1

When I execute the following MAXIMA code:

kill(all);
depends([trt, trz], [r, t, z])$
eq1 : cos(t)*diff(trz,z) + cos(t)*diff(trt,t) = 0$

limit(eq1, t, 0);

I obtain:

enter image description here

How can I remove that limit so that the answer is:

enter image description here

I am using Maxima version: 5.37.2, under Linux Mint 18.3

Diego Andres Alvarez Marin
  • 175
  • 11
  • Why do you think the answer should be `'diff(trz,z,1)+'diff(trt,t,1)=0;`? – miracle173 Feb 18 '20 at 11:03
  • d/dt is an operator that is applied over a function, therefore the limit does not operate here. It operates over the function, that is over trt. – Diego Andres Alvarez Marin Feb 18 '20 at 13:26
  • No, it operates over the function d/dt trt. I think this is correct. The more strange thing is that lim_{t->0} d/dz trz is transformed to d/dt trz. Example: if trz(t,r,z)=t+r+z, then lim_{t->0} d/dz trz = lim_{t->0} t+r = r, but d/dz rtz = t+r, which isn't the same. So removing the lim in the first term is mathematically wrong, keeping it in the second term is correct – miracle173 Feb 18 '20 at 16:11
  • 1
    I think the reason that it vanishes in the first term is that limit ignores the information provided by "depends". The manual says that this information is used when calculating the derivatives. Therefor lim processes trz as if it does not contain t and therefor lim_{t->0} can be skipped. – miracle173 Feb 18 '20 at 16:14
  • But when limit sees d/dt ... it recognizes that this term depends on t and therefore limit can be skipped. This is a rather inconsistent usage of the depends-information. – miracle173 Feb 18 '20 at 16:16

0 Answers0