Sympy is a Python package used to work with symbolic math. Symbolic math refers to calculations that use symbolic variables rather than variables that contain numerical values. Let's take a simple example:

$$ sin(\frac{\pi}{2}) $$

If we define

$$ \pi = 3.1459 $$

Then calculate the arcsine of pi/2, we should get 1. But the value doesn't exactly equal 1:



In [2]:

    
import math
pi = 3.1459
print(math.sin(pi/2))









    



0.9999976808467592

Instead, if we define pi symbolically

$$ \pi = \pi $$

Then when we calculate the sine of pi/2, we get an exact value, 1:

pi = symbolic math symbol version of pi
print(sin(pi/2))
1

Now let's take a concrete problem and solve it with symbolic math



In [3]:

    
import sympy



In [4]:

    
a, T1, T2, L1, L2 = sympy.symbols('a T1 T2 L1 L2')



In [5]:

    
CTE_Eq = sympy.Eq(a*L1*(T2-T1), L2)



In [6]:

    
CTE_Eq.subs(T1, 20)
CTE_Eq.subs(L1, 80.00)
CTE_Eq.subs(L2, 80.10)
CTE_Eq.subs(a, 24e-6)









    Out[6]:





Eq(2.4e-5*L1*(-T1 + T2), L2)



In [7]:

    
CTE_Eq









    Out[7]:





Eq(L1*a*(-T1 + T2), L2)



In [8]:

    
expr = sympy.solveset(CTE_Eq, T2)



In [9]:

    
expr.subs(T1, 20)
expr.subs(L1, 80.00)
expr.subs(L2, 80.10)
expr.subs(a, 24e-6)









    Out[9]:





{T1 + 41666.6666666667*L2/L1}



In [10]:

    
expr









    Out[10]:





{T1 + L2/(L1*a)}



In [11]:

    
T1 = 20
#T2 = ?
a = 24e-6
L1 = 80
L2 = 80.10



In [12]:

    
T2 = T1 + (L2)/(a*L1)
T2









    Out[12]:





41738.74999999999



In [13]:

    
a*L1*(72-20)









    Out[13]:





0.09984



In [14]:

    
T1+ (L2-L1)/(a*L1)









    Out[14]:





72.08333333333037



In [15]:

    
def clearance(cl):
    T1 = 20
    #T2 = ?
    a = 24e-6
    L1 = 80
    L2 = 80.10 + cl
    return T1+ (L2-L1)/(a*L1)



In [19]:

    
clearance(0.10)









    Out[19]:





124.16666666666075



In [ ]: