Ask Your Question
0

Laplace of the differential of another variable in sage

asked 2012-08-21 05:47:19 +0100

anonymous user

Anonymous

updated 2012-08-21 09:32:02 +0100

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?

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted
1

answered 2012-08-21 08:05:04 +0100

calc314 gravatar image

updated 2012-08-21 08:05:41 +0100

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.

edit flag offensive delete link more

Comments

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

yangzb gravatar imageyangzb ( 2012-08-21 09:19:40 +0100 )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 gravatar imageyangzb ( 2012-08-21 23:04:03 +0100 )edit

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

calc314 gravatar imagecalc314 ( 2012-08-22 16:32:57 +0100 )edit

All right:)

yangzb gravatar imageyangzb ( 2012-08-22 23:38:49 +0100 )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 gravatar imagekcrisman ( 2012-08-24 16:39:18 +0100 )edit

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.

yangzb gravatar imageyangzb ( 2012-09-09 12:14:00 +0100 )edit

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.

kcrisman gravatar imagekcrisman ( 2012-09-11 11:31:24 +0100 )edit

All right

yangzb gravatar imageyangzb ( 2012-09-12 07:08:56 +0100 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 2012-08-21 05:47:19 +0100

Seen: 487 times

Last updated: Sep 10 '12