Laplace of the differential of another variable in sage
Why did the diff(y.laplace(t,s),x) come out to be D[0](laplace)(y(x, t), t, s)*D[0](y)(x, t)
? Could someone help me?
Why did the diff(y.laplace(t,s),x) come out to be D[0](laplace)(y(x, t), t, s)*D[0](y)(x, t)
? Could someone help me?
As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating laplace(y,t,s)
as a symbol and gives the derivative w.r.t. x as D[0](laplace(y,t,s))*D[0](y(x,t))
. Taking the second derivative gives something that looks like the product rule and the chain rule were used.
I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.
Yeah, it can account for such a result. I think maybe there is something in maxima to be improved. Thank you!
But, as I run in Maxima:laplace(diff(f(x,t),x),t,s),it seems to output the correct answer:'diff('laplace(f(x,t),t,s),x,1). Thus there might be something wrong in sage.
Good catch. I'll work on submitting a ticket on this.
All right:)
Sorry, I did not ask for permission from my professor before posting it. He told me the code still needs some work. He will contribute it to Sage as a contributor himself when it works reasonably well.
That would be awesome. Please keep us informed, and if he does post some code, put the ticket number here as well for other people who find this question.
All right
Asked: 12 years ago
Seen: 527 times
Last updated: Sep 10 '12