Re: [sage-support] Re: Trouble getting *collect* to work with derivatives.

On Monday, January 25, 2021 at 7:16:00 AM UTC-8 ... wrote: > Is this the same as derivative(f(xp(x, y, z, t), yp(x, y, z, t), zp(x, y, > z, t), tp(x, y, z, t)) , x, 2)? > > No, it is not. Look up "Multivariable Chain rule". -- You received this message because you are subscribed to the Google G

Re: [sage-support] Re: Trouble getting *collect* to work with derivatives.

> > Secondly, what are you trying to collect? The D[0,0] terms or > f(xp, yp, zp, tp), x, 2) which are two different things? What is the difference between those 2? > Given > what you are trying to do I guess it is the first one, in which > case you should have tried > > sage: term = f(

Re: [sage-support] Re: Trouble getting *collect* to work with derivatives.

What are computed operators? Are those the D[0, 0] things? How avoid those? Is that same as second derivative of 1st variable? On Sun, Jan 24, 2021, 11:33 AM Emmanuel Charpentier < emanuel.charpent...@gmail.com> wrote: > Probably because “the given second derivative” has a “computed operator”… >

[sage-support] Re: Trouble getting *collect* to work with derivatives.

I suspect you want to collect wrt. the second partial derivatives of f(x,y,z,t) with respect to x,y,z,t ; evaluated at xp,yp,zp,tp. Those are not the same as the partial second derivatives of f(xp,yp,zp,tp) with respect to (x,y,z,t). If you inspect what derivative(f(xp, yp, zp, tp), x, 2) gives

Re: [sage-support] Re: Trouble getting *collect* to work with derivatives.

Dear Christian, Given the specifications, I suspect that the function collect only works for variables. And indeed sage: expr = (x+y)*(z+t) + (x+y)*(1+z^2) + 2 sage: expr (z^2 + 1)*(x + y) + (t + z)*(x + y) + 2 sage: expr.collect(x+y) (z^2 + 1)*(x + y) + (t + z)*(x + y) + 2 Instead

Re: [sage-support] Re: Trouble getting *collect* to work with derivatives.

Probably because “the given second derivative” has a “computed operator”… BTW : var("x,y,z,t,v,c") f=function("f") xp=(t-v*x)/sqrt(1-v^2/c^2) yp=y zp=z tp=(t-v*x/c^2)/sqrt(1-v^2/c^2) foo=(sum(map(lambda u:derivative(f(xp,yp,zp,tp),u,2), (x, y, z)))-derivative(f(xp,yp,zp,tp),t,2)/c^2).factor()

Re: [sage-support] Re: Trouble getting *collect* to work with derivatives.

Emmanuel But my question is more simple than that. I just want to know why the collect method was not able to collect all the terms with the given second derivative. On Sun, Jan 24, 2021, 2:15 AM Emmanuel Charpentier < emanuel.charpent...@gmail.com> wrote: > Sage has recently acquired a large se

[sage-support] Re: Trouble getting *collect* to work with derivatives.

Sage has recently acquired a large set of tools relative to manifolds . A look at these tools and related tutorials/references may be in order… HTH, Le samedi 23 janvier 2021 à 23:17:26 UTC+1, cseb...@gmail.com a écrit : > What you intend to do isn’t really cl

[sage-support] Re: Trouble getting *collect* to work with derivatives.

> > What you intend to do isn’t really clear… Could you try and clear your > goals ? > Emmanuel Thanks so much for your help. I'm trying to show that the wave equation (https://en.wikipedia.org/wiki/Wave_equation) is invariant under a certain coordinate transformation called the Lorentz tra

[sage-support] Re: Trouble getting *collect* to work with derivatives.

I think that your code doesn’t do what you think it does. Note for example that your declarations are self-contradicting : Pasting code; enter '--' alone on the line to stop or use Ctrl-D. :function("xp yp zp tp f") :var("x y z t v c") :-- (xp, yp, zp, tp, f) (x, y, z, t, v, c) sage: xp.parent(