21-Topaz I

Solved

I want to know the reasons of my Mathcad sheet errors.

Forum|Forum|8 years ago
June 13, 2018
20 replies
7189 views

Using Mathcad the average value of f(t) and convolution of rectangular waves have wrong results.

I want to know the reasons.

1_ERROR.zip

Electrical_Engineering

Best answer by ttokoro

Thanks many replyings to my help. I understand they are bugs.

V

ValeryOchkov

24-Ruby IV

| |, if etc - not for symbolic math! Symbolic mathematics (and nature) does not like sharp corners!

W

Werner_E

25-Diamond I

If the symbolics does not "like" sharp corners it should say so and not return an awfully wrong result.

What we see here is a clear severe bug of Primes symbolics (= MuPad) which is also present in real Mathcad.

The expression should either be not simplified at all or return the correct symbolic result

If you are under maintenance you may consider reporting this bug to PTC but don't expect a fix within a reasonable time.

Luc may be able to show if this bug is present in Mathcad 11, too, which uses Maple for symbolics. Guess MC11 returns the correct result.

Concerning the second error I am not sure what the reason may be. Here the problem is the numerical evaluation (used by any plot) - the symbolics get the correct results:

The precision of numerical integration is dependent on the value of TOL. But changing that value in your sheet does not noticeably affect the outcome.

Here the nature of the integrand might be the cause.

The effect is there in Mathcad 15, too (and I guess it will also be shown in Mathcad 11), but the effect is slighty different depending on the algorithm chosen (we can chose among a couple of algortithms for the integration in real Mathcad - in Prime we can't) and also depending on the value of TOL.

Here some statements from the Mathcad manual/user guide (the last manual which deserved that name was delivered with Mathcad 11, but most statements about numerics still apply):

Like all numerical methods, Mathcad's integration algorithm can have difficulty with illbehaved
integrands. If the expression to be integrated has singularities, discontinuities, or large
and rapid fluctuations, Mathcad's solution may be inaccurate.
Mathcad’s numerical integration algorithm makes successive estimates of the value of the
integral and returns a value when the two most recent estimates differ by less than the value of
the built-in variable TOL.

L

LucMeekes

23-Emerald IV

I can only agree with Valery: Be very careful when using the | | operator in combinatioin with symbolics.

Here's Mathcad 11:

But then, it's the 13th today...

Success!
Luc

1_LM_20180613_Error.zip

W

Werner_E

25-Diamond I

At least Maple got the correct symbolic solution when replacing the absolute value by root of square.

Nevertheless I am surprised that even Maple in MC11 has problems with the absolute value in a way that it returns a completely wrong result. This should never happen in a Math software and I see it as a very severe bug (which will not be fixed, I know). If a software returns no result because its not capable to find a solution, then this may be a sign of quality (or the opposite of it). But returning a wrong result, thats an absolute no-go!

L

LucMeekes

23-Emerald IV

What happens in Prime/Mathcad 15 (with symbolic evaluation) if you take the symbolic equivalent of the if() statement: the Heaviside step function:

(Of course, as shown, numeric evaluation gives the right answer with any of the three ways to make the function positive)

Success!

Luc

1_LM_20180613_Error1.zip

W

Werner_E

25-Diamond I

Similar results in MC15. Heaviside works with symbolics, too.

The drawback of course is that we have to manually derive the points of zero and basically split the function manually at those points. Similar to the distinct integrals I used in my first answer to get the correct symbolic result.

A bug stays a bug even if there may be a workaround and this IS a bug (even in MC15/Maple).