[CAS] Integrals

[DrD]

Apologies for the brevity of the original question. The simplicity of the question mark was to indicate curiosity, and stimulate discussion. Not so much an interrogative statement. The reason is that differing languages and translations can be confusing at times. My objective was to let the example demonstrate the subject, rather than a verbose discussion.

My opinion, regarding use of brain vs. tool, is to gain advantage, mental or mechanical.

External constraints can be placed on the advantage, for example if an educator needs to have students demonstrate learned skills. Ultimately though, I want to use a tool to obtain the greatest return on its investment. A corollary to the Prime/Brain thing is aircraft or marine navigation equipment. For example, marine AIS provides marine vessel information in detail. When a target object shows up on the nav screen, that information is immediately useful, rather than braining it out. The result provided contains closest point of approach, time thereof, etc., its easily interpreted, without regard to "ambiguous" questioning. (I hope that makes the point).

Regarding the Prime, one of my interests is in capturing deficiencies, and feed them back to the "team" in order make a better product. I enjoy trying to do that. I have a lot of respect for Bernard, his background, and the product overall. He is very close to the CAS, and very protective of it. That means I have to try my best to make a valid case for any change.

The nuances of issues under discussion, plus language translation issues, tend to make me overthink problems, and I sense that Parisse probably finds that frustrating. In the past I have offered concerns that have not been something Parisse wanted to change. I respect that, but accumulating these discussions, over time, doesn't do much to assure Parisse of my underlying good intent! Anyway, that's my only goal.

Quote:
... that we should not even have to state our questions unambiguously; the tool should just know what we want and infer any context (from what?).

In the OP example, the context comes from the actual information provided. Namely the boundaries. No expectations for any further interpretation, such as if the boundaries are to be segregated, or theoretical approaches applied to undefined regions, (the singularity).

That shouldn't be a restriction, however. A future enhancement might provide an 'option' to treat vanishing points in an exceptional manner. However, the command sent to the tool was to integrate over the continuum. It can't, and that should be the answer.

Returning a theoretical answer, is superfluous, when based on the application of the "tool" to just the information provided. Given, "how to cut a tree," a reasonable result might be "use a chainsaw," without regard to anticipating the size of chainsaw or trees, or depending on what one might encounter in forests, etc. If boundaries WERE provided: small chainsaw and huge trees, in large forests, the result "undef" would be useful, more so than infinity.

As far as other peripheral concerns, settings in the CAS setup, should dominate. (Complex, vs, real, etc.).

That's my perspective, anyway. The tool should assist the brain to operate more efficiently. As technology evolves, we are seeing more examples of this process, ever more frequently. I hope I can contribute along the way...

-Dale-