ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 12 Sep 2012 07:08:56 +0200Laplace of the differential of another variable in sagehttps://ask.sagemath.org/question/9257/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?Tue, 21 Aug 2012 05:47:19 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/Answer by calc314 for <p>Why did the diff(y.laplace(t,s),x) come out to be <code>D[0](laplace)(y(x, t), t, s)*D[0](y)(x, t)</code>? Could someone help me?</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?answer=13948#post-id-13948As 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.Tue, 21 Aug 2012 08:05:04 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?answer=13948#post-id-13948Comment by yangzb for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19070#post-id-19070All right Wed, 12 Sep 2012 07:08:56 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19070#post-id-19070Comment by yangzb for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19190#post-id-19190All right:)Wed, 22 Aug 2012 23:38:49 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19190#post-id-19190Comment by calc314 for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19193#post-id-19193Good catch. I'll work on submitting a ticket on this.Wed, 22 Aug 2012 16:32:57 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19193#post-id-19193Comment by yangzb for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19197#post-id-19197But, 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.Tue, 21 Aug 2012 23:04:03 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19197#post-id-19197Comment by kcrisman for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19075#post-id-19075That 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.Tue, 11 Sep 2012 11:31:24 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19075#post-id-19075Comment by yangzb for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19088#post-id-19088Sorry, 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.
Sun, 09 Sep 2012 12:14:00 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19088#post-id-19088Comment by kcrisman for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19181#post-id-19181@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.Fri, 24 Aug 2012 16:39:18 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19181#post-id-19181Comment by yangzb for <p>As best I can tell, it looks like Sage is doing the chain rule here. So, it is treating <code>laplace(y,t,s)</code> as a symbol and gives the derivative w.r.t. x as <code>D[0](laplace(y,t,s))*D[0](y(x,t))</code>. Taking the second derivative gives something that looks like the product rule and the chain rule were used.</p>
<p>I think Sage is using Maxima to do this. So, this might be an issue with how Maxima handles partial derivatives of Laplace transforms.</p>
https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19199#post-id-19199Yeah, it can account for such a result. I think maybe there is something in maxima to be improved. Thank you!Tue, 21 Aug 2012 09:19:40 +0200https://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19199#post-id-19199