1. Indian TEX Users Group
: http://www.river-valley.com/tug
Introduction
Maths in text
Fraction
11
A
On-line Tutorial on LTEX
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
The Tutorial Team
Indian TEX Users Group,  Buildings, Cotton Hills
Trivandrum 695014, 
2000
Prof. (Dr.) K. S. S. Nambooripad, Director, Center for Mathematical Sciences, Trivandrum, (Editor); Dr. E. Krishnan, Reader
in Mathematics, University College, Trivandrum; Mohit Agarwal, Department of Aerospace Engineering, Indian Institute of
Science, Bangalore; T. Rishi, Focal Image (India) Pvt. Ltd., Trivandrum; L. A. Ajith, Focal Image (India) Pvt. Ltd.,
Trivandrum; A. M. Shan, Focal Image (India) Pvt. Ltd., Trivandrum; C. V. Radhakrishnan, River Valley Technologies,
Software Technology Park, Trivandrum constitute the Tutorial team
A
A
This document is generated from LTEX sources compiled with pdfLTEX v. 14e in an INTEL
Pentium III 700 MHz system running Linux kernel version 2.2.14-12. The packages used
are hyperref.sty and pdfscreen.sty
A
c 2000, Indian TEX Users Group. This document may be distributed under the terms of the LTEX
A
Project Public License, as described in lppl.txt in the base LTEX distribution, either version 1.0
or, at your option, any later version
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2. 11 Mathematics
Introduction
Maths in text
Fraction
Equation
11.1.
Introduction
Definitions for . . .
AMS-LaTeX
TEX is at its best while producing mathematical documents. If you want to test the power of
TEX, do typeset some mathematics. In the foreword of the TEX book, Knuth writes: “TEX is a
new typesetting system intended for the creation of beautiful books—and especially for books
that contain a lot of mathematics”.
Mathematical . . .
Accents and For . . .
Title Page
A
LTEX has a special mode for typesetting mathematics. Mathematical text within a paragraph (inline) is entered between ( and ), between $ and $ or between begin{math} and end{math}.
Normally larger mathematical equations and formula are typesetted in separate lines, in display
mode. To produce this, we enclose them between [ and ], between $$ and $$ or between
begin{displaymath} and end{displaymath}. This produces formula, which are not numbered. If we want to produce equation number, we have to use equation environment.
The spacing for both in-line and displayed mathematics is completely controlled by TEX.
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3. 11.2.
Maths in text
input—file
Using˜(5.64) and the fact that the
$c_n=langlepsi_nvertPsirangle$
and $d_nˆ*=langle Xpsi_nrangle$,
the scalar product $langle Xvert
Psirangle$ can be expressed in the
way as $langle XvertPsirangle=
sum_nd_nˆ*c_n = mathbf{d}ˆdagger
boldsymbol{cdot}mathbf{c}$ where
(mathbf{c}) is a column vector
with elements $c_n$ and row vector
$mathbf{d}ˆdagger$ with elements
$d_nˆ*$. The inverse $mathbf{A}ˆ{-1}$
of a matrix $mathbf{A}$ is such that
$mathbf{AA}ˆ{-1}=mathbf{A}ˆ{-1}
mathbf{A}= mathbf{I}$.
output—dvi
Using (5.64) and the fact that the cn = ψn |Ψ
∗
and dn =
Xψn , the scalar product
X|Ψ can be expressed in the way as
∗
X|Ψ = n dn cn = d† · c where c is a column
vector with elements cn and row vector d†
∗
with elements dn . The inverse A−1 of a
matrix A is such that AA−1 = A−1 A = I.
Where I is the unit matrix, elements
Imn = δmn . For a stationary state ΨE =
ψE exp(−iEt/ ) and a time-independent operator A it is clear that the expectation value
ΨE |A|ΨE = ψE |A|ψE does not depend on
