General Usage

Operators and general syntax

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ans, answer Help Command
help topic 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/s² Avogadro constant N_A
Na = 6.0221415⋅10²³ mol^-1 Loschmidt constant n₀
n0 = 2.6867773⋅10²⁵ 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 p₀
p0 = 101 325 Pa Gravitational constant G
G = 6.674⋅10^-11 m³⋅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 ε₀
eps = 8.854⋅10^-12 F/m Magnetic constant μ₀
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⋅10⁷ m^-1 Rydberg frequency R
Rf = c⋅R_∞ = 3.2898⋅10¹⁵ Hz Rydberg energy R_y
Ry = h⋅c⋅R_∞ = 13.6057 eV Bohr radius a₀
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 Φ₀
flux = 2.06783372⋅10^-15 Wb Josephson constant K_J
Kj = 1/Φ₀ = 483.598⋅10¹² Hz/V Landé g-factor of the electron g_e
ge = 2.0023193043718 Gyromagnetic ratio γ_Proton
gyro = 2.675⋅10⁸ rad⋅s^-1⋅T^-1 Quantum Hall resistance R_K
Rk = 25.812807449⋅10³ Ω

Tensors

Kronecker, Levi-Civita

Kronecker δ_ij
delta(i; j) Levi-Civita ε_ijk
levi(i; j; k)

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