General Usage
Operators and general syntax
Settings
Angle mode, auto updates, etc. Last result
ans, answer Help Command
help topic Standard Operators
+ – ∗ / ^ ! i Relational Operators
< > ≤ Defining Variables
beta=45 Defining Functions
f(x):x^2
Angle mode, auto updates, etc. Last result
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)
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)
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)
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), …
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 NA
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 Vm
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 Ry
Ry = h⋅c⋅R∞ = 13.6057 eV Bohr radius a0
a0 = 0.5291772108⋅10-10 m Bohr magneton μB
mB = 9.27400949⋅10-24 J/T Nuclear magneton μN
mN = 5.05078343⋅10-27 J/T Compton wavelength (electron) λC,e
Ce = 2.426310238⋅10-12 m Compton wavelength (neutron) λC,n
Cn = 1.3195909067⋅10-15 m Compton wavelength (proton) λC,p
Cp = 1.3214098555⋅10-15 m Classical electron radius re
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 KJ
Kj = 1/Φ0 = 483.598⋅1012 Hz/V Landé g-factor of the electron ge
ge = 2.0023193043718 Gyromagnetic ratio γProton
gyro = 2.675⋅108 rad⋅s-1⋅T-1 Quantum Hall resistance RK
Rk = 25.812807449⋅103 Ω
pi = 3.1415926535898 Euler’s number e
E = 2.718281828459 SI prefixes
kilo, nano, … Standard gravity g
g = 9.80665 m/s2 Avogadro constant NA
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 Vm
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 Ry
Ry = h⋅c⋅R∞ = 13.6057 eV Bohr radius a0
a0 = 0.5291772108⋅10-10 m Bohr magneton μB
mB = 9.27400949⋅10-24 J/T Nuclear magneton μN
mN = 5.05078343⋅10-27 J/T Compton wavelength (electron) λC,e
Ce = 2.426310238⋅10-12 m Compton wavelength (neutron) λC,n
Cn = 1.3195909067⋅10-15 m Compton wavelength (proton) λC,p
Cp = 1.3214098555⋅10-15 m Classical electron radius re
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 KJ
Kj = 1/Φ0 = 483.598⋅1012 Hz/V Landé g-factor of the electron ge
ge = 2.0023193043718 Gyromagnetic ratio γProton
gyro = 2.675⋅108 rad⋅s-1⋅T-1 Quantum Hall resistance RK
Rk = 25.812807449⋅103 Ω
Tensors
Kronecker, Levi-Civita
Kronecker δij
Syntax: delta(i; j;&hellip), kronecker(i; j;…)
| Example | Syntax | Output |
|---|---|---|
| &delta1 1 | delta(1; 1) | 1 |
| &delta4 0 | delta(4; 0) | 0 |
| &delta0 -5 | delta(0; -5) | 0 |
| &delta3 4 5 | delta(3; 4; 5) | 0 |
| &delta2 2 2 | delta(2; 2; 2) | 1 |
Kronecker delta returns 1 if all indices have the same value, otherwise it returns 0.