the time.
Where $mathbf{I}$ is the unit matrix, elements $I_{mn}=delta_{mn}$. For a
emph{stationary state} $Psi_E=psi_Eexp(-{rm i}Et/hbar)$ and a
emph{time-independent} operator $A$ it is clear that the expectation value
begin{math}langlePsi_Evert AvertPsi_Erangle=langlepsi_Evert
Avertpsi_Erangleend{math} does not depend on the time.
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
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4. 11.3.
Fraction
$$
frac{{rm d}varepsilon}{{rm d}varepsilon}qquad
frac{frac{a}{x-y}+frac{b}{x+y}}{1+frac{a-b}{a+b}}
$$
dε
dε
a
x−y
+
1+
b
x+y
a−b
a+b
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
11.4.
AMS-LaTeX
Equation
Mathematical . . .
Accents and For . . .
Don’t put blank lines between the dollar signs delimiting the mathematical text. TEX assumes
that all the mathematical text being typeset is in one paragraph, and a blank line starts a new
paragraph; consequently, this will generate an error message.
11.4.1.
Title Page
Equation with numbers
begin{equation}
varphi(x,z) = z - gamma_{10} x - sum_{m+nge2} gamma{mn} xˆm zˆn
end{equation}
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ϕ(x, z) = z − γ10 x −
γmnx z
m n
m+n≥2
(1)
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5. 11.4.2.
Equation without numbers
begin{displaymath}
left(int_{-infty}ˆ{infty} eˆ{-xˆ2}right)
=int_{-infty}ˆ{infty}int_{-infty}ˆ{infty}eˆ{-(xˆ2+yˆ2)}dx,dy
end{displaymath}
Introduction
Maths in text
OR
Fraction
Equation
$$
Definitions for . . .
left(int_{-infty}ˆ{infty} eˆ{-xˆ2}right)
=int_{-infty}ˆ{infty}int_{-infty}ˆ{infty}eˆ{-(xˆ2+yˆ2)}dx,dy
$$
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
∞
e−x
2
−∞
∞
∞
=
e−(x
−∞
2
+y2 )
dx dy
−∞
[
left(int_{-infty}ˆ{infty} eˆ{-xˆ2}right)
=int_{-infty}ˆ{infty}int_{-infty}ˆ{infty}eˆ{-(xˆ2+yˆ2)}dx,dy
Page 5 of 31
]
∞
−x2
e
−∞
∞
∞
−∞
−∞
=
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−(x2 +y2 )
e
dx dy
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6. 11.4.3.
Subequations1
begin{subequations}
begin{equation}
langlePsi_1vertPsi_2rangleequivintPsi_1ˆ*
(mathbf{r})Psi_2 (mathbf{r}){rm d}mathbf{r}
end{equation}
and
begin{equation}
langlePsi_1vertPsi_2rangleequivPsi_1ˆ*(mathbf{r}_1,ldots,
mathbf{r}_N)Psi_2(mathbf{r}_1,ldots,mathbf{r}_N){rm d}
mathbf{r}_1ldots{rm d}mathbf{r}_N.
end{equation}
end{subequations}
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
Ψ1 |Ψ2 ≡
Ψ∗ (r)Ψ2 (r)dr
1
(2a)
and
Ψ1 |Ψ2 ≡ Ψ∗ (r1 , . . . , rN )Ψ2 (r1 , . . . , rN )dr1 . . . drN .
1
11.4.4.
Framed displayed equation
begin{equation}
fbox{$displaystyleint_0ˆinfty f(x),{rm d}x
approxsum_{i=1}ˆnw_i{rm e}ˆ{x_i}f(x_i)$}
end{equation}
1
(2b)
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7. n
∞
wi e xi f (xi )
f (x) dx ≈
0
11.4.5.
(3)
i=1
Introduction
Multiline equations – Eqnarray
Maths in text
Fraction
begin{eqnarray}
barvarepsilon &=& frac{int_0ˆinftyvarepsilon
exp(-betavarepsilon),{rm d}varepsilon}{int_0ˆinfty
exp(-betavarepsilon),{rm d}varepsilon}nonumber
&=& -frac{{rm d}}{{rm d}beta}logBiggl[int_0ˆinftyexp
(-betavarepsilon),{rm d}varepsilonBiggr]=frac1beta=kT.
end{eqnarray}
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
¯
ε=
∞
ε exp(−βε) dε
0
∞
exp(−βε) dε
0
∞
= −
d
log
dβ
exp(−βε) dε =
0
1
= kT.
β
(4)
nonumber is used for suppressing number.
11.4.6.
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Matrix
$$
matrix{1 & 2 & 3cr 2 & 3 & 4cr 3 & 4 & 5}qquad
left(matrix{1 & cdots & 3cr 2 & vdots & 4cr
3 & ddots & 5}right)
$$
1 2 3
2 3 4
3 4 5

