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Symbolic Evaluation.

Alexandrite

Symbolic Evaluation.

Hello,

Symbolic+Evaluation.PNG

The question : Need help with Symbolic Evaluation the above.

Thanks in advance for your time and help.

Regards.

16 REPLIES 16

Re: Symbolic Evaluation.

Solution in MathcadPrime 2.0

Symbolic Evaluation.PNG

Re: Symbolic Evaluation.

This should be simply (x-1)/x.

There's only one term in the summation, since n runs fom 1 to 1.

And with n being 1, the multiplication contains also only one term, since k runs from 1 to n=1.

So with k being 1, the one term is (kx-1)/kx, simplifies to (x-1)/x.

Regards,

Luc

Re: Symbolic Evaluation.

LucMeekes wrote:

This should be simply (x-1)/x.

And that is the last line from the symbolic evaluation above

But ok, I understand your point that you do not require mathcad for this. However, when you try to evaluate the expression in M15 you get

Error.PNG

and probably this was Loi Le's point in posting the thread.

Re: Symbolic Evaluation.

LucMeekes wrote:

This should be simply (x-1)/x.

or 1-1/x. Of course you are right and if you set the upper limit n in the product to 1, Mathcad agrees with your statement 🙂

But I assume its only a simplified example and the upper limit of the outer sum is subject to change.

Nevertheless muPad should not have that many troubles in simplifying this one. It seems the the inner product is evaluated first with an arbitrary variable n, which results in a lot of distinction of case and only after that the outer sum is applied and the branches are not resolved and simplified thereafter.

Here are some partial results using MC15:

symbolic_eval1.png

Re: Symbolic Evaluation.

If you take a look at the Prime 2.0 answer, there are four conditions to be met for the final result. I wouldn't argue with the first two, but the last two are that 1/x must be greater than or equal to 1, and that 1/x must be less than or equal to 1. Then the only possibility is that x=1, and the answer is zero. Wrong!

Incidentally, the Maple engine in MC13 and earlier gets the answer of (x-1)/x in a fraction of a second. I wish we still had the Maple engine

Re: Symbolic Evaluation.

Richard Jackson wrote:

If you take a look at the Prime 2.0 answer, there are four conditions to be met for the final result. I wouldn't argue with the first two, but the last two are that 1/x must be greater than or equal to 1, and that 1/x must be less than or equal to 1. Then the only possibility is that x=1, and the answer is zero. Wrong!

Wrong? Why? Akward, clumsy, unhandy and unuseable, yes!

Its true, the final result refers to x=1 only and it would be zero. But most of the other results using the Gamma function will simplify to the correct result 1-1/x, too, as in the MC15 example I posted above. Obviously "simplify" is not applied in expressions inside the if conditions.

Incidentally, the Maple engine in MC13 and earlier gets the answer of (x-1)/x in a fraction of a second. I wish we still had the Maple engine

Fully agreed, I second that for a multitude of reasons!

Re: Symbolic Evaluation.

One additional spot in evaluating the inner product only - great difference if we use assume or substitute!

"assume" is applied during evaluation of the product, "substitute" obviously only after and Mathcad/muPad is not able to simplify the multitude of branches and it seems to me trhat it even don't try to do, otherwise at least the expressions with the Gamma functions have to be simplified.

symbolic_eval_assume.png

symbolic_eval_subst.png

Re: Symbolic Evaluation.

OK, I guess strictly it is not wrong. It just an extremely special case that should be simplified to zero, and is a subset (consisting of one element!) of a much more general case where the answer is (x-1)/x. It's about as close to wrong as it's possible to get without actually being wrong!

Re: Symbolic Evaluation.

It's about as close to wrong as it's possible to get without actually being wrong!

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