ⇔ \Leftrightarrow ⇐⇒ \Longleftrightarrow ↦→ \mapsto ↦−→ \longmapsto ←↪ \hookleftarrow ↩→ \hookrightarrow ↼ \leftharpoonup ⇀ \rightharpoonup ↽ \leftharpoondown ⇁ \rightharpoondown ⇋ \rightleftharpoons \leadsto ↑ \uparrow ↓ \downarrow ⇑ \Uparrow ⇓ \Downarrow ↑ \uparrow ⇑ \Uparrow ↓ \downarrow ⇓ \Downarrow ↕ \updownarrow ⇕ \Updownarrow ↗ \nearrow ↘ \searrow ↕ \updownarrow ⇕ \Updownarrow A.12 AMS Arrows A.9 Binary Operations ± \pm ∩ \cap ◦ \circ ∓ \mp ∪ \cup • \bullet × \times ⊎ \uplus ⋄ \diamond ÷ \div ⊓ \sqcap ⊳ \lhd · \cdot ⊔ \sqcup ⊲ \rhd ⋆ \star ∨ \vee \unlhd ∗ \ast ∧ \wedge \unrhd † \dagger ⊕ \oplus ⊘ \oslash ‡ \ddagger ⊖ \ominus ⊙ \odot ∐ \amalg ⊗ \otimes ○ \bigcirc □ \Box ♦ \Diamond △ \bigtriangleup ≀ \wr ⊳ \triangleleft ▽ \bigtriangledown \ \setminus ⊲ \triangleright \dashrightarrow \dashleftarrow ⇔ \leftleftarrows ⇆ \leftrightarrows ⇚ \Lleftarrow \looparrowleft ⇌ \leftrightharpoons \curvearrowleft \downdownarrows \curvearrowright ⇈ \upuparrows ↿ \upharpoonleft ⇃ \downharpoonleft ↾ \upharpoonright \leftrightsquigarrow ⇒ \rightrightarrows ⇄ \rightleftarrows ↠ \twoheadrightarrow ↣ \rightarrowtail \looparrowright ⇋ \rightleftharpoons \Lsh \circlearrowright \Rsh \circlearrowleft ⊸ \multimap ⇂ \downharpoonright \rightsquigarrow A.13 Miscellaneous Math Symbol A.10 AMS Binary Operations Requires \usepackage{amssymb} ∔ \dotplus \curlywedge ⊟ \boxminus ⋓ \Cap ⋒ \Cup ⊡ \boxdot ⊼ \barwedge ⊚ \circledcirc \divideontimes ⊺ \intercal ⋊ \rtimes \doublebarwedge ⊠ \boxtimes ⋉ \ltimes \smallsetminus ⊞ \boxplus ⊖ \circleddash \curlyvee \veebar ⊛ \circledast ⋌ \rightthreetimes ⊟ \boxminus \centerdot ⋋ \leftthreetimes . .. \ddots · · · \cdots . .. \vdots . . . \ldots ℵ \aleph ′ \prime ∀ \forall ∞ \infty \hbar ∅ \emptyset ∃ \exists □ \Box ı \imath ∇ \nabla ¬ \neg √ ♦ \Diamond j \jmath \surd ♭ \flat △ \triangle l \ell ⊤ \top ♮ \natural ♣ \clubsuit ℘ \wp ⊥ \bot ♯ \sharp ♦ \diamondsuit R \Re ‖ \| \ \backslash ♥ \heartsuit I \Im ∠ \angle ∂ \partial ♠ \spadesuit Introducing L A TEX (rev. 2012.1) Page 21

A<br />

Symbol Tables<br />

A.1 Math Fonts<br />

\mathbb<br />

\mathcal<br />

\mathfrak<br />

\mathbf<br />

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z<br />

A, B, C, D, E, F, G, H, I, J , K, L, M, N , O, P, Q, R, S, T , U, V, W, X , Y, Z<br />

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z<br />

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z<br />

A.2 Math Accents<br />

∑ ∑ ⋂ ⋂ ⊙ ⊙ |= \models ⊥ \perp ‖ \|<br />

\sum \bigcap \bigodot<br />

∏ ∏ ⋃ ⋃ ⊗ ⊗<br />

≍ \asymp ⊲⊳ \bowtie | \mid<br />

\prod \bigcup \bigotimes ≻ \succ ≽ \succeq ⌢ \frown<br />

∐ ∐ ⊔ ⊔ ⊕ ⊕ ≺ \prec ≼ \preceq ⌣ \smile<br />

\coprod \bigsqcup \bigoplus<br />

∫ ∫<br />

∮ ∮<br />

⊎ ⊎<br />

\int<br />

\oint<br />

\biguplus<br />

∨ ∨ ∧ ∧<br />

\bigvee \bigwedge<br />

A.5 Named Math Functions<br />

â \hat{a} á \acute{a} ā \bar{a}<br />

\arccos \cos \csc \exp \ker \limsup<br />

ȧ \dot{a} ă \breve{a} ǎ \check{a}<br />

\arcsin \cosh \deg \gcd \lg \ln<br />

à \grave{a} ⃗a \vec{a} ä \ddot{a}<br />

\arctan \cot \det \hom \lim \log<br />

ã \tilde{a}<br />

\arg \coth \dim \inf \liminf \max<br />

\min \Pr \sec \sin<br />

\sinh \sup \tan \tanh<br />

A.6 Brackets<br />

α \alpha κ \kappa σ \sigma<br />

The \left and \right commands may be applied to each of these<br />

β \beta λ \lambda ς \varsigma<br />

symbols.<br />

γ \gamma µ \mu τ \tau<br />

( ( / / ↑ \uparrow | |<br />

δ \delta ν \nu υ \upsilon<br />

) ) \ \backslash ↓ \downarrow ‖ \|<br />

ɛ \epsilon ξ \xi φ \phi<br />

[ [ ⌊ \lfloor ↕ \updownarrow 〈 \langle<br />

ε \varepsilon o o ϕ \varphi<br />

] ] ⌋ \rfloor ⇑ \Uparrow 〉 \rangle<br />

ζ \zeta π \pi χ \chi<br />

{ \{ ⌈ \lceil ⇓ \Downarrow<br />

η \eta ϖ \varpi ψ \psi<br />

} \} ⌉ \rceil ⇕ \Updownarrow<br />

θ \theta ϖ \varpi ω \omega<br />

ϑ \vartheta ρ \rho<br />

γ \gamma ϱ \varrho<br />

A.7 Relational Symbols<br />

Γ \Gamma Ξ \Xi Φ \Phi<br />

≤ \le ≥ \ge ≠ \neq<br />

∆ \Delta Π \Pi Ψ \Psi<br />

.<br />

≤ \leq ≥ \geq<br />

= \doteq<br />

Θ \Theta Σ \Sigma Ω \Omega<br />

≪ \ll ≫ \gg ≈ \approx<br />

Λ \Lambda Υ \Upsilon<br />

⊂ \subset ⊃ \supset ∼ = \cong<br />

⊆ \subseteq ⊇ \supseteq ≡ \equiv<br />

⊏ \sqsubset ⊐ \sqsupset ∝ \propto<br />

⊑ \sqsubseteq ⊒ \sqsupseteq ∼ \sim<br />

∈ \in ∋ \ni ≃ \simeq<br />

⊢ \vdash ⊣ \dashv ‖ \parallel<br />

A.3 Greek Letters<br />

A.4 Variable Size Symbols<br />

<strong>Introducing</strong> L A TEX (rev. 2012.1) Page 20

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