1





2







3
···
.
.
.

3






4




.. 
. 5
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8. 11.4.7.
Array
$$
begin{array}{lcll}
Psi(x,t) &=& A({rm e}ˆ{{rm i}kx}-{rm e}ˆ{-{rm i}kx})
{rm e}ˆ{-{rm i}omega t}&
&=& Dsin kx{rm e}ˆ{-{rm i}omega t}, & D=2{rm i}A
end{array}
Introduction
Maths in text
Fraction
$$
Equation
Definitions for . . .
AMS-LaTeX
Ψ(x, t) = A(eikx − e−ikx )e−iωt
= D sin kxe−iωt ,
D = 2iA
Mathematical . . .
Accents and For . . .
Title Page
11.4.8.
Cases
$$
psi(x)=cases{A{rm e}ˆ{{rm i}kx}+B{rm e}ˆ{{-rm i}kx},
& for $x=0$cr
D{rm e}ˆ-{kappa x}, & for $x=0$.}
$$
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
Aeikx + Be−ikx ,


ψ(x) =  −κx
De ,

for x = 0
for x = 0.
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9. 11.4.9.
Stackrel
$$
astackrel{def}{=} alpha + betaquad
stackrel{thermo}{longrightarrow}
de f
a = α+β
thermo
−→
$$
Introduction
Maths in text
Fraction
11.4.10.
Equation
Atop
Definitions for . . .
AMS-LaTeX
$$
sum_{k=1 atop k=0} qquad
sum_{123 atop{234 atop {890 atop 456}}}
$$
Mathematical . . .
k=1
k=0
123
234
890
456
Accents and For . . .
Title Page
11.4.11.
Square root
$$
sqrt[n]{frac{xˆn-yˆn}{1+uˆ{2n}}}
n
$$
x n − yn
1 + u2n
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11.4.12.
Choose
$$
{123 choose 456}qquad {xˆn-yˆn choose 1+uˆ{2n}}
$$
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123
456
xn − yn
1 + u2n
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10. 11.5.
Definitions for Theorems
We should define newtheorem{thm}{Theorem} etc in preamble.
Introduction
newtheorem{thm}{Theorem}
begin{thm}
This is body matter for testing this environment.
end{thm}
Maths in text
Theorem 1 This is body matter
for testing this environment.
Fraction
Equation
Definitions for . . .
AMS-LaTeX
newtheorem{rmk}{Remark}[section]
begin{rmk}
This is body matter for testing this environment.
end{rmk}
Remark 11.5.1 This is body
matter for testing this environment.
Mathematical . . .
Accents and For . . .
Title Page
newtheorem{col}{Corollary}
begin{col}[Richard, 1987]
This is body matter for testing this environment.
end{col}
Corollary 1 (Richard, 1987)
This is body matter for testing
this environment.
newtheorem{lem}{Lemma}[thm]
begin{lem}
This is body matter for testing this environment.
end{lem}
Lemma 1.1 This is body matter
for testing this environment.
newtheorem{exa}{Example}[lem]
begin{exa}
This is body matter for testing this environment.
end{exa}
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Example 1.1.1 This is body matter for testing this environment.
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11. 11.6.
A
AMS-LTEX2
Following are some of the component parts of the amsmath package, available individually and
can be used separately in a usepackage command:
Introduction
amsbsy
defines the amsmath boldsymbol and (poor man’s bold) pmb commands.
amscd
defines some command for easing the generation of commutative diagrams.
defines the frak and Bbb commands and set up the fonts msam (extra math
amsfonts
symbols A), msbm (extra math symbols B, and blackboard bold), eufm (Euler Fraktur),
extra sizes of cmmib (bold math italic and bold lowercase Greek), and cmbsy (bold math
symbols and bold script), for use in mathematics.
amssymb
lection.
amstext
11.6.1.
defines the names of all the math symbols available with the AMS fonts col-
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
defines the amsmath text command.
Align environment
Page 11 of 31
Align environment is used for two or more equations when vertical alignment is desired (usually binary relations such as equal signs are aligned).
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CTAN: /tex-archive/macros/latex/packages/amslatex
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12. begin{align}
F_{rm fer}(k)
=& -frac{16 x_0 ˆ3 t}{3pi }bigg( sum_{l=1}ˆinfty
-frac{nuˆ5}{tˆ4 (x_0ˆ2-l-frac{1}{4})ˆ3}bigg[S
bigg(frac{sqrt{x_0ˆ2+lˆ2}}{t};2 bigg)
+ 2Sbigg(frac{nu}{t};2 bigg)bigg] bigg)
F_{rm red}(t) =& -frac{16 x_0 ˆ3 t}{3pi }sum_{l=1}ˆinfty
bigg{ frac{1}{2nu (x_0ˆ2+lˆ2)ˆ2} nonumber
& -frac{nuˆ5}{tˆ4 (x_0ˆ2-l-frac{1}{4})ˆ3}bigg[S
bigg( frac{sqrt{x_0ˆ2+lˆ2}}{t};2 bigg)
+2Sbigg(frac{nu}{t};2 bigg)bigg] nonumber
& +V(x_e ,x_{alpha}) -g delta (x_e - x_{alpha}) bigg}.
end{align}
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
3
16x0 t
Ffer (k) = −
3π
Fred (t) = −
3
16x0 t
3π
∞
−
l=1
∞
l=1
ν
S
2
t4 (x0 − l − 1 )3
4
5
t
; 2 + 2S
ν
;2
t
(5)
1
+ l2 )2
2
2ν(x0
ν5
S
−
2
t4 (x0 − l − 1 )3
4
2
x0 + l2
t
+ V(xe , xα ) − gδ(xe − xα ) .
11.6.2.
2
x0 + l2
; 2 + 2S
ν
;2
t
Page 12 of 31
(6)
Gather environment
Gather environment is used for two or more equations, but when there is no alignment desired
among them each one is centered separately between the left and right margins.
