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Operators and general syntax
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Standard Operators
+ – ∗ / ^ ! i
Relational Operators
< > ≤
Defining Variables
beta=45
Defining Functions
f(x):x^2
Standard Functions
sqrt, lg, etc.
Square Root
sqrt(x)
n-th Root
rt(x; n[; k])
Exponential Function
exp(x)
Natural Logarithm
ln(x)
Logarithm
log(x; b)
Common Logarithm
lg(x)
Binary Logarithm
ld(x)
k-th Branch of the Ln
lk(x; k)
Argument
arg(z)
Absolute Value
abs(z)
Complex Conjugate
conj(z)
Modulo
mod(a; b)
Sign Function
sign(x)
Heaviside step function
H(x), heavi(x)
Gamma Function
gamma(z), gammaf(z)
Maximum
max(a;b;c;…)
Minimum
min(a;b;c;…)
Rounding
round(x)
Ceiling Function
ceil(x)
Floor Function
floor(x)
Fraction
frac(x)
Truncate
trunc(x)
Stochastics
avg, binomial, etc.
Average (Mean)
avg(a;b;c;…), mean(a;b;c;…)
Random Number
random(min; max)
Binomial Coefficient
nk(n; k)
Permutation without repetition
perm(n;k), vari(n;k)
Binomial Distribution
binomial(n; k; p)
Trigonometric Functions
sin, cos, asin, etc.
Radian
rad(x)
Radian (Multiple of π)
radpi(x)
Degrees
deg(x)
Sine
sin(x)
Cosine
cos(x)
Tangent
tan(x)
Cosecant
csc(x), cosec(x)
Secant
sec(x)
Cotangent
cot(x)
Arcsine
asin(x), arcsin(x)
Arccosine
acos(x), arccos(x)
Arctangent
atan(x), arctan(x)
Arccosecant
acsc(x), arccsc(x), …
Arcsecant
asec(x), arcsec(x)
Arccotangent
acot(x), arccot(x)
Hyperbolic Functions
sinh, cosh, asinh, etc.
Hyperbolic Sine
sinh(x), sinhyp(x)
Hyperbolic Cosine
cosh(x), coshyp(x)
Hyperbolic Tangent
tanh(x), tanhyp(x)
Hyperbolic Cosecant
csch(x), cschyp(x), …
Hyperbolic Secant
sech(x), sechyp(x)
Hyperbolic Cotangent
coth(x), cothyp(x)
Area Hyperbolic Sine
asinh(x), arsinh(x), asinhyp(x), …
Area Hyperbolic Cosine
acosh(x), arcosh(x), acoshyp(x), …
Area Hyperbolic Tangent
atanh(x), artanh(x), atanhyp(x), …
Area Hyperbolic Cosecant
acsch(x), arcsch(x), acschyp(x), …
Area Hyperbolic Secant
asech(x), arsech(x), asechyp(x), …
Area Hyperbolic Cotangent
acoth(x), arcoth(x), acothyp(x), …
Constants
pi, E, etc.
Circular constant π
pi = 3.1415926535898
Euler’s number e
E = 2.718281828459
SI prefixes
kilo, nano, …
Standard gravity g
g = 9.80665 m/s
2
Avogadro constant N
A
Na = 6.0221415⋅10
23
mol
-1
Loschmidt constant n
0
n0 = 2.6867773⋅10
25
m
-3
Atomic mass u
u = 1.66053886⋅10
-27
kg
Rest masses of elementary particles
me, mp, mn, etc.
Boltzmann constant k
kB = 1.3806505⋅10
-23
J/K
Universal gas constant R
R = 8.314472 J⋅mol
-1
⋅K
-1
Molar gas volume V
m
Vm = 22.413996 l/mol
Standard atmosphere p
0
p0 = 101 325 Pa
Gravitational constant G
G = 6.674⋅10
-11
m
3
⋅kg
-1
⋅s
-2
Vacuum speed of light c
c = 299 792 458 m/s
Elementary charge e
el = 1.60217653⋅10
-19
C
Electric constant ε
0
eps = 8.854⋅10
-12
F/m
Magnetic constant μ
0
m0 = 12.566⋅10
-7
N⋅A
-2
Faraday constant F
F = 96 485.3383 C/mol
Wien’s displacement constant b
b = 2.8977685⋅10
-3
m⋅K
Stefan-Boltzmann constant σ
sb = 5.6704⋅10
-8
W⋅m
-2
⋅K
-4
Planck constant h
h = 6.6260693⋅10
-34
Js
Reduced Planck constant ħ
hp = h/2π = 1.05457⋅10
-34
Js
Rydberg constant R
∞
ryd = 1.09737⋅10
7
m
-1
Rydberg frequency R
Rf = c⋅R
∞
= 3.2898⋅10
15
Hz
Rydberg energy R
y
Ry = h⋅c⋅R
∞
= 13.6057 eV
Bohr radius a
0
a0 = 0.5291772108⋅10
-10
m
Bohr magneton μ
B
mB = 9.27400949⋅10
-24
J/T
Nuclear magneton μ
N
mN = 5.05078343⋅10
-27
J/T
Compton wavelength (electron) λ
C,e
Ce = 2.426310238⋅10
-12
m
Compton wavelength (neutron) λ
C,n
Cn = 1.3195909067⋅10
-15
m
Compton wavelength (proton) λ
C,p
Cp = 1.3214098555⋅10
-15
m
Classical electron radius r
e
re = 2.817940325⋅10
-15
m
Fine-structure constant α
fine = 7.297352568⋅10
-3
Fluxon Φ
0
flux = 2.06783372⋅10
-15
Wb
Josephson constant K
J
Kj = 1/Φ
0
= 483.598⋅10
12
Hz/V
Landé g-factor of the electron g
e
ge = 2.0023193043718
Gyromagnetic ratio γ
Proton
gyro = 2.675⋅10
8
rad⋅s
-1
⋅T
-1
Quantum Hall resistance R
K
Rk = 25.812807449⋅10
3
Ω
Tensors
Kronecker, Levi-Civita
Kronecker δ
ij
delta(i; j)
Levi-Civita ε
ijk
levi(i; j; k)
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Compton wavelength (proton) λ
C,p
Syntax:
Cp
λ
C,p
= 1.3214098555⋅10
-15
m
Compton wavelength