Automatic Error Propagation

If you take a physics class, you may need to deal with error propagation, which gets really annoying as the equation gets longer. If you are using this, make sure you are actually allowed to and you understand how error propagation works. Consider using this the same way you'd use wolfram alpha -- it can get you an answer easily but it won't make you better at math.

Installation

pip install errorpp

Function and Scope

As of the moment, the error propagation only supports expanding addition, multiplication, division and real number exponent. If you input anything else such as sin(x) it will throw an error. If you want see more functions implemented, open an issue, or better yet, make a pull request!

How to use

In its core, it uses sympy to process the expression. the errorpp.propagate function will take a sympy expression as the argument return the sympy expression with the error propagated. If your variables are all positive, you can pass in absolute=False to prevent the program from wrapping variables in absolute sign, which makes a cleaner output as sympy can cancel variables more easily.

You can also use the counterpart errorpp.propagate_latex which takes a string of latex expression as the argument and output the latex expression with the error propagated.

Alternatively, you directly call this from the terminal, which takes an latex equation as its first argument and print the latex expression with the error propagated to standard output. Use --no-absolute to prevent the program from wrapping variables in absolute sign.

Since the code base is quite small, I won't make a website with the documentation, but instead I will write the explanation in the docstring in the source code.

Code Example

You can use this directly in terminal

python -m errorpp '\\frac{- c_{w} m_{1} \\left(- T_{1} + T_{f}\\right) + c_{w} m_{2} \\left(T_{2} - T_{f}\\right)}{- T_{1} + T_{f}}' --no-absolute
# output
# \frac{\sqrt{\frac{c_{w}^{2} m_{1}^{2} \left(- T_{1} + T_{f}\right)^{2} \left(\frac{\Delta^{2}{\left(T_{1} \right)} + \Delta^{2}{\left(T_{f} \right)}}{\left(- T_{1} + T_{f}\right)^{2}} + \frac{\Delta^{2}{\left(m_{1} \right)}}{m_{1}^{2}} + \frac{\Delta^{2}{\left(c_{w} \right)}}{c_{w}^{2}}\right) + c_{w}^{2} m_{2}^{2} \left(T_{2} - T_{f}\right)^{2} \left(\frac{\Delta^{2}{\left(T_{2} \right)} + \Delta^{2}{\left(T_{f} \right)}}{\left(T_{2} - T_{f}\right)^{2}} + \frac{\Delta^{2}{\left(m_{2} \right)}}{m_{2}^{2}} + \frac{\Delta^{2}{\left(c_{w} \right)}}{c_{w}^{2}}\right)}{\left(- c_{w} m_{1} \left(- T_{1} + T_{f}\right) + c_{w} m_{2} \left(T_{2} - T_{f}\right)\right)^{2}} + \frac{\Delta^{2}{\left(T_{1} \right)} + \Delta^{2}{\left(T_{f} \right)}}{\left(- T_{1} + T_{f}\right)^{2}}} \left(- c_{w} m_{1} \left(- T_{1} + T_{f}\right) + c_{w} m_{2} \left(T_{2} - T_{f}\right)\right)}{- T_{1} + T_{f}}

Or import this as a module

import errorpp
import sympy

eq = sympy.parse_latex('\\frac{- c_{w} m_{1} \\left(- T_{1} + T_{f}\\right) + c_{w} m_{2} \\left(T_{2} - T_{f}\\right)}{- T_{1} + T_{f}}')
p = errorpp.propagate(eq, absolute=False)
print(pretty(eq, use_unicode=False))

# Output
#          _____________________________________________________________________
#         /                         /     2             2             2         
#        /     2    2             2 |Delta (T_1) + Delta (T_f)   Delta (m_1)   D
#       /   c_w *m_1 *(-T_1 + T_f) *|------------------------- + ----------- + -
#      /                            |                  2                2       
#     /                             \      (-T_1 + T_f)              m_1        
#    /      --------------------------------------------------------------------
#   /                                                                           
# \/                                                                 (-c_w*m_1*(
# ------------------------------------------------------------------------------
#                                                                               
# 
# ______________________________________________________________________________
#     2     \                          /     2             2             2      
# elta (c_w)|      2    2            2 |Delta (T_2) + Delta (T_f)   Delta (m_2) 
# ----------| + c_w *m_2 *(T_2 - T_f) *|------------------------- + ----------- 
#       2   |                          |                  2                2    
#    c_w    /                          \       (T_2 - T_f)              m_2     
# ------------------------------------------------------------------------------
#                                   2                                           
# -T_1 + T_f) + c_w*m_2*(T_2 - T_f))                                            
# ------------------------------------------------------------------------------
#                                         -T_1 + T_f                            
# 
# ___________________________________________                                   
#        2     \                                                                
#   Delta (c_w)|                                                                
# + -----------|                                                                
#          2   |        2             2                                         
#       c_w    /   Delta (T_1) + Delta (T_f)                                    
# -------------- + ------------------------- *(-c_w*m_1*(-T_1 + T_f) + c_w*m_2*(
#                                    2                                          
#                        (-T_1 + T_f)                                           
# ------------------------------------------------------------------------------
#                                                                               
# 
#            
#            
#            
#            
#            
#            
# T_2 - T_f))
#            
#            
# -----------
#