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13. begin{gather}
frac{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}
varepsilon}{int_0ˆinftyexp(-betavarepsilon),{rm d}varepsilon}
frac{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}varepsilon}
{int_0ˆinftyexp(-betavarepsilon)}
int_0ˆinftyexp(-betavarepsilon),{rm d}exp(-betavarepsilon)nonumber
frac{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}varepsilon}
{int_0ˆinftyexp(-betavarepsilon)}
int_0ˆinftyexp(-betavarepsilon),{rm d}exp(-betavarepsilon)
end{gather}
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
∞
∞
ε exp(−βε) dε 0 ε exp(−βε) dε
0
∞
∞
exp(−βε) dε
exp(−βε)
0
0
∞
exp(−βε) d exp(−βε)
0
∞
0
∞
ε exp(−βε) dε
∞
0
exp(−βε)
exp(−βε) d exp(−βε)
(7)
(8)
(9)
(10)
0
11.6.3.
Title Page
Alignat environment
The align environment takes up the whole width of a display. If you want to have several
“align”-type structures side by side, you can use an alignat environment. It has one required
argument, for specifying the number of “align” structures. For an argument of n, the number
of ampersand characters per line is 2n − 1 (one ampersand for alignment within each align
structure, and ampersands to separate the align structures from one another).
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14. begin{alignat}{2}
L_1 & = R_1 &qquad L_2 & = R_2
L_3 & = R_3 &qquad L_4 & = R_4
end{alignat}
Introduction
Maths in text
Fraction
L1 = R 1
L3 = R 3
L2 = R2
L4 = R4
(11)
(12)
Equation
Definitions for . . .
AMS-LaTeX
11.6.4.
Alignment Environments as Parts of Displays
There are some other equation alignment environments that do not constitute an entire display.
They are self-contained units that can be used inside other formulae, or set side by side. The
environment names are: aligned, gathered and alignedat. These environments take an optional
argument to specify their vertical positioning with respect to the material on either side. The
default alignment is centered ([c]), and its effect is seen in the following example.
begin{equation*}
begin{aligned}
xˆ2 + yˆ2 & = 1
x & = sqrt{1-yˆ2}
end{aligned}
qquad
begin{gathered}
(a+b)ˆ2 = aˆ2 + 2ab + bˆ2
(a+b) cdot (a-b) = aˆ2 - bˆ2
end{gathered}
end{equation*}
Mathematical . . .
Accents and For . . .
Title Page
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15. x2 + y2 = 1
x=
1 − y2
(a + b)2 = a2 + 2ab + b2
(a + b) · (a − b) = a2 − b2
The same mathematics can now be typeset using vertical alignments for the environments.
Introduction
Maths in text
begin{equation*}
begin{aligned}[b]
xˆ2 + yˆ2 & = 1
x & = sqrt{1-yˆ2}
end{aligned}
qquad
begin{gathered}[t]
(a+b)ˆ2 = aˆ2 + 2ab + bˆ2
(a+b) cdot (a-b) = aˆ2 - bˆ2
end{gathered}
end{equation*}
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
x2 + y2 = 1
x=
11.6.5.
1 − y2
(a + b)2 = a2 + 2ab + b2
(a + b) · (a − b) = a2 − b2
Multline environment
The multline environment is a variation of the equation environment used for equations that do
not fit on a single line. The first line of a multline will be at the left margin and the last line at
the right margin except for an indentation on both sides whose amount is equal to multline-gap.
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16. begin{multline}
{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}
varepsilon}{int_0ˆinftyexp(-betavarepsilon),{rm d}
varepsilon}{int_0ˆinftyvarepsilonexp(-betavarepsilon),
{rm d}varepsilon}{int_0ˆinftyexp(-betavarepsilon)}
{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}
varepsilon}{int_0ˆinftyexp(-betavarepsilon),{rm d}
varepsilon}{int_0ˆinftyvarepsilon}
{int_0ˆinftyexp(-betavarepsilon)}
end{multline}
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
∞
∞
ε exp(−βε) dε
0
∞
ε exp(−βε) dε
exp(−βε) dε
0
∞
0
∞
ε exp(−βε) dε
0
11.6.6.
Accents and For . . .
∞
exp(−βε)
0
∞
0
∞
ε
exp(−βε) dε
0
Title Page
exp(−βε)
(13)
0
Split environment
The split environment is for single equations that are too long to fit on a single line and hence
must be split into multiple lines. Unlike multline, however, the split environment provides for
alignment among the split lines.
Page 16 of 31
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begin{equation}
begin{split}
(a+b)ˆ4 & = (a+b)ˆ2(a+b)ˆ2
& = (aˆ2+2ab+bˆ2)(aˆ2+2ab+bˆ2)
& = aˆ4+4aˆ3b+6aˆ2bˆ2+4abˆ3+bˆ4
end{split}
end{equation}
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17. (a + b)4 = (a + b)2 (a + b)2
= (a2 + 2ab + b2 )(a2 + 2ab + b2 )
= a4 + 4a3 b + 6a2 b2 + 4ab3 + b4
(14)
Introduction
11.6.7.
Maths in text
Cases
Fraction
begin{equation}
P_{r-j}=
begin{cases}
0 & text{if $r-j$ is odd},
r!,(-1)ˆ{(r-j)/2} & text{if $r-j$ is even}.
end{cases}
end{equation}
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
Pr− j
11.6.8.

