bc extensions

bc is a powerful, yet somewhat minimalistic "basic calculator' for *ix environments. It is a pure command line tool which offers floating point arithmetics of arbitrary precision as well as large number arithmetics. For further information on bc, visit [https://www.gnu.org/software/bc/manual/html_mono/bc.html](GNU bc's documentations)

These files can be "imported" in bc by passing them to bc on the command line. Make sure, the -l flag is set:

bc -l extensions.bc scientific_constants.bc

Features

In extensions.bc

I mathematical constants

1. pi : defined as 4*atan(1)
2. e : defined as e(1)

II trigonometry

1. sin(x) : returns sine of x
2. cos(x) : returns cosine of x
3. atan(x) : returns arc tangent of x
4. tan(x) : returns tangent of x
5. asin(x) : returns arc sine of x
6. acos(x) : returns arc cosine of x
7. cot(x) : returns cotangent of x
8. acot(x) : returns arc cotangent of x
9. sec(x) : returns secans of x
10. cosec(x),csc(x) : returns cosecans of x
11. asec(x) : returns arc secans of x
12. acosec(x),ascs(x) : returns arc cosecans of x
13. sinh(x) : returns hyperbolical sine of x
14. cosh(x) : returns hyperbolical cosine of x
15. tanh(x) : returns hyperbolical tangent of x
16. coth(x) : returns hyperbolical cotangent of x
17. asinh(x) : returns arc hyperbolical sine of x
18. acosh(x) : returns arc hyperbolical cosine of x
19. atanh(x) : returns arc hyperbolical tangent of x
20. acoth(x) : returns arc hyperbolical cotangent of x
21. sech(x) : returns secans hyperbolicus of x
22. cosech(x),csch(x) : returns cosecans hyperbolicus of x
23. asech(x) : returns arc secans hyperbolicus of x
24. acosech(x),acsch(x) : returns arc cosecans hyperbolicus of x

III exponential functions

1. ln(x) : returns natural logarithm of x
2. log(x) : returns logarithm (base 10) of x
3. lb(x),ld(x) : returns logarithm (base 2) of x
4. pow(x,y) : returns x to the power of y

IV number theory

1. abs(n) : returns absolute value of n
2. mod(a,b) : returns a modulo b
3. factorize(n),fac(n) : prints primefactors of n; returns number of primefactors; returns 0 if n is a prime number; returns -1 if n is +-1 or 0. CAUTION: 13-digit number may need 30 s
4. factorial(n),f(n) : returns n factorial
5. gcd(a,b) : returns the greatest common divisor of a and b
6. lcm(a,b) : returns the least common multiple of a and b
7. bessel(n,x) : returns the Bessel function order n of x

In scientific_constants.bc

I particle masses

1. mp: proton rest mass in kg
2. mn: neutron rest mass in kg
3. me: electron rest mass in kg
4. mpev: proton rest mass in eV
5. mnev: neutron rest mass in eV
6. meev: electron rest mass in eV

II general physical constants

1. c: speed of light in the vacuum in m/s
2. h: Planck constant in Js
3. hbar: Planck constant divided by 2*pi in Js
4. kb: boltzmann constant in J/K
5. ec: elementary charge in C
6. na: avogadro number in 1/mol
7. epsilon0: dielectric constant in C^2/Jm
8. mu0: permeability of vacuum in T^2*m^3/J
9. alpha: fine structure constant
10. mub: Bohr magneton J/T
11. mun: nuclear magneton J/T
12. ge: free electron g factor
13. gammae: free electron gyromagnetic ratio in T/s
14. mue: electron magnetic moment
15. gammap: proton gyromagnetic ratio in water in T/s
16. mup: proton magnetic moment in J/T
17. amu: atomic mass unit in kg
18. a0: Bohr radius in m
19. re: electron radius in m
20. vmol: molar volume in l/mol
21. gh: proton g factor (lande factor)
22. grav: gravitational constant m^3/kg*s^2
23. g: acceleration due to gravity on surface of earth in m/s^2
24. lambdac: compton wavelength of the electron m

in prime_numbers.bc

prime numbers from 0 - 821641, i.e. first 65536 primes