What a quick way to make symbolic integration in sympy

Question

I am doing a project with a lot of symbolic integration.

Functions are something like an erlang probability distribution function.

Here is a simple example of a task.

https://s18.postimg.org/gd7t4bv95/gif_latex.gif

Here is the code for the task above:

import sympy as sym
t=sym.Symbol('t')
t1=sym.Symbol('t1')
t2=sym.Symbol('t2')

###integration for t2
expr=( 1-sym.exp(-(t-t2)) )*( 1-sym.exp(-(t-t2)) )*sym.exp(-t2)
expr=sym.integrate(expr,(t2,0,t))

###substitution and integration for t1
expr=expr.subs(t,t-t1) * (1-sym.exp(-(t-t1)))*sym.exp(-t1)
expr=sym.integrate(expr,(t1,0,t))

Here is a slightly complicated result:

https://s11.postimg.org/x9tw8kw8j/untitle.png

So, for sympy implementation, I use integrate () and subs () most of the time.

However, the speed is very slow. When I have 5 variables (e.g. from t_1 to t_5), I need to wait a bit. But when I have 10 variables, I can not finish the calculation.

The code is pretty complicated, but I'm sure integration is the bottleneck. In the end, from the sampling result, one can imagine how to require the completion of a task.

sympy? ,

Answer 1

- SymPy. , expand(expr) .