is available in a this subthread .

Somewhat connected, in regards to ambiguities,  I have read a bit the documentation  for  MathML 3, and  in chapter 3  there  is a  subsection Invisible operators [quoted from this site]:

Certain operators that are "invisible" in traditional mathematical notation should be represented using specific entity references within mo elements, rather than simply by nothing.

 The reasons for using specific mo elements for invisible operators include:

• such operators should often have specific effects on visual rendering (particularly spacing and linebreaking rules) that are not the same as either the lack of any operator, or spacing represented by mspace or mtext elements;

• these operators should often have specific audio renderings different than that of the lack of any operator;

• automatic semantic interpretation of MathML presentation elements is made easier by the explicit specification of such operators.

it is possible to get different effects with fonts and colors on the Standard GUI, eg:

plot(sin(x),x=0..Pi,labels=[`#mi("x",fontweight = "bold",
fontstyle = "normal")`,`#mi("𝔷",mathcolor = "#c800c8")`]);

it is possible to get different effects with fonts and colors on the Standard GUI, eg:

plot(sin(x),x=0..Pi,labels=[`#mi("x",fontweight = "bold",
fontstyle = "normal")`,`#mi("𝔷",mathcolor = "#c800c8")`]);

eg the Maple-mathml name

`#msub(mi("x"),mi("a"))`;

`#msub(mi(x),mi(a))`;

eg the Maple-mathml name

`#msub(mi("x"),mi("a"))`;

`#msub(mi(x),mi(a))`;

works better for this purpose, in my opinion.

Apparently, an entry for MTM is still missing in the Table of Contents. I think that it should go under  "Connectivity".

works better for this purpose, in my opinion.

Apparently, an entry for MTM is still missing in the Table of Contents. I think that it should go under  "Connectivity".

here is, presumably, Fermi-Dirac. Hence, the first integral seems to be a typo.

And in the exponent of the second integral, it should not be EF but mu, the chemical potential, which differs from the Fermi energy at finite temperature.

Standard approximation schemes for integrals of this form are explained in the textbooks on Statistical Mechanics, depending on whether mu/kT is large or small.
Eg for "small temperature" the FD distribution is close to a step function, and its derivative is significant only on a neighborhood of E/mu=1.

here is, presumably, Fermi-Dirac. Hence, the first integral seems to be a typo.

And in the exponent of the second integral, it should not be EF but mu, the chemical potential, which differs from the Fermi energy at finite temperature.

Standard approximation schemes for integrals of this form are explained in the textbooks on Statistical Mechanics, depending on whether mu/kT is large or small.
Eg for "small temperature" the FD distribution is close to a step function, and its derivative is significant only on a neighborhood of E/mu=1.

I get

combinat[numbpart](11269);

Error, (in combinat/numbpart) too many levels of recursion

For several versions of Maple previous to Maple 9 that I have tried.

combinat[numbpart](11269);

gives the same answer as Maple 11.

At the begining of MaplePrimes there was some option to use this licence for the posts, as explained here. Aparently, it is no longer available.

I find this issue a bit more complex and subtle. Here I just want to sketch some ideas.

In Physics, differential equations arise from theories/models in terms of which their laws and properties may be expressed. These theories/models are abstractions that may arise in  observations or  some other considerations.  Their  success  is  determined  on one hand by their consistency with the available observations and the other established theories/models, and on the other hand by their predictive power. These same facts put limits on their domain of application.

So, solutions of such equations may exist and describe correctly some phenomena within this domain, while outside it such solutions may exist but  unrelated to facts, hence useless.

And the requirement for any theory/model proposed as an alternative to an established one, or pretending to be valid for a larger domain of validity, is that analogous solutions exist in the intersection of their domain of validity.

when I was "ambassador" of Maplesoft in Argentina, I have insisted with them that the way to go was something similar to your proposal, acording to that time: a cheap basic version (internet access  was  hardly available, hence  no thing as a free download).

At most I have got vague answers and no action.

Yes, I know a little bit that as once I have given the course of Physics for mathematicians, ie Mechanics, where they had to solve the equations of motion. But they caught up quickly.

I would not be surprised that Maple fails with partial derivative counterexamples. Either because the algorithms were not designed to deal with them or because they were not used for testing.

I wonder whether there is any other CAS suitable for that task.