ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 12 Sep 2012 00:08:56 -0500Laplace of the differential of another variable in sagehttp://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?Mon, 20 Aug 2012 22:47:19 -0500http://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>
http://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 01:05:04 -0500http://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>
http://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 02:19:40 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19199#post-id-19199Comment 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>
http://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 09:39:18 -0500http://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>
http://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 05:14:00 -0500http://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>
http://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 04:31:24 -0500http://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>
http://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 16:04:03 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19197#post-id-19197Comment 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>
http://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 09:32:57 -0500http://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>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19190#post-id-19190All right:)Wed, 22 Aug 2012 16:38:49 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19190#post-id-19190Comment 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>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19070#post-id-19070All right Wed, 12 Sep 2012 00:08:56 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19070#post-id-19070Answer by yangzb 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>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?answer=12221#post-id-12221xxxxxxxxxxxxSun, 09 Sep 2012 04:43:24 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?answer=12221#post-id-12221Comment by kcrisman for <p>xxxxxxxxxxxx</p>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19082#post-id-19082Hi, can you reformat this in some way? It's very difficult to tell where new lines begin or spaces are, which in Python is essential.Mon, 10 Sep 2012 02:17:15 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19082#post-id-19082Comment by kcrisman for <p>xxxxxxxxxxxx</p>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19081#post-id-19081On the plus side, if this works well, we could incorporate it in Sage proper, giving credit to your teacher!Mon, 10 Sep 2012 02:17:38 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19081#post-id-19081Comment by yangzb for <p>xxxxxxxxxxxx</p>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19080#post-id-19080Sorry, 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.
Mon, 10 Sep 2012 03:16:46 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?comment=19080#post-id-19080Answer by yangzb 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>
http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?answer=14022#post-id-14022Sorry, 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.
Mon, 10 Sep 2012 03:13:45 -0500http://ask.sagemath.org/question/9257/laplace-of-the-differential-of-another-variable-in-sage/?answer=14022#post-id-14022