Symbolical derivative - is it a bug?

[Werner_E]

Is it a bug or is there any reasonable explanation for this effect?

I am aware of the different ways that third root of x and x^(1/3) are implemented for negative arguments

and those negative values sure are the reason for the error because all works OK when I "assume, x>0". Nevertheless I don't clearly see a reason why the symbolical evaluation after der derivative should make the numerics fail.

[LucMeekes]

Here is what Mathcad 11 makes of it:

I guess it's a bug.

Potentially caused by, or related to the feature that roots are shown as roots (instead of as powers) since Mupad is the symbolic engine, and that I was very jealous about

until today.

Luc

[Werner_E]

Thanks!

> I guess it's a bug.

Yes, probably kind of.

From the plots it looks that in MC11 also the numeric evaluation of the third root of -1 yields a non-real result and so nothing is plotted for negative abscissa values.

So obviously the distinction between third root and ^(1/3) was introduced later because people complained about the third root of a negative number not being a negative real. I am not sure if it has something to do with muPad - numeric evaluation treats root and exponentiation differently, too.

> that I was very jealous about until today.

So everything has a positive side, too - even a bug

[-MFra-]

Sometimes I like to think that the truth is this: it is preferred to distribute a poor software rather than a perfect, when it is not known, to those who is sold. Nowadays, we have fierce enemies, and provide them, in some way, something very powerful, it would be to our disadvantage. I, therefore, think that these errors that occasionally come out, are made on purpose.

[Werner_E]

Speculations about conspiracy theories are new in this forum.

So, looking at the development of Prime, PTC should not be seen as incapable but should rather be praised as protector of the free world?

[-MFra-]

it's so indeed, even if it goes against the interests of PTC, which, however, is paradoxical when you consider that the producer is only concerned to make big gains and be quoted on the stock exchange. The mathematical CAD is a tool that goes beyond, way beyond any other CAD. With the "queen of the sciences" you can design whatever you want ... and in the hands of certain individuals, would not be as noble as it is viewed. We have already experienced the last century ... This suggests that the entire scientific world is against the spread of this software.

[LucMeekes]

Ah, so that's why PTC makes no haste with improving Prime such that it can match Mathcad.

But then...what about Mathematica, Maple, Maxima etc.?

Luc

[-MFra-]

Then we must attribute the cause of these errors to the negligence of the software engineers? because these errors are not acceptable!