0


=
r! (−1)(r− j)/2

if r − j is odd,
if r − j is even.
(15)
Matrix
begin{gather*}
begin{matrix}
begin{pmatrix}
begin{bmatrix}
begin{vmatrix}
begin{Vmatrix}
end{gather*}
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0 & 1 1 & 0
0 & -i i & 0
a & b c & d
0 & 1 -1 & 0
f & g e & v
end{matrix}qquad
end{pmatrix}qquad
end{bmatrix}qquad
end{vmatrix}qquad
end{Vmatrix}
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18. 0 1
1 0
11.6.9.
0 −i
i 0
a b
c d
0 1
−1 0
f g
e v
Introduction
substack environment
Maths in text
begin{equation*}
sum_{substack{0leq ileq m 0jn}}
end{equation*}
Fraction
Equation
0≤i≤m
0> j>n
Definitions for . . .
AMS-LaTeX
begin{equation*}
sumˆ{substack{0leq ileq m 0jn}}
end{equation*}
Mathematical . . .
0≤i≤m
0> j>n
Accents and For . . .
Title Page
11.6.10.
Commutative Diagram3
begin{equation*}
begin{CD}
S_Lambdaˆ{mathcal{W}}otimes T @j> T
@VVV @VV{{rm End}P}V
(Sotimes T)/I @=
(Zotimes T)/J
end{CD}
end{equation*}
3
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19. j
W
SΛ ⊗ T −−−
−−→





(S ⊗ T )/I
T




EndP
(Z ⊗ T )/J
Introduction
Maths in text
begin{equation*}
begin{CD}
S_Lambdaˆ{mathcal{W}}otimes T @j>
@V{{Out}p}VV
&
(Sotimes T)/I
@=
end{CD}
end{equation*}
Fraction
T_{XF}
@xyz> T
&
@AA{{rm End}P}A
X_{mathcal{F}} @fg> (Zotimes T)/J
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
j
xyz
W
S Λ ⊗ T − − − T XF − − −
−−→
−−→





