constant¶
Returns the value of various mathematical and physical constants.
Synopsis¶
constant (name, unit)
Required Arguments¶
- char
name(Input) - Character string containing the name of the desired constant. The case of
the character string
namedoes not matter. The names “PI”, “Pi”, “pI”, and “pi” are equivalent. Spaces and underscores are allowed and ignored. - char
unit(Input) - Character string containing the units of the desired constant. If
None, then Système International d’Unités (SI) units are assumed. The case of the character stringunitdoes not matter. The names “METER”, “Meter” and “meter” are equivalent.unithas the formU1*U2*...*Um/V1/.../Vn, whereUiandViare the names of basic units or are the names of basic units raised to a power. Basic units must be separated by*or/. Powers are indicated by^, as in “m^2” for \(\text{m}^2\). Examples are, “METER*KILOGRAM/SECOND”, “M*KG/S”, “METER”, or “M/KG^2”.
Return Value¶
By default, constant returns the desired constant. If no value can be
computed, NaN is returned.
Description¶
The names allowed are listed in the following table. Values marked with a ‡ are exact (to machine precision). The references in the right-hand column are indicated by the code numbers: [1] for Cohen and Taylor (1986), [2] for Liepman (1964), and [3] for precomputed mathematical constants.
| Name | Description | Value | Reference |
|---|---|---|---|
| Amu | Atomic mass unit | 1.6605655 × \(10^{-27}\) kg | 1 |
| ATM | Standard atm pressure | 1.01325 × \(10^5\) \(N/m^2\) ‡ | 2 |
| AU | Astronomical unit | 1.496 × \(10^{11}\) m | |
| Avogadro | Avogadro’s number, N | 6.022045 × \(10^{23}\) 1/mole | 1 |
| Boltzman | Boltzman’s constant, k | 1.380662 × \(10^{-23}\) J/K | 1 |
| C | Speed of light, c | 2.997924580 × \(10^8\) m/s | 1 |
| Catalan | Catalan’s constant | 0.915965…‡ | 3 |
| E | Base of natural logs, e | 2.718…‡ | 3 |
| ElectronCharge | Electron charge, e | 1.6021892 × \(10^{-19}\) C | 1 |
| ElectronMass | Electron mass, \(m_e\) | 9.109534 × \(10^{-31}\) kg | 1 |
ElectronVolt Euler |
ElectronVolt, ev Euler’s constant, γ |
1.6021892 \(x10 ^{-19}\) J 0.577…‡ |
1 3 |
| Faraday | Faraday constant, F | 9.648456 × \(10^4\) C/mole | 1 |
| FineStructure | Fine structure, α | 7.2973506 × \(10^{-3}\) | 1 |
| Gamma | Euler’s constant, γ | 0.577…‡ | 3 |
| Gas | Gas constant, \(R_0\) | 8.31441 J/mole/K | 1 |
| Gravity | Gravitational constant, G | 6.6720 × \(10^{-11}\) N \(m^2/kg^2\) | 1 |
| Hbar | Planck’s constant/2π | 1.0545887 × \(10^{-34}\) J s | 1 |
| PerfectGasVolume | Std vol ideal gas | 2.241383 × \(10^{-2}\) \(m^3\)/mole | 1 |
| Pi | Pi, π | 3.141…‡ | 3 |
| Planck | Planck’s constant, h | 6.626176 × \(10^{-34}\) J s | 1 |
| ProtonMass | Proton mass, \(M_p\) | 1.6726485 × \(10^{-27}\) kg | 1 |
| Rydberg | Rydberg’s constant, \(R_\mu\) | 1.097373177 × \(10^7\)/m | 1 |
| Speedlight | Speed of light, c | 2.997924580 × \(10^8\) m/s | 1 |
| StandardGravity | Standard g | 9.80665 \(m/s^2\) ‡ | 2 |
| StandardPressure | Standard atm pressure | 1.01325 × \(10^5\) \(N/m^2\) ‡ | 2 |
| StefanBoltzman | Stefan-Boltzman, σ | 5.67032 × \(10^{-8}W/K^4/m^2\) | 1 |
| WaterTriple | Triple point of water | 2.7316× \(10^2\) K | 2 |
The units allowed are as follows:
| Unit | Description |
|---|---|
| Time | day, hour = hr, min, minute, s = sec = second, year |
| Frequency | Hertz = Hz |
| Mass | AMU, g = gram, lb = pound, ounce = oz, slug |
| Distance | Angstrom, AU, feet = foot, in = inch, m = meter = metre, micron, mile, mill, parsec, yard |
| Area | Acre |
| Volume | 1 = liter=litre |
| Force | dyne, N = Newton |
| Energy | BTU, Erg, J = Joule |
| Work | W = watt |
| Pressure | ATM = atmosphere, bar |
| Temperature | degC = Celsius, degF = Fahrenheit, degK = Kelvin |
| Viscosity | poise, stoke |
| Charge | Abcoulomb, C = Coulomb, statcoulomb |
| Current | A = ampere, abampere, statampere |
| Voltage | Abvolt, V = volt |
| Magnetic induction | T = Telsa, Wb = Weber |
| Other units | I, farad, mole, Gauss, Henry, Maxwell, Ohm |
The following metric prefixes may be used with the above units. The one or two letter prefixes may only be used with one letter unit abbreviations.
A |
d |
||||
|---|---|---|---|---|---|
F |
femto | \(10^{-15}\) | dk |
deca | \(10^2\) |
P |
pico | \(10^{-12}\) | k |
kilo | \(10^3\) |
N |
nano | \(10^{-9}\) | myria | \(10^4\) | |
U |
micro | \(10^{-6}\) | mega | \(10^6\) | |
M |
milli | \(10^{-3}\) | g |
giga | \(10^9\) |
C |
centi | \(10^{-2}\) | t |
tera | \(10^{12}\) |
There is no one letter unit abbreviation for myria or mega since m means milli.
Examples¶
Example 1¶
In this example, Euler’s constant γ is obtained and printed. Euler’s constant is defined to be
\[\gamma = \lim_{n \to \infty}
\left[
\sum_{k=1}^{n-1} \tfrac{1}{k} - \ln n
\right]\]
from __future__ import print_function
from pyimsl.math.constant import constant
gamma = constant("gamma", "")
print("gamma = ", gamma)
Output¶
gamma = 0.5772156649015329
Example 2¶
In this example, the speed of light is obtained using several different units.
from __future__ import print_function
from pyimsl.math.constant import constant
# Get speed of light in meters/second
speed_light = constant("speed_light", "meter/second")
print("Speed of light = ", speed_light, " meters/sec")
# Get speed of light in miles/second
speed_light = constant("speed_light", "mile/second")
print("Speed of light = ", speed_light, " mile/sec")
# Get speed of light in centimeters/nanosecond
speed_light = constant("speed_light", "cm/ns")
print("Speed of light = ", speed_light, " cm/ns")
Output¶
Speed of light = 299792458.0 meters/sec
Speed of light = 186282.39705122088 mile/sec
Speed of light = 29.979245800000015 cm/ns
Warning Errors¶
IMSL_MASS_TO_FORCE |
A conversion of units of mass to units of force was required for consistency. |