The use of invfunc can be implemented like this:

restart:
phi:= u-> (u^(-theta)-1)/theta:
invphi:= unapply(solve(phi(x)=u, x), u):
unprotect(invfunc): invfunc[phi]:= invphi: invfunc[invphi]:= phi: protect(invfunc):
C:= (u,v)-> simplify((phi@@(-1))(phi(u)+phi(v))):
C(u,v);
            

To understand better what's going on here, check out showstat(`@@`).

@janhardo I don't find it at all surprising that ChatGPT can give you an extensive discussion of the infinitude of primes, which is one of the most-ancient topics of formal abstract mathematics. But how does it involve Maple or any computer language?

Yes, I have noticed that most operations on MaplePrimes have been much slower for a few weeks.

I deleted your Question from today because it is essentially the same as this one. If you have additional information, put it in this thread. 

@Preben Alsholm Indeed, "contrived".

A type check (including those constructed with satisfies) should only return either true or false; returning anything else including errors is a bad idea, and in some situations can be critically dangerous (such as causing kernel death). This includes all type checks, not just those used for checking calling sequences.

And, the overload mechanism reacts only to error messages beginning with "invalid input", which your parse error does not. The help page line that you quoted is thus wrong, and should be corrected. So, IMO, the only bug is that erroneous statement in the help page.

@sand15 The culprit is implicit multiplucation in input; it shouldn't be allowed in 2D Input. I'm not saying that a multiplication operator should be explicitly shown in the input, just that the user should be requited to enter an operator.

@emendes A DataFrame is an object (in Maple's implementation of object-oriented programming (OOP)). When a procedure exported by an object's "master" module is applied to that object, the procedure is automatically recognized as the module's export without needing with or a module prefix. These procedures are called the object's "methods", which is an OOP term that I think is ridiculous because there's no need for a yet another new word for "procedure". So, Tabulate is a DataFrame method that simply invokes DocumentTools:-Tabulate.

@WA573  @Rouben Rostamian  Certain assumptions tacitly imply other assumptions. Of couse, any mathematician knows that. What I specifically mean is that certain assumptions formally made in Maple cause other assumptions to be formally (but tacitly) made. A common example is that assuming a < b is equivalent to assuming a < b, a::real, b::real. So, assuming a < b will cause conjugate(a) to be treated as a, and likewise for b.

I just mention this "for what it's worth"; I don't know if this knowledge can help to explain the OP's situation. I'm just saying that while making that assumption may cause confusion for a human reader if it's done without comment, it doesn't cause any confusion for Maple.

What do you mean by "do this is by using the Tabulate (plain command and not from DocumentTools) function"? As far as I can tell, there is no "plain" top-level Tabulate, only Tabulate commands in packages DataFrame, DocumentTools, and StringTools. Are you converting a Matrix to a DataFrame before using Tabulate?

I have had that bug on my computer before (many times), but I haven't seen any reasonable explanation for it, nor can I reproduce it. It doesn't seem to be widely reported. It is intermittent. When it's happened to me, other symbols also change, such as + and - becoming C and K. Does that happen for you? And when it happens to one of my worksheets, all open worksheets are affected. If I save my worksheets and close the entire Maple session, the bug is gone when I restart Maple---the errors are not stored in the saved worksheets.

@Mike Mc Dermott If I made a suggestion in this thread, it seems to have disappeared. I recall thinking about a suggestion for this thread. What is the thing that you think is "even better"?

@JAMET Using that code, I do get [4, 18/5, 1].

@Rouben Rostamian The YouTube video that you linked is an excellent demonstration and explanation of the motion of balls on rotating platters. And it explains why certain patterns can be explained entirely by the moments of inertia.

If there's no friction, then why would the carousel have any effect at all on the cube, regardless of whether or not it's self-propelled?

I think that using the principles from, say, a first university physics-for-majors course, the only approach to the problem is for it to be a round object (cylinder or sphere, solid or hollow) rolling without slipping. The moment of inertia of the object comes into play, which can be easily calculated for spheres and cylinders (uniform solid or hollow).

Do you intend for &x to represent the vector cross product of two 3-D vectors? That's what &x usually means in Maple. Or do you want the product of a Matrix, the inverse of Mat, with a vector?