Outp
(S ⊗ T )/I
11.6.11.
Equation
Title Page
T

EndP



fg
XF − − − (Z ⊗ T )/J
−−→
Binom
Page 19 of 31
begin{equation*}
binom{x}{y}
end{equation*}
x
y
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11.6.12.
AMS symbols
Close
iint
iiint
iiiint
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20. 11.7.
Mathematical Symbols
11.7.1.
Lowercase Greek letters
α
β
γ
δ
ε
ζ
η
11.7.2.
θ
ϑ
ι
κ
λ
µ
ν
ξ
theta
vartheta
iota
kappa
lambda
mu
nu
xi
o
π
ρ
σ
ς
o
pi
varpi
rho
varrho
sigma
varsigma
τ
υ
φ
ϕ
χ
ψ
ω
tau
upsilon
phi
varphi
chi
psi
omega
Gamma
Delta
Theta
Λ
Ξ
Π
Lambda
Xi
Pi
hat{a}
check{a}
a
´
a
`
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Title Page
Σ
Υ
Φ
Sigma
Upsilon
Phi
Ψ
Ω
Psi
Omega
Math mode accents
a
ˆ
a
ˇ
Introduction
Accents and For . . .
Uppercase Greek letters
Γ
∆
Θ
11.7.3.
alpha
beta
gamma
delta
epsilon
varepsilon
zeta
eta
acute{a}
grave{a}
Page 20 of 31
a
¯
a
bar{a}
vec{a}
a
˙
a
¨
dot{a}
ddot{a}
a
˘
a
˜
breve{a}
tilde{a}
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21. 11.7.4.
Binary Operation Symbols
±
×
÷
∗
◦
•
·
a
11.7.5.
pm
mp
times
div
ast
star
circ
bullet
cdot
∩
∪
∨
∧
cap
cup
uplus
sqcap
sqcup
vee
wedge
setminus
wr
⊕
diamond
bigtriangleup
bigtriangledown
triangleleft
triangleright
lhda
rhda
unlhda
unrhda
⊗
†
‡
oplus
ominus
otimes
oslash
odot
bigcirc
dagger
ddagger
amalg
Not predefined in NFSS. Use the latexsym or amssymb package.
Relation symbols
≤
⊂
⊆
∈
leq
prec
preceq
ll
subset
subseteq
sqsubset
sqsubseteq
in
vdash
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
≥
⊃
⊇
geq
succ
succeq
gg
supset
supseteq
sqsupset
sqsupseteq
ni
dashv
≡
∼
≈
equiv
sim
simeq
asymp
approx
cong
neq
doteq
notin
|=
⊥
|
∝
models
perp
mid
parallel
bowtie
Join
smile
frown
propto
Page 21 of 31
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22. 11.7.6.
Arrow symbols
←
⇐
→
⇒
↔
⇔
|→
←
11.7.7.
leftarrow
Leftarrow
rightarrow
Rightarrow
leftrightarrow
Leftrightarrow
mapsto
hookleftarrow
leftharpoonup
leftharpoondown
rightleftharpoons
←−
⇐=
−→
=⇒
←→
⇐⇒
−→
→
longleftarrow
Longleftarrow
longrightarrow
Longrightarrow
longleftrightarrow
Longleftrightarrow
longmapsto
hookrightarrow
rightharpoonup
rightharpoondown
leadsto
↑
⇑
↓
⇓
uparrow
Uparrow
downarrow
Downarrow
updownarrow
Updownarrow
nearrow
searrow
swarrow
nwarrow
ldots
prime
exists
Diamonda
∃
⊥
···
∀
top
bot
mho
cdots
forall
ı
flat
clubsuit
Re
.
.
.
∞
√

vdots
infty
surd
jmath
natural
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Title Page
imath
♣
Maths in text
Accents and For . . .
Miscellaneous symbols
...
Introduction
Im
..
.
♥
∠
ℵ
aleph
ddots
hbar
Boxa
∅
emptyset
triangle
neq
ell
sharp
heartsuit
angle
nabla
℘
♠
∂
wp
spadesuit
partial
♦
diamondsuit
Page 22 of 31
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a
Not predefined in NFSS. Use the latexsym or amssymb package.
Close
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23. 11.7.8.
Variable-sized symbols
sum
bigcap
bigodot
prod
bigcup
bigotimes
coprod
bigsqcup
bigoplus
int
bigvee
biguplus
oint
bigwedge
Introduction
Maths in text
11.7.9.
Delimiters
Fraction
Equation
↑
{
|
⇑
uparrow
{
lfloor
langle
}
|
↓
Uparrow
}
rfloor
rangle
|
downarrow
updownarrow
/
⇓
Definitions for . . .
lceil
/
Downarrow
Updownarrow
rceil
backslash
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
11.7.10.
A
LTEX math constructs
abc
←−
−
abc
abc
widetilde{abc}
overleftarrow{abc}
overline{abc}
abc
−→
−
abc
abc
widehat{abc}
overrightarrow{abc}
underline{abc}
Page 23 of 31
abc
√
abc
f
overbrace{abc}
sqrt{abc}
f’
abc
√
n
abc
abc
xyz
underbrace{abc}
sqrt[n]{abc}
frac{abc}{xyz}
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11.7.11.
AMS Greek and Hebrew (available with amssymb package)
Close
digamma
κ
varkappa
beth
daleth
gimel
Quit

