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2020-06-06 10:59:34 +0200 commented question How to simplify dirac_delta?

Ah, sorry, that is a feature of https://doc.cocalc.com/sagews.html (Sage worksheets) on CoCalc. It is the same thing. I will remove it.

2020-06-06 08:16:37 +0200 asked a question How to simplify dirac_delta?

Various manipulations are possible with dirac_delta and its derivatives. How can I teach sage to simplify these? For example, the following Green's function for a free particle in 1D could simplify to simply dirac_delta(x):

sage: var('x,k')
sage: G = heaviside(x)*sin(k*x)/k
sage: simplify(k**2*G + diff(G, x, x))
2*cos(k*x)*dirac_delta(x) + sin(k*x)*diff(dirac_delta(x), x)/k

How can I teach sage to perform the following simplifications

f(x)*dirac_delta(x)
    -> f(0)*dirac_delta(x)
f(x)*diff(dirac_delta(x),x)
    -> diff(f(x), x)*dirac_delta(x) 
    -> diff(f(x), x).subs(x=0)*dirac_delta(x)

which would bring the answer into the desired form dirac_delta(x)?

2019-02-04 20:02:27 +0200 commented answer Is there a way to store and sync the files from sage cloud on local hard drive?

Note: Dropbox no longer supports appropriate drive formats to allow it to work with CoCalc. See https://github.com/sagemathinc/cocalc/issues/11 (issue 11) for details.