Symbolic bug

[Werner_E]

YASB

Yet Another Symbolics Bug

I don't expect PTC to fix this bug in the near or far future but just out of curiosity - does anybody has an explanation or idea whats going wrong internally in the symbolics here (other than "its a bug").

I did not take the time to convert to Prime but I expect the same error there, too.

MC15 worksheet attached.

[LucMeekes]

Here's Mathcad 11 / Maple. Of course without error  Might help to clarify...

In the attached file, I've put the simplified, expanded and the expanded-simplified expressions as new variables. Maybe working with those in M15 brings you further in clarifying.

Success!
Luc

[Werner_E]

Thanks for the reply, Luc!

I had no doubt that Maple in MC11 would do it correct.

The simplifications done using the various keywords are completely different as our screenshots show - not surprising.

Its well known that Maple is far superior compared to MuPad, but that error in a simple numeric only expression is quite alarming!

[LucMeekes]

Taking a closer look, I'd guess (just guess...) that 'simplify' causes the error. Look at how all answers (except the obviously wrong one) are 2.43342766, except for the numeric result of simplification only: 2.43342768.

A difference of 2 at position 7, that's too large to simply result from numeric inaccuracy (17 positions!) alone.

Luc

[Werner_E]

You may be right about that. I hadn't noticed that small difference so far.

There is also a small difference with the "expand" result.

Not sure if we see numerical inaccuracies here or really wrong symbolic expressions.

As far as i had checked the result of simplify manually, it seems to be correct.

[LucMeekes · Accepted solution]

Notice how 133-3sqrt(1965) is close to 0.

Taking that to the fourth power (in the third term of the 'expand' result) gets it even closer to 0.

I renamed 133 to a and sqrt(1965) to r.

a-3r=0.015, (1-3r)^4=5e-8

The second term of the numerator of the 'expand-simplfy' result would be:

And that's a real zero. A non-zero number raised to whatever (real) power should never become 0, or am I going crazy?

Luc

[Werner_E]

Hmm, here is what it looks like in MC15

But I think I got the "answer" to my initial question now thanks to your pointing out the tiny values involved.

What we experience here is not a bug in the symbolics but are "simple" inaccuracies of the numerics. Even the 2.37 vs. 2.43.

Guess I should have tried the float evaluation sooner

Amazing, but no bug at all.

[VladimirN]

What service release of Mathcad 15?

[Fred_Kohlhepp]

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@VladimirN wrote:

What service release of Mathcad 15?

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There is anecdotal evidence that Prime is using a very old version of MuPad.  It's highly improbable that they would have upgraded 15 on service release when the current software is so dated.

[VladimirN]

Here is a result in Mathcad 15 M045:

And in Mathcad Prime 3.1:

[Fred_Kohlhepp]

Q E D

Same MuPad version