In [1]:

    

from sympy import *
from sympy.interactive.printing import init_printing
init_printing()


    

In [2]:

    

from sympa import domath


    

In [3]:

    

import pandas as pd


    

In [4]:

    

df = pd.DataFrame({'x' : range(7)})
df['x'] = df.x * 10
df['y'] = df.x * 0.05
df['r'] = pi * df['y'] / 2
df


    

    
Out[4]:






  

    

      

      
x
      
y
      
r
    
  
  

    

      
0
      
  0
      
 0.0
      
       0
    
    

      
1
      
 10
      
 0.5
      
 0.25*pi
    
    

      
2
      
 20
      
 1.0
      
  0.5*pi
    
    

      
3
      
 30
      
 1.5
      
 0.75*pi
    
    

      
4
      
 40
      
 2.0
      
  1.0*pi
    
    

      
5
      
 50
      
 2.5
      
 1.25*pi
    
    

      
6
      
 60
      
 3.0
      
  1.5*pi
    
  

In [5]:

    

#for those who don't know..."pi" is irrational...
df['r'][1]


    

    
Out[5]:





$$0.25 \pi$$

In [6]:

    

x,y,r,rn1,x1,xn1,yn1 = symbols('x y r r_-1 x_1 x_-1 y_-1')
f = x + xn1
g = x**y + x*y*3.0 + (x1 * 0.5 + xn1 * pi / (yn1 + 1.0))**2
h = sin(r)
i = sin(r) / cos(rn1 + 1)


    

In [7]:

    

f, g, h, i


    

    
Out[7]:





$$\left ( x + x_{-1}, \quad 3.0 x y + x^{y} + \left(\frac{\pi x_{-1}}{y_{-1} + 1.0} + 0.5 x_{1}\right)^{2}, \quad \sin{\left (r \right )}, \quad \frac{\sin{\left (r \right )}}{\cos{\left (r_{-1} + 1 \right )}}\right )$$

In [8]:

    

df.x + df.x.shift(1) #this is easy...but not exactly


    

    
Out[8]:





0    NaN
1     10
2     30
3     50
4     70
5     90
6    110
Name: x, dtype: float64

In [9]:

    

#3.0 * df.x * df.y + df.x.mul(df.y) + (df.shift(1).mul(pi).div(df.shift(1) + 1.0))# + (0.5 * df.x.shift(-1))) # what the heck am I doing???


    

In [10]:

    

df['f'] = domath(df,f)
df['g'] = domath(df,g)
df['h'] = domath(df,h)
df['i'] = domath(df,i)


    

In [11]:

    

#round the excessive decimals...
df.g, df.h, df.i = (df[c].round(4) for c in ('g','h','i')); df


    

    
Out[11]:






  

    

      

      
x
      
y
      
r
      
f
      
g
      
h
      
i
    
  
  

    

      
0
      
  0
      
 0.0
      
       0
      
 NaN
      
        NaN
      
 0.0000
      
    NaN
    
    

      
1
      
 10
      
 0.5
      
 0.25*pi
      
  10
      
   118.1623
      
 0.7071
      
 1.3087
    
    

      
2
      
 20
      
 1.0
      
  0.5*pi
      
  30
      
  1371.9676
      
 1.0000
      
-4.6958
    
    

      
3
      
 30
      
 1.5
      
 0.75*pi
      
  50
      
  2942.9143
      
 0.7071
      
-0.8403
    
    

      
4
      
 40
      
 2.0
      
  1.0*pi
      
  70
      
  5771.1786
      
 0.0000
      
 0.0000
    
    

      
5
      
 50
      
 2.5
      
 1.25*pi
      
  90
      
 23220.5400
      
-0.7071
      
 1.3087
    
    

      
6
      
 60
      
 3.0
      
  1.5*pi
      
 110
      
        NaN
      
-1.0000
      
-4.6958
    
  

In [12]:

    

assert f.subs([(x,50),(xn1,40)]) == df['f'].iloc[5]
assert round(g.subs([(x,50),(y,2.5),(xn1,40),(x1,60),(yn1,2.0)]),4) == df['g'].iloc[5]
assert round(h.subs([(r,1.25*pi)]),4) == df['h'].iloc[5]
assert round(i.subs([(r,1.25*pi),(rn1,pi)]),4) == df['i'].iloc[5]


    

In [12]:

    




    

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