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Excluding a common factor in a sum

asked 2015-04-23 04:29:25 -0500

drs663 gravatar image

I'm trying to figure out how to simplify this expression in Sage:

y = tau1*exp(-t/tau1)/(tau1 - tau2) - tau1*exp(-t/tau2)/(tau1-tau2)

When I try factor(y) or simplify(y), I get this:

-tau1*(e^(t/tau1) - e^(t/tau2))*e^(-t/tau1 - t/tau2)/(tau1 - tau2)

However, the result I would like to see is this:

 tau1/(tau1 - tau2)*(exp(-t/tau1) - exp(-t/tau2))

which seems like the simplest form to me. I've not been able to get this result with the various simplify commands or with assumptions (BTW, all variables are real, and tau1 & tau2 > 0).

In this case the simplest form is obvious, of course, but it would be a great help to be able to get this right for larger expressions.

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answered 2019-10-27 01:42:11 -0500

Emmanuel Charpentier gravatar image

Try:

sage: var("t, tau, tau_1, tau_2")
(t, tau, tau_1, tau_2)
sage: f = tau_1*exp(-t/tau_1)/(tau_1 - tau_2) - tau_1*exp(-t/tau_2)/(tau_1-tau_2)
....: 
sage: f.collect_common_factors()
tau_1*(e^(-t/tau_1) - e^(-t/tau_2))/(tau_1 - tau_2)

(i. e. $\frac{\tau_{1} {\left(e^{\left(-\frac{t}{\tau_{1}}\right)} - e^{\left(-\frac{t}{\tau_{2}}\right)}\right)}}{\tau_{1} - \tau_{2}}$), which, IMHO, is what you seek.

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Asked: 2015-04-23 04:29:25 -0500

Seen: 200 times

Last updated: Oct 27 '19