Formula Database Tutorial

outline:
1. How to better write your formulas in the database.
2. Comming soon!

import numpy as np
import pandas as pd
import sympy as sp

import FormulaLab as fl

1. How to write your formulas in the database

FormulaLab has specific assumptions when reading formulas, such as:

1. Case sensitivity. (A does not equal a)
2. Follows python syntax, such as, power (**) not (^)
3. Follow SymPy syntax, such as, sin, cos, integrate, diff, ...
4. All different variables must have different names in one database,
to avoid mixing physics!
5. Constants should ends with "_" (eg., speed_of_light_, plank_, gravity_).
   Because constants does not help with derivation and slow the searching
   speed.
6. (Optional) It is recomended to use capital letters with Vector quantities
and small letters with scalar quantities(eg., Force, mass).
(FormulaLab will tell the difference in future versions)

Suggestions:

1- Write a full and uniqe name of all of the variables in your formula
database.
2- Add as many column in your database as you can, so you can use them
later as filters.
Because formulas can be mixed with unrelated field of study, which leads
to wrong answers.
3- Add underscore "_" at the end of constants.

# Example of a formula database
df = pd.read_csv('Example Database.csv')
df

	ID	Formula	Field	Reference	Note
0	1	Displacement = Velocity * time	Mechanics	NaN	NaN
1	2	Acceleration = Velocity / time	Mechanics	NaN	NaN
2	3	Force = mass * Acceleration	Mechanics	NaN	NaN
3	4	Weight = mass * Gravety	Mechanics	NaN	NaN
4	5	Momentum = mass * Velocity	Mechanics	NaN	NaN
5	6	Centerpetal_acceleration = Velocity**2 / radious	Mechanics	NaN	NaN
6	7	work = Force * Displacement	Mechanics	NaN	NaN
7	8	Kinetic_energy = mass * Velocity**2 / 2	Mechanics	NaN	NaN
8	9	Power = work / time	Mechanics	NaN	NaN
9	10	pressure = Force / Area	Mechanics	NaN	NaN
10	11	frequency = c_ / wavelength	Waves	NaN	NaN
11	12	time_perioud = 1 / frequency	Waves	NaN	NaN
12	13	refractive_index = c_ / Velocity	Waves	NaN	NaN
13	14	Electric_field = Force / charge	EM	NaN	NaN
14	15	Electric_potential = Electric_field * Displace...	EM	NaN	NaN

phyfos = fl.FormulaSearch(data=df, formula_col='Formula')

d = phyfos.find('Displacement','time')
d

[Velocity*time]

d = phyfos.derive('Displacement','time')
d

[Velocity*time,
 Acceleration*time**2,
 time*work/(Velocity*mass),
 Power*time/Force]

wl = phyfos.find('wavelength',id=11)
wl

[c/frequency]