24. 11.7.12.
AMS delimiters (available with amssymb package)
ulcorner
11.7.13.
urcorner
llcorner
lrcorner
AMS miscellaneous (available with amssymb package)
∅
hbar
triangledown
circledS
nexists
Game
varnothing
blacksquare
sphericalangle
diagup
∠
k
hslash
square
angle
mho
Bbbk
blacktriangle
blacklozenge
complement
diagdown
♦
ð
vartriangle
lozenge
measuredangle
Finv
backprime
blacktrinagledown
bigstar
eth
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
a
Not defined in old releases of the amssymb package; define with the DeclareMathSymbol
command.
11.7.14.
AMS negated arrows (available with amssymb package)
Page 24 of 31
nleftarrow
nRightarrow
nrightarrow
nleftrightarrow
nLeftarrow
nLeftrightarrow
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25. 11.7.15.
AMS binary relations (available with amssymb package)
≈
∝
leqq
lesssim
lessdot
lesseqgtr
risingdotseq
backsimeq
sqsubset
precsim
trianglelefteq
smallsmile
Bumpeq
eqslantgtr
gtrdot
gtreqless
circeq
thickapprox
sqsupset
succsim
trianglerighteq
shortparallel
varpropto
backepsilon
leqslant
lessapprox
lll
lesseqqgtr
fallingdotseq
subseteqq
preccurlyeq
precapprox
vDash
smallfrown
geqq
gtrsim
ggg
gtreqqless
triangleq
supseteqq
succcurlyeq
succapprox
Vdash
between
blacktriangleleft
blacktriangleright
∼
∴
eqslantless
approxeq
lessgtr
doteqdot
backsim
Subset
curlyeqprec
vartriangleleft
Vvdash
bumpeq
geqslant
gtrapprox
gtrless
eqcirc
thicksim
Supset
curlyeqsucc
vartriangleright
shortmid
pitchfork
therefore
because
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
Page 25 of 31
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26. 11.7.16.
AMS binary operators (available with amssymb package)
dotplus
Cup
doublebarwedge
boxdot
ltimes
rightthreetimes
circleddash
centerdot
smallsetminus
barwedge
boxminus
boxplus
rtimes
curlywedge
circledast
intercal
Cap
veebar
boxtimes
divideontimes
leftthreetimes
curlyvee
circledcirc
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
11.7.17.
AMS negated binary relations (available with amssymb package)
nless
nleqq
lvertneqq
nprec
precnapprox
nmid
ntriangleleft
subsetneq
varsubsetneqq
ngeqslant
gneqq
gnapprox
succnsim
nshortparallel
nVDash
nsupseteq
varsupsetneq
nleq
lneq
lnsim
npreceq
nsim
nvdash
ntrianglelefteq
varsubsetneq
ngtr
ngeqq
gvertneqq
nsucc
succnapprox
nparallel
ntriangleright
nsupseteqq
supsetneqq
nleqslant
lneqq
lnapprox
precnsim
nshortmid
nvDash
nsubseteq
subsetneqq
ngeq
gneq
gnsim
nsucceq
ncong
nvDash
ntrianglerighteq
supsetneq
varsupsetneqq
Mathematical . . .
Accents and For . . .
Title Page
Page 26 of 31
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27. 11.7.18.
AMS arrows (available with amssymb package)
dashrightarrow
leftrightarrows
leftarrowtail
curvearrowleft
upuparrows
multimap
rightleftarrows
twoheadrightarrow
rightleftharpoons
Rsh
downharpoonright
11.7.19.
dashleftarrow
Lleftarrow
looparrowleft
circlearrowleft
upharpoonleft
leftrightsquigarrow
rightrightarrows
rightarrowtail
curvearrowright
downdownarrows
rightsquigarrow
leftleftarrows
twoheadleftarrow
leftrightharpoons
Lsh
downharpoonleft
rightrightarrows
rightleftarrows
looparrowright
circlearrowright
upharpoonright
arccos
cos
csc
exp
ker
limsup
min
sinh
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
Log-like symbols
arccos
cos
csc
exp
ker
lim sup
min
sinh
Introduction
arcsin
cosh
deg
gcd
lg
ln
Pr
sup
arcsin
cosh
deg
gcd
lg
ln
Pr
sup
arctan
cot
det
hom
lim
log
sec
tan
arctan
cot
det
hom
lim
log
sec
tan
arg
coth
dim
inf
lim inf
max
sin
tanh
arg
coth
dim
inf
liminf
max
sin
tanh
Page 27 of 31
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28. 11.7.20.
Double accents in math (available with amssymb package)
´
´
A
˘
˘
A
¨
A
`
`
A
˜
A
Bar{Bar{A}}
Grave{Grave{A}}
¯
A
ˇ
ˇ
A
˙
A
ˆ
ˆ
A
Tilde{Tilde{A}}
A
Vec{Vec{A}}
Acute{Acute{A}}
Breve{Breve{A}}
Ddot{Ddot{A}}
Check{Check{A}}
Dot{Dot{A}}
Introduction
Hat{Hat{A}}
Maths in text
Fraction
Equation
Definitions for . . .
11.7.21.
Other Styles
AMS-LaTeX
Mathematical . . .
11.7.21.1.
Accents and For . . .
Caligraphic letters
ABCDEF GH IJ K LMN OPQRST UVWXYZ
Title Page
use mathcal{}
11.7.21.2.
Mathbb letters
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Page 28 of 31
use mathbb{}
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11.7.21.3.
Mathfrak letters
Full Screen
ABCDEFGHIJKLMNOPQRSTUVWXYZ
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use mathfrak{} with amssymb package
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29. 11.7.21.4.
Math bold italic letters
ABCDEFGHIJKLMNOPQRSTUVWXYZ
use mathbi{}
Introduction
Maths in text
11.7.21.5.
Math Sans serif letters
Fraction
Equation
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Definitions for . . .
AMS-LaTeX
use mathsf{}
Mathematical . . .
Accents and For . . .
11.7.21.6.
Math bold letters
Title Page
ABCDEFGHIJKLMNOPQRSTUVWXYZ
use mathbf{}
11.7.22.
Accents–Symbols
´
o
`
o
˙
o
oo
o
¯
ß
ø
Ø
s
.
’{o}
‘{o}
.{o}
t{oo}
b{o}
¨
o
˜
o
˘
o
o
¸
Å
"{o}
˜{o}
u{o}
c{o}
AA
ˆ
o
¯
o
˝
o
o
.
å
ˆ{o}
={o}
H{o}
d{o}
aa
ss
o
O
d s
ı
s
¶
˚
s
i
t s
P
r s

