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Factoring expression involving exponentials

asked 2015-10-08 03:34:33 -0500

mforets gravatar image

I've got a complicated expression, which looks like: e(4ik+3iω+ip)−e(4ik+2iω+2ip)−e(4ik+2iω)+e(4ik+iω+ip)+2e(2ik+4iω+ip)−e(2ik+3iω+2ip)−e(2ik+3iω) + ...

How would you do to factor the exponentials with the same power of k, i.e. e(4ik)(...) + e(2ik)(...) and so on?

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answered 2015-10-11 15:46:40 -0500

mforets gravatar image

Using both ideas we can formulate a complete answer (assume that expr(k) is the expression in terms of phases in powers of k that we want to factor):

f1(k) = expr(-I*log(k)); f1
g1(k) = f1.canonicalize_radical(); g1
g1(k).coefficient(k,4)
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answered 2015-10-10 16:54:33 -0500

updated 2015-10-10 16:56:57 -0500

Maybe by a change of variables:

sage: var('k,w,p')

sage: expr(k,w,p)=exp(4ik+3iw+ip)-exp(4ik+2iw+2ip)-exp(4ik+2iw)+exp(4ik+iw+ip)+2exp(2ik+4iw+ip)-
exp(2
ik+3iw+2ip)-exp(2ik+3i*w)

sage: f(k,w,p)=expr(log(k),log(w),log(p))

sage: g(k,w,p)=f.canonicalize_radical()

sage: g(exp(k),exp(w),exp(p)).factor()

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This answer was useful, thanks. But at the end factor doesn't work as expected (it just leds to the original expression). We can use instead use the coefficient function to conclude.

mforets gravatar imagemforets ( 2015-10-11 15:42:31 -0500 )edit
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answered 2015-10-08 09:21:53 -0500

fidbc gravatar image

I would probably try using the factor method.

sage: var('x,y,z')
(x, y, z)
sage: expr=exp(4*x-2*y+4*z)+exp(4*x-3*y+5*z)
sage: expr.factor()
(e^y + e^z)*e^(4*x - 3*y + 4*z)

Perhaps the manual will contain useful info on that as well.

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Thanks, but you can see this doesn't do the job: the goal was to collect the terms in exp(4x), and so on (try adding for instance exp(2x-3y+5z) and factoring, it does something correct but is not what I need). I thought it'd be useful a previous step transforming the exp(2x) into z and exp(4x) into z^2, etc and then factoring, but I am not able to get the substitution done..

mforets gravatar imagemforets ( 2015-10-08 16:07:46 -0500 )edit

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Asked: 2015-10-08 03:34:33 -0500

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Last updated: Oct 11 '15