In [1]:

    

# This will setup our sympy powered jupyter environment
from IPython.display import display
from sympy.interactive import printing
printing.init_printing()

import sympy
from sympy import S, symbols, exp, log, solve
print(sympy.__version__)
from batemaneq import bateman_parent


    

    




0.7.6

In [4]:

    

N = 3
zero, one, t = S('0'), S('1'), symbols('t')
lmbd = symbols('lambda:'+str(N))


    

In [5]:

    

bateman_parent(lmbd, t, one, zero, exp)


    

    
Out[5]:





$$\left [ e^{- \lambda_{0} t}, \quad \lambda_{0} \left(\frac{e^{- \lambda_{1} t}}{\lambda_{0} - \lambda_{1}} + \frac{e^{- \lambda_{0} t}}{- \lambda_{0} + \lambda_{1}}\right), \quad \lambda_{0} \lambda_{1} \left(\frac{e^{- \lambda_{2} t}}{\left(\lambda_{0} - \lambda_{2}\right) \left(\lambda_{1} - \lambda_{2}\right)} + \frac{e^{- \lambda_{1} t}}{\left(\lambda_{0} - \lambda_{1}\right) \left(- \lambda_{1} + \lambda_{2}\right)} + \frac{e^{- \lambda_{0} t}}{\left(- \lambda_{0} + \lambda_{1}\right) \left(- \lambda_{0} + \lambda_{2}\right)}\right)\right ]$$

In [7]:

    

k = symbols('k')
bateman_parent([i*k for i in range(1, 7)], one, one, zero, exp)


    

    
Out[7]:





$$\left [ e^{- k}, \quad k \left(\frac{e^{- k}}{k} - \frac{1}{k} e^{- 2 k}\right), \quad 2 k^{2} \left(\frac{e^{- k}}{2 k^{2}} - \frac{1}{k^{2}} e^{- 2 k} + \frac{e^{- 3 k}}{2 k^{2}}\right), \quad 6 k^{3} \left(\frac{e^{- k}}{6 k^{3}} - \frac{e^{- 2 k}}{2 k^{3}} + \frac{e^{- 3 k}}{2 k^{3}} - \frac{e^{- 4 k}}{6 k^{3}}\right), \quad 24 k^{4} \left(\frac{e^{- k}}{24 k^{4}} - \frac{e^{- 2 k}}{6 k^{4}} + \frac{e^{- 3 k}}{4 k^{4}} - \frac{e^{- 4 k}}{6 k^{4}} + \frac{e^{- 5 k}}{24 k^{4}}\right), \quad 120 k^{5} \left(\frac{e^{- k}}{120 k^{5}} - \frac{e^{- 2 k}}{24 k^{5}} + \frac{e^{- 3 k}}{12 k^{5}} - \frac{e^{- 4 k}}{12 k^{5}} + \frac{e^{- 5 k}}{24 k^{5}} - \frac{e^{- 6 k}}{120 k^{5}}\right)\right ]$$