Laplace of the differential of another variable in sage

answered 2012-08-21 08:05:04 +0200

calc314
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updated 2012-08-21 08:05:41 +0200

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.

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Yeah, it can account for such a result. I think maybe there is something in maxima to be improved. Thank you!

yangzb ( 2012-08-21 09:19:40 +0200 )edit

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.

yangzb ( 2012-08-21 23:04:03 +0200 )edit

Good catch. I'll work on submitting a ticket on this.

calc314 ( 2012-08-22 16:32:57 +0200 )edit

All right:)

yangzb ( 2012-08-22 23:38:49 +0200 )edit

@calc314 - Please cc: me if you do get the ticket open. The formal derivative stuff still needs some better integration with Maxima - no pun intended.

kcrisman ( 2012-08-24 16:39:18 +0200 )edit

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