Looking for real zeros

[AlfredFlaßhaar]

MathCad 14 factored the function sinx(x). It is known from other investigations that this function has only real zeros. If you now look for the zeros of each factor (the terms are in parentheses), then MathCad calculates complex zeros that cannot be simplified. Where is the saw stuck here 😉 .

Kind regards, Alfred Flasshaar

[LucMeekes]

The saw is stuck at numerical precision when calculating numerical results, even from symbolic expressions. I get all real results, sometimes with an imaginary part that is below numerical precision. That is: where the real part is in the order of 1, the imaginary part is in the order of 10^-19  to 10^-21. You can/should discard such imaginary parts.

(Forum doesn't let me insert pictures, alas)

Success!
Luc

[AlfredFlaßhaar]

Then MathCad isn't that precise with algebra (Galois, Rufini, ...)? In the complex plane, a number is to be regarded as real from arithmetic point of view if it is not only represented exactly on the x-axis, but is also contained in an x-strip of finite but small width along the x-axis. That takes some getting used to for me.

BTW:
I'm not familiar with the rules of the PTC forum, although I've been using MathCad since version 6 and haven't updated it since 14. Where can I find rules? Dumb question: what are "kudos"?

Greetings Alfred

[LucMeekes]

There are no dumb questions.

From the Oxford dictionary:

kudos

/ˈkjuːdɒs/

noun

noun: kudos

1. praise and honour received for an achievement.

   "she was looking for kudos rather than profit"

   On this forum you can give Kudos to reactions that you like.

   Also it is appreciated that you select an answer as being the solution to your question.

   Success!
   Luc

[LucMeekes]

In general Mathcad is pretty precise as long as it can remain in symbolic mode. However, as soon as it needs to switch from symbolic mode to numerical (floating point) mode, the precision drops to IEEE floating point precision, which means that you get about 16 digits of precision:

Now the symbolic solver will switch to floating point mode e.g. when solving higher order polynomes, since the symbolic solutions only exist for 4th order polynomes.

Success!

Luc

[Werner_E · Accepted solution]

In the sheet you attached I can find no attempts to find any zeros!

Mathcad often displays real numbers using expressions with the imaginary unit. Nonetheless those expressions are real numbers as you can confirm by using "float" or numeric evaluation:

Actually the first solution

is equivalent to

but I have no algebraic expression without using the imaginary unit at hand.

[LucMeekes]

This is as close as I get:

Luc

[Werner_E]

---

@LucMeekes wrote:

This is as close as I get:

Luc

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Yes, but Mathcad is just applying the elementary equation

neither algebraic nor avoiding the imaginary unit.

In MC15 it something similar can be achieved with

I am not sure if a simple pure algebraic expression could be found.

[AlfredFlaßhaar]

The Re and Im functions are convincing.

[lvl107]

It seems to be:

Best Regards.

[lvl107]