ˇ
s
§
˝
s
j
v s
S
H s
Page 29 of 31
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30. 11.8.
11.8.1.
Accents and Foreign Letters
Printing command characters
Introduction
The characters # $ ˜ ˆ % { } are interpreted as commands. If they are to be printed as text, the
character must precede them:
$ = $
& = &
% = %
# = #
= _ { = {
} = }
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
11.8.2.
Mathematical . . .
The special characters
Accents and For . . .
These special characters do not exist on the computer keyboard. They can however be generated
by special commands as follows:
§= S
11.8.3.
†= dag
‡= ddag
¶= P
c = copyright
Title Page
£= pounds
Foreign letters
Special letters that exist in European languages other than English can also be generated with
TEX. These are:
Page 30 of 31
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œ= oe
ø= o
Œ= OE
Ø= O
æ= ae
ł= l
Æ= AE
Ł= L
å= aa
ß= ss
Å= AA
SS= SS
¡ = !‘
¿ = ?‘
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31. 11.8.4.
Accents
`
o = ‘o
¯
o = =o
oo = t{oo}
´
o = ’o
˙
o = .o
o = c o
¸
ˆ
o = ˆo
˘
o = u o
o = d o
.
¨
o = "o
ˇ
o = v o
o = b o
¯
˜
o = ˜o
˝
o = H o
˚
o = r o
A
The last command, r, is new to LTEX 2ε . The o above is given merely as an example: any
letter may be used. With i and j it should be pointed out that the dot must first be removed. This
is carried out by prefixing these letters with . The command i yield ı.
Introduction
Maths in text
Fraction
Equation
Definitions for . . .
AMS-LaTeX
Mathematical . . .
Accents and For . . .
Title Page
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