Multiplication of exponential to exponential of the sum in sympy

Question

How can an expression of the form exp(a * x) * exp(b * x) be transformed to exp(a * x +b * x) using sympy?

The starting point would be something like:

from sympy import symbols, exp
from sympy import exp
x, a, b = symbols('x, a, b', real=True)
f = exp(a*x)*exp(b*x)

The inverse transformation has been explained in [1]

From your code, I think you want that `exp(a*x)*exp(b*x)` become `exp((a+b)*x)`, right? — Hemerson Tacon, Sep 27 '18 at 17:20
exp(a*x + b*x) is fine too. As long as there is only one exp is fine for what I am trying now. (i edited the question to correct two typos). — Juan Osorio, Sep 27 '18 at 17:29

score 3 · Answer 1 · answered Sep 27 '18 at 17:32

I found that powsimp could do what you want

from sympy import symbols, exp
from sympy import exp, powsimp
x, a, b = symbols('x, a, b', real=True)
f = exp(a*x)*exp(b*x)
powsimp(f)

Output

exp(a*x + b*x)

powdenest also (in this case) do the same

Reference to powsimp

Reference to powdenest

score 2 · Answer 2 · answered Nov 15 '18 at 07:20

2

The simplify command does the job

from sympy import symbols, simplify, exp
x, a, b = symbols('x, a, b', real=True)
f = exp(a*x)*exp(b*x)
fs = simplify(f)

Output

>>> f
exp(ax)exp(bx)
>>> fs
exp(x(a + b))

answered Nov 15 '18 at 07:20

Aaron-S

2 Answers2